02-MadaAccess.Rmd

# How geographic access to care shapes disease burden: the current impact of post-exposure prophylaxis and potential for expanded access to prevent human rabies deaths in Madagascar

```{r, echo=FALSE}
knitr::opts_chunk$set(echo = FALSE, warning = FALSE, 
                message=FALSE, out.width="80%")
```

*This chapter will be published in:*

*__Rajeev, M.__ Guis, H., Edosoa G., Hanitriniaina, C., Andriamandimby, S.F., Randrianarijaona A., Mangahasimbola, RT, Ramiandrasoa, R., Baril, L., Metcalf, C.J.E, & Hampson, K. (2020). How geographic access to care shapes disease burden: the current impact of post-exposure prophylaxis and potential for expanded access to prevent human rabies deaths in Madagascar. medRxiv: 10.02.20205948. Accepted at PLoS NTD.*

*Minor formatting modifications and edits have been made for the dissertation.*

\newpage
\setlength{\parskip}{2em}

## Abstract {-}

### Background {-}

Post-exposure prophylaxis (PEP) is highly effective at preventing human
rabies deaths, however access to PEP is limited in many rabies endemic
countries. The 2018 decision by Gavi to add human rabies vaccine to its
investment portfolio should expand PEP availability and reduce rabies
deaths. We explore how geographic access to PEP impacts the rabies
burden in Madagascar and the potential benefits of improved
provisioning.

### Methodology & Principal Findings {-}

We use spatially resolved data on numbers of bite patients seeking PEP
across Madagascar and estimates of travel times to the closest clinic
providing PEP (N = 31) in a Bayesian regression framework to estimate
how geographic access predicts reported bite incidence. We find that
travel times strongly predict reported bite incidence across the
country. Using resulting estimates in an adapted decision tree, we
extrapolate rabies deaths and reporting and find that geographic access
to PEP shapes burden sub-nationally. We estimate 960 human rabies deaths
annually (95% Prediction Intervals (PI):790 - 1120), with PEP averting
an additional 800 deaths (95% PI: 800 (95% PI: 640 - 970) each year.
Under these assumptions, we find that expanding PEP to one clinic per
district (83 additional clinics) could reduce deaths by 19%, but even
with all major primary clinics provisioning PEP (1733 additional
clinics), we still expect substantial rabies mortality. Our quantitative
estimates are most sensitive to assumptions of underlying rabies
exposure incidence, but qualitative patterns of the impacts of travel
times and expanded PEP access are robust.

### Conclusions & Significance {-}

PEP is effective at preventing rabies deaths, and in the absence of
strong surveillance, targeting underserved populations may be the most
equitable way to provision PEP. Given the potential for countries to use
Gavi funding to expand access to PEP in the coming years, this framework
could be used as a first step to guide expansion and improve targeting
of interventions in similar endemic settings where PEP access is
geographically restricted and baseline data on rabies risk is lacking.
While better PEP access should save many lives, improved outreach,
surveillance, and dog vaccination will be necessary, and if rolled out
with Gavi investment, could catalyze progress towards achieving zero
rabies deaths.

## Author Summary {-}

Canine rabies causes an estimated 60,000 deaths each year across the
world, primarily in low- and middle-income countries where people have
limited access to both human vaccines (post-exposure prophylaxis or PEP)
and dog rabies vaccines. Given that we have the tools to prevent rabies
deaths, a global target has been set to eliminate deaths due to canine
rabies by 2030, and recently, Gavi, a multilateral organization that
aims to improve access to vaccines in the poorest countries, added human
rabies vaccine to it's portfolio. In this study, we estimated reported
incidence of patients seeking PEP in relation to travel times to clinics
provisioning PEP and extrapolate human rabies deaths in Madagascar. We
find that PEP currently averts around 800 deaths each year, but that the
burden remains high (1000 deaths/ year), particularly in remote,
hard-to-reach areas. We show that expanding PEP availability to more
clinics could significantly reduce rabies deaths in Madagascar, but our
results reaffirm that expansion alone is will not achieve the global
goal of zero human deaths from dog-mediated rabies by 2030. Combining
PEP expansion with outreach, surveillance, and mass dog vaccination
programs will be necessary to move Madagascar, and other Low- and
Middle-Income countries, forward on the path to rabies elimination.

## Introduction

Inequities in access to care are a major driver of disease burden
globally [1]. Often, the populations at greatest risk of a given
disease are the most underserved [2]. Delivering interventions to
these groups is challenging due to financial and infrastructural
limitations and requires careful consideration of how best to allocate
limited resources [3].

Canine rabies is estimated to cause approximately 60,000 human deaths
annually [4]. Mass vaccination of domestic dogs has been demonstrated
to be a highly effective way to control the disease in both animals and
humans. While dog vaccination can interrupt transmission in the
reservoir, human deaths can also be prevented through prompt
administration of post-exposure prophylactic vaccines (PEP) following a
bite by a rabid animal [5]. However, access to the human rabies
vaccine is limited in many countries where canine rabies is endemic
[6--8], and within countries these deaths are often concentrated in
rural, underserved communities [9].

In 2015, a global framework to eliminate deaths due to canine rabies by
2030 ('Zero by 30') through a combination of PEP provisioning and dog
vaccination was established by the World Health Organization (WHO) and
partners [10]. Furthermore, in 2018, Gavi, the Vaccine Alliance, added
human rabies vaccines to their proposed investment portfolio [11].
From 2021, Gavi-eligible countries should be able to apply for support
to expand access to these vaccines, with potential to greatly reduce
deaths due to rabies.

A primary challenge in expanding access effectively is the lack of data
on rabies exposures and deaths in humans and incidence in animals in
most rabies-endemic countries [12]. Deaths due to rabies are often
severely underreported, with many people dying outside of the health
system, often in remote and marginalized communities [13]. Instead of
directly measuring rabies deaths, the majority of rabies burden studies
use bite patient data on reported bites at clinics provisioning PEP and
a decision tree framework to extrapolate deaths, assuming that overall
reported bite incidence (i.e. both bites due to non-rabid and rabid
animals) is proportional to rabies incidence (i.e. the more bites
reported in a location, the higher the incidence of rabies exposures),
and that reporting to clinics for PEP is uniform across space
[8,14,15]. If applied subnationally, these assumptions would likely
underestimate rabies deaths in places with poor access to PEP and may
overestimate rabies deaths in places with better access to PEP.

In Madagascar, the Institut Pasteur de Madagascar (IPM) provides PEP to
30 Ministry of Health clinics, in addition to its own vaccine clinic,
where PEP is available at no direct cost to patients [15]. Other than
at these 31 clinics, PEP is not available at any other public clinics or
through the private sector. In addition, there is limited control of
rabies in dog populations and the disease is endemic throughout the
country [16,17]. Due to the spatially restricted nature of PEP
provisioning and lack of direct costs for PEP, geographic access is
likely to be a major driver of disease burden within the country.
Previously, we estimated the burden of rabies in Madagascar nationally
using data from a single district to extrapolate to the country, but did
not account for spatial variation in access [15]. Here, we provide
revised estimates of human rabies deaths by incorporating the impact of
access to PEP at the sub-national level on preventing human rabies
deaths and explore the potential impact of expanding provisioning of
human rabies vaccines on further reducing these deaths. This framework
may usefully apply to other countries where PEP availability is
currently geographically restricted in considering how to most
effectively and equitably provision these life-saving vaccines.

