Analysis and dynamically consistent nonstandard discretization for a rabies model in humans and dogs

Abstract

Rabies is a fatal disease in dogs as well as in humans. A possible model to represent rabies transmission dynamics in human and dog populations is presented. The next generation matrix operator is used to determine the threshold parameter R0, that is the average number of new infective individuals produced by one infective individual intro- duced into a completely susceptible population. If R0 < 1, the disease-free equilibrium is globally asymptotically stable, while it is unstable and there exists a locally asymptot- ically stable endemic equilibrium when R0 > 1. A nonstandard nite di erence scheme that replicates the dynamics of the continuous model is proposed. Numerical tests to support the theoretical analysis are provided.