# Model the birth death process with delay?

Posted 1 year ago
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 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
 Here is my try. How can I store the values and plot list? Can someone check I am doing right? Probably Reap&Sow is the way to do it. I basically need last list of each row to plot.Thanks in advance.  SeedRandom@12; x = 1; t0 = {RandomVariate@ExponentialDistribution[1 x]}; td0 = {RandomVariate@GammaDistribution[4, 2]}; s = t0 + td0; Should be in different cell. SeedRandom@12 sim = Do[Print[t = RandomVariate@ExponentialDistribution[1 x]; td = RandomVariate@GammaDistribution[4, 2]; time = AppendTo[t0, t]; Which[ Total@time < First[Sort@s], {s = Sort[Append[s, Total@time + td]], {Total@time, x}}, Total@time >= First[Sort@s], {s = Rest[Sort@Append[s, Total@time + td]], {First[Sort@s], x += 1}} ]], 20]  {{7.49653,9.45693},{3.92079,1}} {{7.49653,8.0122,9.45693},{4.84659,1}} {{7.49653,8.0122,9.45693,25.0336},{5.13493,1}} {{7.49653,8.0122,9.45693,11.2873,25.0336},{5.24162,1}} {{7.49653,8.0122,9.45693,11.2873,13.0339,25.0336},{5.55033,1}} {{8.0122,9.45693,11.2873,11.3798,13.0339,25.0336},{8.0122,2}} {{8.0122,9.45693,11.2873,11.3798,13.0339,14.9935,25.0336},{7.80638,2}} {{9.45693,11.2873,11.3798,11.4994,13.0339,14.9935,25.0336},{9.45693,3}} {{8.90055,9.45693,11.2873,11.3798,11.4994,13.0339,14.9935,25.0336},{8.06442,3}} {{8.90055,9.45693,11.2873,11.3798,11.4994,13.0339,14.0301,14.9935,25.0336},{8.13769,3}} {{8.90055,9.45693,11.2873,11.3798,11.4994,13.0339,14.0301,14.9935,17.6418,25.0336},{8.23758,3}} {{8.90055,9.45693,11.2873,11.3798,11.4994,13.0339,14.0301,14.9935,15.3168,17.6418,25.0336},{8.59103,3}} {{9.45693,11.2873,11.3798,11.4994,13.0339,14.0301,14.9935,15.3168,17.6418,17.6816,25.0336},{9.45693,4}} {{9.45693,11.2873,11.3798,11.4994,13.0339,14.0301,14.9935,15.3168,17.6418,17.6816,17.9959,25.0336},{9.22169,4}} {{9.45693,11.2873,11.3798,11.4994,13.0339,14.0301,14.5392,14.9935,15.3168,17.6418,17.6816,17.9959,25.0336},{9.33083,4}} {{11.2873,11.3798,11.4994,13.0339,14.0301,14.5392,14.9935,15.3168,16.9029,17.6418,17.6816,17.9959,25.0336},{11.2873,5}} {{11.2873,11.3798,11.4994,13.0339,14.0301,14.5392,14.9935,15.3168,15.3674,16.9029,17.6418,17.6816,17.9959,25.0336},{9.72798,5}} {{11.2873,11.3798,11.4994,13.0339,14.0301,14.5392,14.9935,15.3168,15.3674,16.9029,17.6418,17.6816,17.9959,18.6717,25.0336},{10.0076,5}} {{11.2873,11.3798,11.4994,13.0339,14.0301,14.5392,14.9142,14.9935,15.3168,15.3674,16.9029,17.6418,17.6816,17.9959,18.6717,25.0336},{10.2981,5}} {{11.2873,11.3798,11.4994,13.0339,14.0301,14.5392,14.9142,14.9935,15.3168,15.3674,16.9029,17.6418,17.6816,17.9959,18.6717,25.0336,25.6939},{10.5045,5}}