## Methods

### Estimating geographic access to PEP

To estimate mean and population weighted travel times to the nearest
clinic, we used two raster datasets: 1) the friction surface from the
Malaria Atlas Project [18] at an \~1 km^2^ scale (Fig S1.1A) and 2)
the population estimates from the 2015 UN adjusted population
projections from World Pop ([19], originally at an \~100m^2^
resolution, Fig S1.1B), which we aggregated to the friction surface.

From GPS locations of the 31 clinics that currently provision PEP, we
estimated the travel time to the nearest clinic at an approximately 1 x
1 km scale as described in [18]. We then extracted the mean and
population-weighted mean travel times for each district (2nd level
administrative division, N = 114) and commune (the administrative unit
below the district, N = 1579), and Euclidean distance, i.e. the minimum
distance from the administrative unit centroid to any clinic. We used
shapefiles from the UN Office for the Coordination of Humanitarian
Affairs for the district and communes boundaries (as of October 31,
2018). To see which metric best predicted ground-truthed travel time
data, we compared travel times and distance estimates to driving times
collected by IPM during field missions, i.e. time it took to travel by
car between two locations excluding break times (N =
`r`nrow(ttime_driving)\`), and patient reported travel times from a
subset of Moramanga clinic bite patients (N = 1057), see Fig S1.2 for
raw data) by seeing which worked best to predict estimated travel times
in a linear model.

### Estimating bite incidence

We used two datasets on bite patients reporting to clinics for PEP:

1)  A national database of individual bite patient forms from the 31
    clinics provisioning PEP across the country between 2014 - 2017.
    These forms were submitted to IPM with frequencies ranging from
    monthly to annually, included the patient reporting date and were
    resolved to the district level (patient residence).

2)  33 months of data (between October 2016 and June 2019) on patients
    reporting to the Moramanga clinic resolved to the commune level.

For the national data, some clinics did not submit any data, or had
substantial periods (months to a whole year), with no submitted data. To
correct for this, we exclude periods of 15 consecutive days with zero
submitted records (see Supplementary Appendix, section S2). For each
clinic we divided the total number of bites reported in a given year by
the estimated proportion of forms which were not submitted
(under-submission). Due to yearly variation in submissions, we took the
average of annual bite incidence estimates aggregated to district level.
We validated this approach by comparing estimated vial demand given the
total reported bites corrected for under-submission to vials provisioned
to clinics for 2014-2017 (see Supplementary Appendix, section S2). At
both the commune and district administrative level, we assigned clinic
catchments by determining which were closest in terms of travel times
for the majority of the population within the administrative unit. For
national data, we excluded any districts in a catchment of a clinic
which submitted less than 10 forms and any years for which we estimated
less than 25% of forms were submitted.

### Modeling reported bite incidence as a function of access

We modeled the number of reported bites as a function of travel time
($T$) using a Poisson regression:

$$\mu_{i} = e^{(\beta_{t}T_{i}\  + \ \beta_{0}\ )}P_{i}$$

$$y_{i} = Poisson(\mu_{i})$$

where $y_{i}$ is the average number of bites reported to a clinic
annually and $\mu_{i}$ the expected number of bite patients presenting
at the clinic as a function of travel time ($T_{i}$) and human
population size ($P_{i}$) (an offset which scales the incidence to the
expected number of bites) for a given source location (district or
commune). We fit this model to both the national data (district level)
and the Moramanga data (commune level). To more directly compare
estimates between datasets, we also modeled the national data with a
latent commune-level travel time covariate ($T_{j}$):

$$\mu_{i} = \sum_{j = 1}^{j}e^{(\beta_{t}T_{j}\ \  + \ \beta_{0j})}P_{j}$$

As travel times are correlated with population size (Fig S3.1), we also
compared how well bites were predicted by population size alone, and in
combination with travel times. For the models with population size, we
removed the offset and used either population size alone
($\mu_{i} = e^{(\beta_{p}P_{i} + \beta_{0})}$) or population size and
travel times
($\mu_{i} = e^{(\beta_{t}T_{i} + \beta_{p}P_{i} + \beta_{0}))}$) as
predictors.

For the models fit to the national data, we also modeled variation
between clinics with a catchment random effect:
$B_{0,k} \sim norm(\mu,\ \sigma_{0})$), where $\mu$ is the mean and
$\sigma_{0}$ is standard deviation and $B_{0,k}$ is the catchment level
intercept.

We tested whether the catchment random effect captured overdispersion in
the data (i.e. variance \> mean -- the expectation given a Poisson
distribution) rather than any catchment specific effects by extending
these models with an overdispersion parameter:
$\epsilon_{i} \sim norm(0,\ \sigma_{e})$, where $\sigma_{e}$ is the
standard deviation around a random variable with mean of zero [20]:

$$\mu_{i} = e^{(\sum_{j = 1}^{j}\beta_{j}X_{j}\  + \ \epsilon_{i})}P_{i}$$

where $\sum_{j = 1}^{j}\beta_{j}X_{j}$ is the sum of the all parameters
for a given model. We fit all models in a Bayesian regression framework
via MCMC using the R package 'rjags' [21]. We used model estimates to
generate fitted and out-of-fit predictions, and examined the sensitivity
of estimates to adjustments for under-submission of forms (Supplementary
Appendix, section S3).

### Modeling human rabies deaths

We estimate rabies deaths as a function of the number of bites predicted
by our model and estimates of endemic rabies exposure incidence using an
adapted decision tree framework. Table \@ref(tab:ch3-tab1) lists all parameter values and
their sources. Fig \@ref(fig:ch3-fig1) describes how these parameters are used in the
decision tree and the key outputs ($A_{i}$, deaths averted by PEP, and
$D_{i}$, deaths due to rabies).

Table: (\#tab:ch3-tab1) Model predictions of average annual reported bite incidence, total deaths, and deaths averted at the national level for the two models (commune level and district level models with travel time predictor and an overdispersion parameter); 95% prediction interval in parentheses.

| Parameter |                            Value                           | Description                                                                                                                                                    |                  Source                 |
|-----------|:----------------------------------------------------------:|----------------------------------------------------------------------------------------------------------------------------------------------------------------|:---------------------------------------:|
| $B_{i}$   | Function of travel time to closest clinic provisioning PEP | Modeled estimates of reported bite incidence                                                                                                                   | Bayesian regression model (see Methods) |
| $E_{i}$     |             Triangular(a = 15, b = 76, c = 42)             | Annual exposures per 100,000 persons                                                                                                                           |           [4,15], see Fig S4.1          |
| $p_{rabid}$    |            Triangular(a = 0.2, b = 0.6, c = 0.4)           | Proportion of reported bites that are rabies exposures1                                                                                                        |                   [15]                  |
| $\rho_{max}$          |                            0.98                            | The maximum reporting possible for any location; data from the commune closest to the Moramanga PEP clinic (average of 3.12 minutes travel time to the clinic) |                   [15]                  |
| $p_{death}$         |                            0.16                            | The probability of death given a rabies exposure                                                                                        
-   ^1^ $p_{rabid}$ is constrained so that rabid reported bites cannot
    exceed the total expected number of rabies exposures ($E_{i}$) or
    maximum reporting in a given simulation ($\rho_{max}$).

```{r ch3-fig1, out.width="90%", fig.cap = '(ref:ch3-fig1-cap)', fig.scap='Decision tree for burden estimation given model predicted bite incidence spatially.'}
knitr::include_graphics("figs/ch2/fig1.jpeg")
```

(ref:ch3-fig1-cap) Decision tree for burden estimation. For a given administrative unit $i$, human deaths due to rabies ($D_{i}$) are calculated from model predicted reported bites
($B_{i}$). To get $R_{i}$, the number of reported bites that were
rabies exposures, we multiply $B_{i}$ by $p_{rabid}$, the proportion
of reported bites that are rabies exposures. $R_{i}$ is subtracted
from $E_{i}$ to get the number of unreported bites ($U_{i}$) and
then multiplied by the probability of death given a rabies exposure
($p_{death}$) to get deaths due to rabies ($D_{i}$). Similarly,
deaths averted by PEP, $A_{i}$, are estimated by multiplying $R_{i}$
by $p_{death}$, i.e. those who would have died given exposure, but
instead received PEP. Both $E_{i}$ and $p_{rabid}$ are drawn from a
triangular distribution. Parameter values and sources are in Table \@ref(tab:ch3-tab1).

