How to simulate two coupled birth-death-immigration processes? - Mathematica Stack Exchange most recent 30 from mathematica.stackexchange.com 2019-10-19T18:58:28Z https://mathematica.stackexchange.com/feeds/question/171392 https://creativecommons.org/licenses/by-sa/4.0/rdf https://mathematica.stackexchange.com/q/171392 1 How to simulate two coupled birth-death-immigration processes? Mlo27 https://mathematica.stackexchange.com/users/57039 2018-04-18T09:04:11Z 2018-04-18T09:04:11Z <p>I am simulating a birth-death-immigration process for two coupled populations that interact by virtue of the birth-rate in one population being equal to the death-rate in the other population. The two coupled populations contain the 3 mechanisms births, deaths and immigrations. The birth/death rate mu is dependent on the amount in the population whereas the immigrations rate nu is independent.</p> <p><a href="https://i.stack.imgur.com/PLEk6.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/PLEk6.png" alt="rate equation"></a></p> <p>The first row is births, second row is deaths and the third row is immigrations.</p> <p>My thought process on how to simulate these coupled populations is by, if a death occurs, I need to decide which population the death occurs in. I do this by flipping a coin weighted by the sizes of the two populations. I then need to decide whether the death dies out completely or whether it goes into the other population as a birth. A similar thing happens if a birth occurs. I need to decide which population the birth occurs in (using weighted coin), and then determine whether the birth was due to a death in the other population or not. For immigrations I just flip a coin 50/50 to see which population it goes in, since immigrations are independent on the number in the population.</p> <p>If this is correct, how would I determine if the death/birth in one population was due to a birth/death in the other population?</p> <p>If my thought process is not correct, how would I got about simulating this type of process?</p>