I am trying to solve and plot delayed SIRD model. My code is:
S4 =
NDSolve[
{x'[t] == - (0.3/(80*10^6)) x[t] y[t],
y'[t] == (0.3/(80*10^6)) x[t] y[t] -
(0.3/(80*10^6)) x[t - 14] y[t - 14] - 0.01 y[t],
z'[t] == (0.3/(80*10^6)) x[t - 14] y[t - 14], a'[t] == 0.01 y[t],
x[0] == 80*10^6, y[t /; t <= 0] == E^t, y[0] == 150, z[0] == 0,
a[0] == 0 }, {x, y, z, a}, {t, 0, 200}]`
In the solution I am getting the error message:
NDSolve::ndsz: At t == 164.8072392646089, step size is effectively zero; singularity or stiff system suspected.
And this results in values of graph that shouldnt be possible, active cases can't be negative.
What am I doing wrong?