For $E_{i}$, we center the distribution at the lower end of our
estimated exposure incidence from the Moramanga District (42
exposures/100,000 persons), with a range applied assuming 1% rabies
incidence in dogs (estimated across a range of human-to-dog ratios
between 5 - 25) and that on average a rabid dog exposes 0.39 persons
[4] (see Fig S4.1). As there is little data on dog population size and
human exposure incidence in Madagascar[16,23], the range we used
encompasses both observed human-to-dog ratios across Africa [14,24]
and recent subnational estimates from Madagascar [25], and generates
similar exposure incidences as observed previously across Africa
[26,27]. Given previously high observed compliance in Madagascar
[15], we assume that all rabies exposed patients who report to a
clinic receive and complete PEP, and PEP is completely effective at
preventing rabies.

### Estimating the impact of expanding PEP provisioning

We developed a framework to rank clinics by how much their PEP provision
improves access for underserved communities, estimating incremental
reductions in burden and increases in vaccine demand. Specifically, we
aggregated our model-predicted estimates of annual bites to the clinic
level. As multiple clinics may serve a single district or commune, we
allocated bites to clinics according to the proportion of the population
in each administrative unit which were closest. For each clinic, we
simulate throughput by randomly assigning patient presentation dates,
and then assume perfect compliance (i.e. patients report for all doses)
to generate subsequent vaccination dates. We use these dates to estimate
vial usage given routine vial sharing practices in Madagascar [15],
but assuming adoption of the WHO-recommended abridged intradermal
regimen (2 x 0.1 ml injections on days 0, 3, and 7 [28]). For both
burden and vial estimates, we take the mean of 1000 simulations as each
clinic is added.

We simulate expansion first to each district (N = 114) and then to each
commune in the country for all communes with a clinic. We select the
primary clinic (primary health facility, usually with capacity to
provision vaccines) in the highest density grid cell of the
administrative unit as candidates for expansion. For the 85 communes
without a primary clinic, we chose the secondary clinic (secondary
health facility, often without formal vaccination capacity) in the
highest density grid cell. 94 communes lacked any health facilities.
Finally, we explore a scenario where all additional primary clinics
(totaling 1733) provision PEP.

We tested three metrics for ranking additional clinics: 1) The
proportion of people living \>3 hours from a existing PEP clinic that
provisions PEP for which travel times were reduced; 2) This proportion
(1), weighted by the magnitude of the change in travel times and 3) The
mean reduction in travel times for people living \>3 hours from an
existing PEP clinic. We simulated expansion of clinics provisioning PEP
to each district using these three metrics and chose the metric which
decreased burden the most compared to simulations (N = 10) where clinics
were added randomly to districts for the full expansion of PEP. For the
full simulation of expanded access, once clinics reduced travel times
for less than 0.01% of the population (\< 2400 living greater than $x$
hrs away, starting with $x$ = 3 hrs), we reduced the travel time
threshold by 25%.

### Sensitivity analysis

To test the effect of our model assumptions on estimates of rabies
burden and vial demand, we did a univariate sensitivity analysis of both
parameters from the models of bite incidence and the decision tree (see
Table S6.1 & S6.2 for parameter ranges used). We also examined how
systematic variation in rabies incidence with human population size
affected burden estimates. Specifically, if human-to-dog ratios are
positively correlated with human populations (i.e. dog
ownership/populations are higher in more populated, urban areas), we
might expect higher rabies exposure incidence as population size
increases. Alternatively, if human-to-dog ratios inversely correlate
with population size (i.e. dog ownership is more common in less
populated, rural areas), we might expect exposure incidence to scale
negatively with population size. We use scaling factors to scale
incidence either positively or negatively with observed population sizes
at the district and commune levels, while constraining them to the range
of exposure incidence used in the main analyses (15.6 - 76 exposures per
100,000 persons, Fig S4.2) and simulated baseline burden, as well as
expanded PEP access.

### Data and analyses

All analyses were done in R version 4.0.2 (2020-06-22) [29] and using
the packages listed in the supplementary references (Supplementary
appendix, section S7). All processed data, code, and outputs are
archived on Zenodo at [http://doi.org/10.5281/zenodo.4064312](http://doi.org/10.5281/zenodo.4064312) and
[https://doi.org/10.5281/zenodo.4064304](https://doi.org/10.5281/zenodo.4064304), and maintained at
[https://github.com/mrajeev08/MadaAccess](https://github.com/mrajeev08/MadaAccess). The raw bite patient data at
the national level are maintained in two secure REDCap
(project-redcap.org) databases, one for IPM and another for all
peripheral clinics provisioning PEP. These databases were last queried
on September 19, 2019 for these analyses. The IPM GIS unit provided the
data on geolocated clinics across the country. Anonymized raw bite
patient data and full data on geolocated clinics are available from IPM
following institutional data transfer protocols. Anonymized raw data
collected from the Moramanga District were retrieved from the Wise
Monkey Portal (wisemonkeyfoundation.org) on the same date and are shared
in the archived repository. 

### Ethics statement

Data collection from the Moramanga District was approved by the
Princeton University IRB (7801) and the Madagascar Ministry of Public
Health Ethics Committee (105-MSANP/CE). Oral informed consent was
obtained from all interviewed participants. Data collected from bite
patients at the national level are maintained jointly by the Ministry of
Health and IPM as a routine part of PEP provisioning.

## Results

### Estimates of travel times to clinics are high and variable across Madagascar.

Based on the estimates from the friction surface, approximately 36% of
the population of Madagascar are estimated to live over 3 hours from a
clinic (Fig \@ref(fig:ch3-fig2)). However, we found that these estimates underestimated
both driving times across the country and patient-reported travel times
to the Moramanga PEP clinic (Fig \@ref(fig:ch3-fig2)C). Patient reported travel times were
highly variable for a given commune compared to the estimated travel
times (Fig S1.2), potentially due to the fact that the friction surface
assumes that the fastest available mode of transport is used across each
grid cell (i.e. the presence of a road indicates that all travel through
that grid cell is by vehicle). However, patients reported using multiple
modes of transport, with some individuals walking days to the Moramanga
PEP clinic (Fig S1.3).

While the travel time estimates may not reflect exact distributions of
travel times, they were correlated with ground-truthed driving and
patient-reported times and likely reflect patterns of access over the
country (Fig \@ref(fig:ch3-fig3)C, Fig S1.4). Travel times weighted by population at the
grid cell level were a better predictor than unweighted travel times or
distance (R^2^ = 0.43, Table S1.1), therefore, we use
population-weighted travel time as a proxy for access at the
commune/district level in subsequent analyses.


```{r ch3-fig2, out.width="90%", fig.cap = '(ref:ch3-fig2-cap)', fig.scap='Travel times to clinics provisioning PEP across Madagascar.'}
knitr::include_graphics("figs/ch2/fig2.jpeg")
```

(ref:ch3-fig2-cap) Travel times to clinics provisioning PEP across Madagascar. (A) Estimated at an ~ 1 km2 scale. (B) Distribution of the population
across travel times. (C) Correlation between ground-truthed travel times
(mean of patient reported travel times to the Moramanga PEP clinic at
the commune level and reported driving times between GPS points) and
friction surface travel time estimates. The vertical lines show the 95%
quantiles for reported travel times and the point size shows the number
of observations for each commune. The best fit lines (red and grey) from
a linear model where observed travel times are predicted by estimated
travel times for each data source are also shown. The dashed black line
is the 1:1 line.

