Spatio-temporal numerical modelling of whooping cough dynamics

Abstract

The SIR (Susceptible/Infectious/Recovered) whooping cough model involving nonlinear ordinary differential equations is studied and extended to incorporate (i) diffusion (ii) convection and (iii) diffusion-convection in one-space dimension. Firstand second-order finite-difference methods are developed to obtained the numerical solutions of the ordinary differential equations. Though implicit in nature, with the resulting improvements in stability, the methods are applied explicitly. The proposed methods are economical and reliable in comparison to classical numerical methods. When extended to the numerical solutions of the partial differential equations, the solutions are found by solving a system of linear algebraic equations at each time step, as opposed to solving a non-linear system, which often happens when solving non-linear partial differential equations.