Population Systems: Stochastic versus Deterministic

Thursday, June 7, 2018 - 2:00pm - 2:50pm
Lind 305
Xuerong Mao (University of Strathclyde)
One of the important problems in population and biological systems is the specification of the stochastic process governing the behaviour of an underlying quantity. We here use the term underlying quantity to describe any interested object whose value is known at present but is liable to change in the future. In this talk we will explain how the ordinary differential equations (ODEs) are not enough to model the underlying stochastic quantity and why stochastic differential equations (SDEs) appear naturally. Several well-known SDE models will be presented including the Logistic population model. We will then compare the ODE models with the SDEs models to show the significant differences. Many Monte Carlo simulations will be used for illustrations.