### As travel times increase, reported bite incidence decreases.

Bite incidence estimates generally increased with decreasing weighted
travel times at both administrative scales (district and commune),
although there was considerable variation between catchments for the
magnitude of this relationship (Fig \@ref(fig:ch3-fig3)C and D). After additionally
excluding any year with less than 25% of forms submitted, our final
dataset consisted of estimates of average bite incidence for 83 of 114
districts (Fig \@ref(fig:ch3-fig3)C), and 58 communes within the catchment of the
Moramanga District (Fig \@ref(fig:ch3-fig3)D, see Supplementary Appendix section S2 for
more details). For the national data, there were two outliers, Toamasina
II (the sub-urban district surrounding the city of Toamasina) and
Soanierana Ivongo, with higher bite incidence when compared to other
districts with similar travel times. While the estimates from the
Moramanga data showed higher reported incidence at low travel times at
the commune level compared to the district estimates, when aggregated to
the district, bite incidence estimates fell within the ranges observed
from the national dataset.

```{r ch3-fig3, out.width="90%", fig.cap = '(ref:ch3-fig3-cap)', fig.scap='The network of patient presentations and estimates of annual bite incidence across Madagascar.'}
knitr::include_graphics("figs/ch2/fig3.jpeg")
```

(ref:ch3-fig3-cap) The network of patient presentations and estimates of annual bite incidence. (A) at the district level for the national data and (B) commune level
for the Moramanga data: circles with a black outline represent the total
number of patients reporting to each clinic for which we have data.
Color corresponds to the clinic catchment. Circles with a white outline
are the total number of bites reported for that administrative unit
(plotted as the centroid). Lines show which clinic those patients
reported to, with the line width proportional to number of patients from
that district reporting to the clinic; flows of less than 5 patients
were excluded. Out-of-catchment reporting is indicated where points and
line colors are mismatched. For panel (A) districts in catchments
excluded due to lack of forms submitted by the clinic are colored in
grey. For (B) the inset of Madagascar shows the location of the enlarged
area plotted, which shows the district of Moramanga (outlined in black),
all communes included in it's catchment (red polygons), and other
communes where bites were reported to colored by their catchment (C) The
estimated average annual bite incidence from the national and Moramanga
data plotted at the district scale (both datasets) and at the (D)
commune scale (Moramanga dataset). Colors correspond to the clinic
catchment, shape indicates the dataset, and the size of the point
indicates the number of observations (i.e. the number of years for which
data was available for the national data; note for Moramanga 33 months
of data were used). The point lines indicate the range of estimated bite
incidence for each district.

Our modeling results show that travel times were a strong and consistent
predictor of reported bite incidence in both datasets and across scales
with the best fitting models including travel times and an
overdispersion parameter (Fig \@ref(fig:ch3-fig4), see Supplementary Appendix section S3
for comparisons to models with catchment effects and with population
size as a covariate). As the predictions of the model fit to the
Moramanga data without accounting for overdispersion fall within the
prediction intervals for the models fit to the national data (Fig \@ref(fig:ch3-fig4)A),
for subsequent predictions, we used the parameter estimates from models
fit to the national data, which encompass the range of travel time
effects observed in our datasets. Moreover, our out-of-fit predictions
to the data across scales suggest that the commune model is able to
capture travel time impacts at the commune level (Fig S3.3), therefore
we use both the district and commune model to disaggregate burden to the
finest scale possible. Finally, we examined the sensitivity of models to
how we corrected for underreporting of data and found that parameter
estimates of travel time impacts were similar across models and
performed similarly in prediction (Fig S3.8 and Fig S3.9).


```{r ch3-fig4, out.width="90%", fig.cap = '(ref:ch3-fig4-cap)', fig.scap='Travel times as a predictor of reported bite incidence per 100,000 persons.'}
knitr::include_graphics("figs/ch2/fig4.jpeg")
```

(ref:ch3-fig4-cap) Travel times as a predictor of reported bite incidence per 100,000 persons. (A) The estimated relationship between travel time in hours (x-axis)
and mean annual reported bite incidence (y-axis). The lines are the mean
estimates and the envelopes are the 95% prediction intervals generated
by drawing 1000 independent samples from the parameter posterior
distributions for three candidate models: model with travel times at the
1) commune- and 2) district-level fitted to the national data with an
overdispersion parameter ($\sigma_{e}$) and 3) travel times at the
commune level fitted to the Moramanga data with a fixed intercept and
unadjusted for overdispersion. The points show the data: National data
(circles) at the district level used to fit the District and Commune
models, and Moramanga data (triangles) at the commune level used to fit
the Moramanga model. (B) The posterior distribution of parameters from
the respective models for the model intercept, travel time effect, and
for overdispersion (national data only).

### Current provisioning of PEP substantially reduces human rabies deaths, but incidence of deaths remains high in areas with poor access

In general, the incidence of rabies deaths increases with travel times
to clinics, and there is significant sub-national variation when deaths
are modeled at the district and commune scale, with the least accessible
communities having most deaths (Fig \@ref(fig:ch3-fig5)B & C). We estimate that under the
current system of 31 clinics in Madagascar provisioning PEP that
approximately 800 (95% PI: 600 - 1000) deaths due to rabies are
prevented through PEP each year. Overall, we estimate close to 1000
rabies deaths (95% PI: 800 - 1100) annually in Madagascar. Our estimates
vary only slightly depending on the scale of the model (Table \@ref(tab:ch3-tab2)), but
disaggregating deaths to the commune level shows considerable variation
in predicted burden within districts (Fig \@ref(fig:ch3-fig5)A).

Table: (\#tab:ch3-tab2) Model predictions of average annual reported bite incidence, total deaths, and deaths averted at the national level for the two models (commune level and district level models with travel time predictor and an overdispersion parameter); 95% prediction interval in parentheses.

| Model    | Reported bite incidence per 100k | Burden of deaths | Deaths averted by current PEP provisioning |
|----------|----------------------------------|------------------|--------------------------------------------|
| Commune  | 85 (56 - 129)                    | 963 (795 - 1118) | 801 (644 - 968)                            |
| District | 85 (52 - 136)                    | 958 (752 - 1156) | 807 (609 - 1005)                           |



```{r ch3-fig5, out.width="90%", fig.cap = '(ref:ch3-fig5-cap)', fig.scap='Spatial variation in predicted incidence of human rabies deaths per 100,000 persons.'}
knitr::include_graphics("figs/ch2/fig5.jpeg")
```

(ref:ch3-fig5-cap) Spatial variation in predicted incidence of human rabies deaths per 100,000 persons. (A) for each district (y-axis) in Madagascar. Diamonds show the
predicted incidence for the district model and squares show predicted
incidence for the commune model fit to the National data for all
communes in a district. Points are colored and districts ordered by
travel times. The vertical lines show the average national incidence of
human rabies deaths for the commune (grey) and district (black) models.
Incidence mapped to the (B) commune- and (C) district-level from the
respective models; grey X's show locations of current clinics
provisioning PEP.

