Evaluating the Expected Time to Population Extinction with Semi-Stochastic Models

“Semi-stochastic” or “piecewise-deterministic” Markov processes generalize continuous-time Markov chains, allowing for deterministic flow between Markovian jumps. They have been employed as models for the effect of environmental catastrophes on biological populations, for the progress of infectious diseases within and between hosts, and for the management of fisheries. One application is to solve first-exit time problems, which include calculations of the expected time or of the expected value from the present to extinction of processes with state-dependent rewards or costs. A simple and robust numerical method gives the solution of first-exit time problems for a wide range of semi-stochastic processes.