A Positivity-preserving Mickens-type Discretization of an Epidemic Model

A deterministic model for the transmission dynamics of two strains of an epidemic in the presence of a preventive vaccine is considered. Theoretical results on the existence and stability of the associated equilibria of the model are given. A robust, positivity-preserving, non-standard finite-difference scheme, having the same qualitative features as the continuous model, is constructed. The theoretical and numerical analyses of the model enable the determination of a threshold level of vaccination coverage needed for community-wide eradication of the epidemic.