### Expanding PEP access to underserved populations is effective at reducing human rabies deaths, but this effect saturates as more clinics provision PEP

We found that targeted expansion of PEP to clinics based on the
proportion of the population they reduced travel times for resulted in
fewest deaths (Fig S5.1). Here we report results from the commune model,
as estimates were consistent across models (Fig \@ref(fig:ch3-fig6) and Supplementary
appendix, section S5). We estimated that strategic PEP expansion to
these additional 83 clinics (1 per district) reduced rabies deaths by
19% (95% PI: 14 - 23%) (Fig \@ref(fig:ch3-fig6)A). With one clinic per commune (where
available, N = 1696), we see a further reduction of 38% (95% PI: 30 -
46%). However, reductions in burden saturate as more clinics are added
(Fig S5.2). Even when all primary clinics provision PEP, our model still
predicts 600 (95% PI: 400 - 800) deaths per annum, and average reporting
of rabies exposures remains approximately 66% (95% PI: 33 - 78%) (Fig
S5.5); as more clinics are added, reported bite incidence saturates (Fig
S5.4), and patients shift which clinic they report to (S5.7 & S5.8).

Vial demand also outpaces reductions in burden (Fig \@ref(fig:ch3-fig6)B), with more vials
needed per death averted (Fig \@ref(fig:ch3-fig6)C). Our model predicts an increase from
33500 vials (95% PI: 22900 - 49400) per annum under current provisioning
but with the abridged intradermal regimen (i.e. visits on days 0, 3, 7),
to \~56900 vials (95% PI: 40200 - 77800) with 250 clinics providing PEP,
and \~86400 vials (95% PI: 61600 - 118000) if all primary clinics
provision PEP. In these scenarios, clinic catchment populations and
throughput decrease, with clinics seeing fewer patients per day (S5.6).


```{r ch3-fig6, out.width="90%", fig.cap = '(ref:ch3-fig6-cap)', fig.scap='Impact of expanded PEP access on deaths, deaths averted, and vial demand.'}
knitr::include_graphics("figs/ch2/fig6.jpeg")
```

(ref:ch3-fig6-cap) Impact of expanded PEP access on deaths, deaths averted, and vial demand. (A) Decrease in deaths due to rabies, (B) increase in total \# of vials
as additional clinics provisioning PEP are added at the national level,
and (C) increase in vials needed per death averted based on the two
models of reported bites. Lines are the mean of 1000 simulations with
envelopes representing 95% prediction intervals. The points show when
all additional primary clinics and secondary clinics (N = 1733) clinics
have been added).

### Burden estimates are most sensitive to assumptions of underlying rabies incidence.

While qualitative patterns of the current impact of geographic access on
human rabies deaths and the impact of expanding access to PEP on
reducing these deaths is robust across a wide range of parameter
estimates, our sensitivity analyses show that assumptions of the
underlying rabies exposure incidence ($E_{i}$) contribute the most
uncertainty to our quantitative estimates (Fig S6.1 & 2). Uncertainty in
bite model parameters contribute less to uncertainty in estimates of
burden or impacts of expanded access. For the estimates of vial demand,
uncertainty around the model intercept (i.e. the baseline reported bite
incidence) has most impact, rather than the travel time effect or the
overdispersion parameter (Fig S6.3). Finally, scaling of incidence with
population size (Fig S4.2) modulates the impact of travel times on
deaths, with positive scaling of rabies incidence with population size
(i.e. more rabies in more populated places) dampening and negative
scaling exacerbating the relationship between access and deaths (Fig
S6.4A). However, the impact of adding clinics remains broadly the same
(Fig S6.4B).

## Discussion

### Main findings

We find that the burden of rabies in Madagascar is likely concentrated
in areas with poor PEP access. We estimate that current PEP provisioning
(at 31 clinics) averts 45%of deaths that would otherwise occur, and that
expanding PEP access should reduce mortality, with provisioning in one
clinic per district (N = 83), or per commune (N = 1733), expected to
reduce mortality by 16% and 33%, respectively. However, improved PEP
provisioning is unlikely to eliminate rabies deaths; with over 600
deaths expected even with PEP at all primary clinics (N = 1733). This is
partly because travel times remain high (> 2 hrs as estimated by the
friction surface for over 10% of the population, Fig S5.4) even after
expanding PEP to all primary clinics. With reduced travel times, over
20% of exposures will still not seek PEP (Fig S5.5), resulting in ~1.65
rabies deaths per 100,000 people. PEP is expected to remain
cost-effective as provisioning expands, to a maximum of 450 USD per
death averted (assuming 5 USD per vial), similar to other estimates
[4]. While our quantitative predictions depend on assumptions of
underlying rabies exposure incidence, the qualitative patterns regarding
travel time impacts remain robust and are useful in identifying
strategies for provisioning PEP.

### Limitations

Data limitations introduced bias and uncertainty to our estimates. For
example, travel times from the Malaria Atlas Project friction surface
underestimated patient-reported travel times, with discrepancies between
assigned transport speeds (from the Open Street Map user community, or
country cluster data [18]) and realities of local travel. In
Madagascar, the presence of paved roads does not necessarily reflect
their quality or the modes of transport used. Patients seeking PEP at
the Moramanga clinic reported various transport methods and highly
variable travel times even within a single commune. While
patient-reported travel times may lack precision from recall and
estimation error, they likely better reflect lived experience; validated
travel times [30] could improve estimates of spatial health
inequities. Similarly, modeled estimates of population distribution
[19] also introduce uncertainty. Our analysis of data from the
Moramanga District indicates that variation at the sub-district level is
high and impacts health seeking behavior. However, we lacked fine-scale
data from other catchments for comparison. Additionally, we had to
correct for underreporting and incomplete data; strengthening
surveillance and routine data collection should improve understanding of
health seeking behavior and access, and support monitoring and
evaluation of PEP provisioning.

While we rely on a number of assumptions, they are based on data
specific to Madagascar or from other similar settings and consistent
with estimates from the literature more broadly (see Table \@ref(tab:ch3-tab1) and section
S4). Our burden estimates were most sensitive to assumptions about
rabies exposure incidence, drawn from studies in the Moramanga District
[15] and elsewhere [4]. As incidence of rabies exposures varies over
time and space [31,32], we incorporated uncertainty into our
estimates, but we did not find qualitative differences in the effects of
travel times on rabies deaths. Our simplifying assumptions regarding
patient compliance, which is generally high in Madagascar [15], and on
complete efficacy of PEP are unlikely to greatly influence our burden
estimates [22]. Likewise, we do not account for differential risk for
severely exposed patients not receiving Immunoglobulins (RIG), which is
only available at IPM in the captial of Antananarivo, but recent studies
show that even in the absence of RIG, PEP is extremely effective [4].
We also assume that clinics reliably provision PEP, but a 2019 KAP
survey reported clinics experiencing stock-outs [25].

We assumed geographic access to PEP was the primary driver of
health-seeking behavior, but socioeconomic status, education and
awareness about rabies [[33]; [27]; [34]; [35];
castillo2020behavioral] all play a role. For example, most PEP clinics
also charge fees (from 0.50 - 3.00 USD for consultations, wound
treatment, etc. [25]) which may also act as barriers to PEP access. In
Madagascar, where PEP is free-of-charge, the main cost to patients is
transport and time lost. More remote communities tend to be of lower
socioeconomic and educational status [2], so travel time may be a
proxy for these correlated variables. Significant overdispersion in the
data that cannot be explained by travel times suggests that clinic-level
variation (e.g. vaccine availability and charges) and regional
differences (e.g. dog populations, outbreaks, awareness) further
influence health-seeking behavior and vaccine demand. Although our
estimates could be improved with better data on rabies incidence,
health-seeking behavior, and PEP provisioning, predicting PEP impacts
will remain challenging given the complex interactions between
socioeconomic factors, access to and quality of care, and human
behavior, as illustrated by the case studies in Box 1. However, it is
very likely that the impacts of improving access to PEP could be further
increased with outreach and awareness raising efforts that we were
unable to parameterize.

