A Non-Standard Finite-difference (NSFD) Scheme for Simultaneous Infection Model

Abstract

A continuous-time differential equation model for the transmission dynamics of two different strains, with possibility of simultaneous infection, for arbitrary incurable disease(s) is formulated. A non-standard -finite-difference (NSFD) scheme is constructed based on Mikens' discretization framework and analysed. The basic features of the discrete model such as positivity of solutions, the dissipativity of the system and conservation law are shown. Numerical simulations using the NSFD method confirm these results, while the standard numerical integrators (such as Euler and Runge-Kutta methods) perform poorly: they exhibit some numerical instabilities and spurious behaviour.