Output of delay differential equation system not as expected

[andreaskuster]

The simulation with our system of delay differential equations (to model the phages from infection to the burst of the cell) is broken in the current implementation.
(1) The simulation result does not behave as expected. (I will review your code for any bugs, You should do this too.)
(2) From my understanding, JiTCDDE does not support piecewise defined functions (we could use a sharp sigmoidal function, but this makes thinks more complicated and is kind of hackish). This is a mandatory requirement i.e. for defining 'sharp' temperature profiles. I will look around for a different library that natively supports this feature.

[andreaskuster]

i found ddeint, a python library providing all our required capabilities. Please update your implementation to be compatible with ddeint. I wrote a small getting started example for you:

import numpy as np
from ddeint import ddeint
from pylab import array, sin, linspace, subplots

tau = 30.0


def foo(t):
    if t < 10.0:
        return 0.0
    elif 10.0 <= t < 10.0 * np.pi:
        return 1.0
    else:
        return 10.0 * sin(t * 0.5)


def values_before_zero(t):
    return array([0.0, 0.0])


def model(Y, t):
    x, y = Y(t)
    x_tau, y_tau = Y(t - tau)
    return array([foo(t), x_tau])


tt = linspace(0, 100, 1000)
yy = ddeint(model, values_before_zero, tt)

fig, ax = subplots(1, figsize=(8, 4))

ax.plot(tt, [x[0] for x in yy], label="trace1")
ax.plot(tt, [x[1] for x in yy], label="trace2")
fig.legend(loc='upper center', borderaxespad=2.0)
fig.show()

The function foo(t) is a piecewise defined and the delay differential equation trace2 looks plausible (30ish units 'behind' foo(t)).