#### Box 2: case studies of of health seeking behavior for PEP in Madagascar

1.  Anosibe An'ala District (population \~ 100,265), south of Moramanga,
    has moderate incidence of bite patients (\~ 54/100,000 persons) even
    though travel times often exceed 24 hours. While a road connects the
    main Anosibe An'ala commune to the Moramanga PEP clinic, it is only
    passable by large trucks during much of the rainy season, with
    speeds usually \< 10km per hour. Over 9% of patients from Anosibe
    An'ala had been in close proximity or touched a person that died
    from rabies (four suspect human rabies deaths of patients who did
    not receive any PEP), whilst of patients with Category II and III
    exposures that were interviewed, 11/19 (58%) were bitten by probable
    rabid dogs. Given the high travel times (although underestimated by
    the friction surface) and incidence of reported rabies exposures and
    deaths, we predict a large but unobserved rabies burden in this
    remote community (\~6.02 deaths per year) and we ranked a clinic
    provisioning PEP in Anosibe An'ala 28th for travel time reductions.
    Other remote communities likely experience similar high and
    unrecognized burden, but improved surveillance is necessary to
    identify such areas. Notably, bite patients in this district
    demonstrate willingness to travel for free PEP (in some cases
    walking 3 days to a clinic) with awareness of rabies risk. Community
    outreach and active surveillance in other remote areas could also
    greatly improve people's awareness of risk and health seeking
    behavior.

2.  Recently, a middle-aged taxi driver died of rabies in suburban
    Antananarivo. The day after being bitten by an unknown dog, he
    reported to a clinic that referred him to the closest clinic
    provisioning PEP, approximately one hour's drive from his home. His
    family urged him to go, but he did not believe his risk was high and
    decided not to seek further care. He developed symptoms two weeks
    later and was confirmed as a rabies death by the National Rabies
    Reference Laboratory. Despite prompt reporting, appropriate
    referral, and socioeconomic indicators suggesting a high
    care-seeking probability, this person did not receive PEP. His story
    highlights the need for sensitization about rabies, how PEP
    provisioning at peripheral clinics (even in areas with reasonable
    access) could prevent additional deaths, and ultimately that PEP
    alone is unlikely to prevent all rabies deaths.

### Broader context

Recent studies have estimated access to health-seeking behavior and PEP
completion and adherence, but not directly linked these estimates to
burden [7,36,37]. Our approach for incorporating access to vaccines
(echoing [38--42]) into burden estimation methods could guide
provisioning of PEP to maximize impacts. This approach will have most
value in settings with limited PEP access and poor health seeking, but
will be less valuable where rabies exposures make up a small fraction of
patients reporting for PEP e.g. [43,44]. In other settings, similar
statistical approaches could be used to identify and quantify key
barriers to PEP seeking behavior. For example, reducing the direct cost
of PEP is likely to be of more importance than increasing geographic
access where PEP costs are high.

Our revised estimate of rabies deaths in Madagascar using this approach
was higher than previously estimated (between 280 - 750 deaths/year)
[15], which assumed uniform reporting of 85%, but remained within the
range of other empirical and modeling studies from low-income countries
[26,27,45--47]. Our estimates of vial demand depend on use of the new
abridged intradermal regimen [28], which has been adopted by the
Ministry of Health in Madagascar. However, most clinic staff were not
aware of WHO classifications of exposure categories, and vaccination of
Category I exposures (those not requiring PEP) remains common practice,
comprising 20% of vial demand in Moramanga [15].

We predict that as clinics are expanded, throughput (daily patients
reporting to a clinic) will decrease. This may complicate the supply
chain and make provisioning PEP more challenging as vial demand becomes
less predictable, leading to stock outs or wastage. Decentralized
provisioning mechanisms, for example adopting routine childhood vaccine
supply chains, or novel vaccine delivery methods such as drones [48],
may mitigate these challenges. When nerve tissue vaccines were used in
Madagascar, clinics requested vaccines upon demand and PEP access was
more widespread, but provisioning the more expensive cell culture
vaccines to all clinics became too costly [16]. Widespread vaccine
provisioning is therefore feasible given Madagascar's health
infrastructure, if cost barriers are removed.

Gavi investment could greatly reduce the access and cost barriers to PEP
[6,7,22,49]. Currently, each clinic in Madagascar serves an average
catchment of 780,000 persons. Latin American countries, where
significant progress has been made towards elimination, aim for one PEP
clinic per 100,000 persons. In Madagascar this would require around 212
additional clinics provisioning PEP. We predict that Gavi investment
would be highly cost-effective, greatly reducing deaths by expanding PEP
supply to underserved areas.

However, our results suggest that PEP expansion alone cannot prevent the
majority of rabies deaths, and even given maximal access, achieving 'the
last mile,' preventing deaths in the most remote populations, will
require disproportionate resources [50]. To achieve 'Zero by 30,' mass
dog vaccination will be key to interrupting transmission and eliminating
deaths. Integrated Bite Case Management (IBCM) uses bite patient risk
assessments to determine rabies exposure status, guide PEP
administration, and trigger investigations of rabid animals, potentially
identifying other exposed persons [15,51,52]. IBCM is one way to
manage PEP effectively [43] and as it relies on exposed persons
reporting to clinics, expanding PEP access could strengthen this
surveillance framework. These same issues of access, however, apply to
both dog vaccination and surveillance, and understanding spatial
heterogeneities will be critical to determining how control and
prevention interventions can be best implemented [53,54].

## Conclusion

Our study suggests that rabies deaths in Madagascar disproportionately
occur in communities with the poorest access to PEP and that expanding
PEP access should reduce deaths. Without data on rabies incidence and
exposure risk, targeting PEP expansion to underserved areas is a
strategic way to reduce rabies burden and provide equitable access, for
example, by expanding provisioning to clinics serving populations that
target an evidence-based travel time threshold or catchment size.
Implementing outreach programs to raise awareness should further
increase the efficacy of PEP expansion by improving care seeking. Better
surveillance is also needed to understand the geographical distribution
of rabies exposures and identify populations most at risk, and to
evaluate the effectiveness of PEP expansion at preventing human rabies
deaths. Gavi investment could support countries to more equitably
provision PEP and overcome barriers to access ([9], see Box 1 for case
studies), but as PEP alone cannot prevent all rabies deaths, investment
should be used to catalyze mass dog vaccination to interrupt
transmission, and eventually eliminate rabies deaths.

## Acknowledgements

We thank all the clinicians and staff at the clinics across the country.
We are grateful to IPM and the Ministry of Public Health who collect and
maintain data on PEP provisioning. In particular, we thank the GIS unit
for assistance with spatial data, Michael Luciano Tantely for sharing
driving time data, and Claire Leblanc, Rila Ratovoson, and Daouda Kassie
for sharing results of their work in the Moramanga District. In
addition, we thank Jean Hyacinthe Randrianarisoa, Ranaivoarimanana,
Fierenantsoa Randriamahatana, Esther Noiarisaona, Cara Brook, Amy
Winter, Christian Ranaivoson, John Friar, and Amy Wesolowski for
assistance.

