Hi All,

I would like to implement Birth Death Process with Delay.

Here is the code for Birth Death Process without Delay.

SeedRandom@2
With[{A = 5, initialPop = 10}, sim = NestList[(

      \[CapitalDelta]t = 
       RandomVariate@ExponentialDistribution[A #[[2]]];

      {#[[1]] + \[CapitalDelta]t, #[[2]] + 1}

      ) &, {0, initialPop}, 10]];

ListLinePlot[sim, Epilog -> {Red, PointSize[Medium], Point[sim]}, 
 Frame -> True, PlotTheme -> "Detailed", 
 FrameLabel -> {"Time", "Population"}, ImageSize -> Large, 
 InterpolationOrder -> 0]

I don't know how to implement if there is a delay this process with delay. I would like to extend this for Birth-Death process later.

Here is the algorithm for Birth Death Process with Delay.

Any Suggestion. Cross posted at mathematica.stackexchange.com