A1702
Title: Monte Carlo integration of differential equation systems with epidemiological applications
Authors: Willard Braun - UBC (Canada) [presenting]
Kyeongah Nah - National Institute for Mathematical Sciences (Korea, South)
Abstract: Monte Carlo (MC) integration is a well-known method for evaluating integrals for which deterministic numerical methods struggle, particularly in higher dimensions. MC integration is a straightforward application of the Law of Large Numbers applied to simulated data. Integrating a differential equation requires different tactics. Two new methods are presented. The first method is based on the Mean Value Theorem and performs well in comparison to other recently proposed MC approaches, even on stiff systems. Its performance is studied on the Susceptible-Infected-Removed (SIR) model, which is commonly used in epidemic modelling and forecasting. The second method is based on an approximation to continuous-time Markov chains and can be applied to delay-differential equations. An application to a delayed infection and recovery version of the SIR model is considered.