## Supplementary Appendices

All supplementary figures and tables can be viewed with the full manuscript at this link:
[https://mrajeev08.github.io/MadaAccess](https://mrajeev08.github.io/MadaAccess). A link to the supplementary materials will be included in this dissertation once published. 

## References
\setlength{\parskip}{1em}

[1] World Health Organization. World health statistics 2018: Monitoring
health for the SDGs Sustainable Development Goals. World Health
Organization; 2018.

[2] Peters DH, Garg A, Bloom G, Walker DG, Brieger WR, Hafizur Rahman M.
Poverty and access to health care in developing countries. Annals of the
New York Academy of Sciences. 2008;1136: 161--171.

[3] Maina J, Ouma PO, Macharia PM, Alegana VA, Mitto B, Fall IS, et al.
A spatial database of health facilities managed by the public health
sector in sub Saharan Africa. Scientific Data. 2019;6: 134.
doi:[10.1038/s41597-019-0142-2](https://doi.org/10.1038/s41597-019-0142-2)

[4] WHO Rabies Modelling Consortium. The potential effect of improved
provision of rabies post-exposure prophylaxis in Gavi-eligible
countries: A modelling study. The Lancet Infectious Diseases. 2019;19:
102--111.

[5] Organization WH, others. Rabies vaccines: WHO position paper, April
2018--recommendations. Vaccine. 2018;36: 5500--5503.

[6] Sreenivasan N, Li A, Shiferaw M, Tran CH, Wallace R, Blanton J, et
al. Overview of rabies post-exposure prophylaxis access, procurement and
distribution in selected countries in Asia and Africa, 2017--2018.
Vaccine. 2019;37: A6--A13.

[7] Tarantola A, Blanchi S, Cappelle J, Ly S, Chan M, In S, et al.
Rabies postexposure prophylaxis noncompletion after dog bites:
Estimating the unseen to meet the needs of the underserved. American
Journal of Epidemiology. 2018;187: 306--315.

[8] Hampson K, Coudeville L, Lembo T, Sambo M, Kieffer A, Attlan M, et
al. Estimating the global burden of endemic canine rabies. PLoS Negl
Trop Dis. 2015;9: e0003709.

[9] Wentworth D, Hampson K, Thumbi SM, Mwatondo A, Wambura G, Chng NR. A
social justice perspective on access to human rabies vaccines. Vaccine.
2019;37: A3--A5.

[10] World Health Organization. Zero by 30: The global strategic plan to
end human deaths from dog-mediated rabies by 2030. World Health
Organization; 2018.

[11] Gavi: Vaccine investment strategy.
https://www.gavi.org/our-alliance/strategy/vaccine-investment-strategy;
Gavi, the vaccine alliance;

[12] Scott TP, Coetzer A, Fahrion AS, Nel LH. Addressing the disconnect
between the estimated, reported, and true rabies data: The development
of a regional african rabies bulletin. Frontiers in veterinary science.
2017;4: 18.

[13] Taylor LH, Hampson K, Fahrion A, Abela-Ridder B, Nel LH.
Difficulties in estimating the human burden of canine rabies. Acta
tropica. 2017;165: 133--140.

[14] Knobel DL, Cleaveland S, Coleman PG, Fèvre EM, Meltzer MI, Miranda
MEG, et al. Re-evaluating the burden of rabies in Africa and Asia.
Bulletin of the World health Organization. 2005;83: 360--368.

[15] Rajeev M, Edosoa G, Hanitriniaina C, Andriamandimby SF, Guis H,
Ramiandrasoa R, et al. Healthcare utilization, provisioning of
post-exposure prophylaxis, and estimation of human rabies burden in
Madagascar. Vaccine. 2019;37: A35--A44.

[16] Andriamandimby SF, Heraud J-M, Ramiandrasoa R, Ratsitorahina M,
Rasambainarivo JH, Dacheux L, et al. Surveillance and control of rabies
in La Reunion, Mayotte, and Madagascar. Veterinary Research. 2013;44:
1--9.

[17] Reynes J-M, Andriamandimby SF, Razafitrimo GM, Razainirina J,
Jeanmaire EM, Bourhy H, et al. Laboratory surveillance of rabies in
humans, domestic animals, and bats in Madagascar from 2005 to 2010.
Advances in preventive medicine. 2011;2011.

[18] Weiss DJ, Nelson A, Gibson HS, Temperley W, Peedell S, Lieber A, et
al. A global map of travel time to cities to assess inequalities in
accessibility in 2015. Nature. 2018;553: 333--336.
doi:[10.1038/nature25181](https://doi.org/10.1038/nature25181)

[19] Linard C, Gilbert M, Snow RW, Noor AM, Tatem AJ. Population
distribution, settlement patterns and accessibility across Africa in
2010. PloS one. 2012;7: e31743--e31743.
doi:[10.1371/journal.pone.0031743](https://doi.org/10.1371/journal.pone.0031743)

[20] Gelman A, Hill J. Data analysis using regression and
multilevel/hierarchical models. Cambridge university press; 2006.

[21] Plummer M. Rjags: Bayesian graphical models using MCMC. 2019.
Available: <https://CRAN.R-project.org/package=rjags>

[22] Changalucha J, Steenson R, Grieve E, Cleaveland S, Lembo T, Lushasi
K, et al. The need to improve access to rabies post-exposure vaccines:
Lessons from Tanzania. Vaccine. 2019;37: A45--A53.

[23] Ratsitorahina M, Rasambainarivo JH, Raharimanana S,
Rakotonandrasana H, Andriamiarisoa M-P, Rakalomanana FA, et al. Dog
ecology and demography in Antananarivo, 2007. BMC Veterinary Research.
2009;5: 21.

[24] Sambo M, Hampson K, Changalucha J, Cleaveland S, Lembo T, Lushasi
K, et al. Estimating the size of dog populations in Tanzania to inform
rabies control. Veterinary sciences. 2018;5: 77.

[25] Leblanc C. Rabies in Madagascar: A three-pronged survey of
knowledge and practices among health care providers from anti-rabies
treatment centers, veterinarians and the community of Moramanga. PhD
thesis, Cnam de Sante Publique. 2019.

[26] Beyene TJ, Mourits MC, Kidane AH, Hogeveen H. Estimating the burden
of rabies in Ethiopia by tracing dog bite victims. PLoS One. 2018;13:
e0192313.

[27] Hampson K, Dobson A, Kaare M, Dushoff J, Magoto M, Sindoya E, et
al. Rabies exposures, post-exposure prophylaxis and deaths in a region
of endemic canine rabies. PLoS Negl Trop Dis. 2008;2: e339.

[28] Tarantola A, Ly S, Chan M, In S, Peng Y, Hing C, et al. Intradermal
rabies post-exposure prophylaxis can be abridged with no measurable
impact on clinical outcome in Cambodia, 2003-2014. Vaccine. 2019;37:
A118--A127.

[29] R Core Team. R: A language and environment for statistical
computing. Vienna, Austria: R Foundation for Statistical Computing;
2019. Available: <https://www.R-project.org/>

[30] Ray N, Ebener S. AccessMod 3.0: Computing geographic coverage and
accessibility to health care services using anisotropic movement of
patients. International Journal of Health Geographics. 2008;7: 63.
doi:[10.1186/1476-072X-7-63](https://doi.org/10.1186/1476-072X-7-63)

[31] Hampson K, Dushoff J, Bingham J, Bruckner G, Ali Y, Dobson A.
Synchronous cycles of domestic dog rabies in sub-Saharan Africa and the
impact of control efforts. Proceedings of the National Academy of
Sciences. 2007;104: 7717--7722.

