Numerical solution of stochastic differential problems in the biosciences

摘要

Stochastic differential equations (SDEs) models play a prominent role in many application areas including biology, epidemiology and population dynamics, mostly because they can offer a more sophisticated insight through physical phenomena than their deterministic counterparts do. So, suitable numerical methods must be introduced to simulate the solutions of the resulting stochastic differential systems. In this work we take into account both Euler–Taylor expansion and Runge–Kutta-type methods for stochastic ordinary differential equations (SODEs) and the Euler–Maruyama method for stochastic delay differential equations (SDDEs), focusing on the most relevant implementation issues. The corresponding Matlab codes for both SODEs and SDDEs problems are tested on mathematical models arising in the biosciences.