[32] Hampson K, Dushoff J, Cleaveland S, Haydon DT, Kaare M, Packer C,
et al. Transmission dynamics and prospects for the elimination of canine
rabies. PLoS Biology. 2009;7: e1000053.

[33] Etheart MD, Kligerman M, Augustin PD, Blanton JD, Monroe B,
Fleurinord L, et al. Effect of counselling on health-care-seeking
behaviours and rabies vaccination adherence after dog bites in haiti,
2014--15: A retrospective follow-up survey. The Lancet Global Health.
2017;5: e1017--e1025.

[34] Barbosa Costa G, Gilbert A, Monroe B, Blanton J, Ngam Ngam S,
Recuenco S, et al. The influence of poverty and rabies knowledge on
healthcare seeking behaviors and dog ownership, Cameroon. PloS one.
2018;13: e0197330.

[35] Sambo M, Lembo T, Cleaveland S, Ferguson HM, Sikana L, Simon C, et
al. Knowledge, attitudes and practices (KAP) about rabies prevention and
control: A community survey in Tanzania. PLoS Neglected Tropical
Diseases. 2014;8: e3310.

[36] Zaidi SMA, Labrique AB, Khowaja S, Lotia-Farrukh I, Irani J,
Salahuddin N, et al. Geographic variation in access to dog-bite care in
Pakistan and risk of dog-bite exposure in Karachi: Prospective
surveillance using a low-cost mobile phone system. PLoS Negl Trop Dis.
2013;7: e2574.

[37] De la Puente-León M, Levy MZ, Toledo AM, Recuenco S, Shinnick J,
Castillo-Neyra R. Spatial inequality hides the burden of dog bites and
the risk of dog-mediated human rabies. The American Journal of Tropical
Medicine and Hygiene. 2020;103: 1247--1257.
doi:[10.4269/ajtmh.20-0180](https://doi.org/10.4269/ajtmh.20-0180)

[38] Hegde ST, Salje H, Sazzad HM, Hossain MJ, Rahman M, Daszak P, et
al. Using healthcare-seeking behaviour to estimate the number of Nipah
outbreaks missed by hospital-based surveillance in Bangladesh.
International journal of epidemiology. 2019;48: 1219--1227.

[39] MacPherson P, Khundi M, Nliwasa M, Choko AT, Phiri VK, Webb EL, et
al. Disparities in access to diagnosis and care in Blantyre, Malawi,
identified through enhanced tuberculosis surveillance and spatial
analysis. BMC medicine. 2019;17: 21.

[40] Poletti P, Parlamento S, Fayyisaa T, Feyyiss R, Lusiani M, Tsegaye
A, et al. The hidden burden of measles in Ethiopia: How distance to
hospital shapes the disease mortality rate. BMC medicine. 2018;16:
1--12.

[41] Metcalf CJE, Tatem A, Bjornstad O, Lessler J, O'Reilly K, Takahashi
S, et al. Transport networks and inequities in vaccination: Remoteness
shapes measles vaccine coverage and prospects for elimination across
Africa. Epidemiology & Infection. 2015;143: 1457--1466.

[42] Alegana VA, Wright J, Pezzulo C, Tatem AJ, Atkinson PM.
Treatment-seeking behaviour in low-and middle-income countries estimated
using a Bayesian model. BMC medical research methodology. 2017;17: 67.

[43] Rysava K, Miranda M, Zapatos R, Lapiz S, Rances P, Miranda L, et
al. On the path to rabies elimination: The need for risk assessments to
improve administration of post-exposure prophylaxis. Vaccine. 2019;37:
A64--A72.

[44] Wallace RM, Reses H, Franka R, Dilius P, Fenelon N, Orciari L, et
al. Establishment of a canine rabies burden in Haiti through the
implementation of a novel surveillance program. PLoS Neglected Tropical
Diseases. 2015;9: e0004245.

[45] Ly S, Buchy P, Heng NY, Ong S, Chhor N, Bourhy H, et al. Rabies
situation in Cambodia. PLoS Negl Trop Dis. 2009;3: e511.

[46] Sudarshan MK, Madhusudana SN, Mahendra BJ, Rao NSN, Ashwath
Narayana DH, Abdul Rahman S, et al. Assessing the burden of human rabies
in India: Results of a national multi-center epidemiological survey.
International Journal of Infectious Diseases. 2007;11: 29--35.

[47] Dhand NK, Gyeltshen T, Firestone S, Zangmo C, Dema C, Gyeltshen R,
et al. Dog bites in humans and estimating human rabies mortality in
rabies endemic areas of Bhutan. PLoS Neglected Tropical Diseases.
2011;5: e1391.

[48] Boeras DI, Collins BC, Peeling RW. The use of drones in the
delivery of rural healthcare. Revolutionizing Tropical Medicine:
Point-of-Care Tests, New Imaging Technologies and Digital Health. 2019;
615--632.

[49] Li AJ, Sreenivasan N, Siddiqi UR, Tahmina S, Penjor K, Sovann L, et
al. Descriptive assessment of rabies post-exposure prophylaxis
procurement, distribution, monitoring, and reporting in four Asian
countries: Bangladesh, Bhutan, Cambodia, and Sri Lanka, 2017--2018.
Vaccine. 2019;37 Suppl 1: A14--A19.
doi:[10.1016/j.vaccine.2018.10.011](https://doi.org/10.1016/j.vaccine.2018.10.011)

[50] Del Rio Vilas VJ, Freire de Carvalho MJ, Vigilato MA, Rocha F,
Vokaty A, Pompei JA, et al. Tribulations of the last mile: Sides from a
regional program. Frontiers in Veterinary Science. 2017;4: 4.

[51] Lechenne M, Mindekem R, Madjadinan S, Oussiguéré A, Moto DD,
Naissengar K, et al. The importance of a participatory and integrated
one health approach for rabies control: The case of N'Djamena, Chad.
Tropical medicine and infectious disease. 2017;2: 43.

[52] Undurraga EA, Meltzer MI, Tran CH, Atkins CY, Etheart MD, Millien
MF, et al. Cost-effectiveness evaluation of a novel integrated bite case
management program for the control of human rabies, Haiti 2014--2015.
The American journal of tropical medicine and hygiene. 2017;96:
1307--1317.

[53] Ferguson EA, Hampson K, Cleaveland S, Consunji R, Deray R, Friar J,
et al. Heterogeneity in the spread and control of infectious disease:
Consequences for the elimination of canine rabies. Scientific reports.
2015;5: 18232.

[54] Metcalf CJE, Cohen C, Lessler J, McAnerney J, Ntshoe G, Puren A, et
al. Implications of spatially heterogeneous vaccination coverage for the
risk of congenital rubella syndrome in South Africa. Journal of the
Royal Society Interface. 2013;10: 20120756.

[55] Hampson K, Abela-Ridder B, Brunker K, Bucheli STM, Carvalho M,
Caldas E, et al. Surveillance to establish elimination of transmission
and freedom from dog-mediated rabies. bioRxiv. 2016.

[56] Cleaveland S, FEvre EM, Kaare M, Coleman PG. Estimating human
rabies mortality in the United Republic of Tanzania from dog bite
injuries. Bulletin of the World Health Organization. 2002.

[57] Castillo-Neyra R, Buttenheim AM, Brown J, Ferrara JF, Arevalo-Nieto
C, Borrini-Mayorı́ K, et al. Behavioral and structural barriers to
accessing human post-exposure prophylaxis and other preventive practices
in arequipa, peru, during a canine rabies epidemic. PLOS Neglected
Tropical Diseases. 2020;14: e0008478.