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

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 , that is the average number of new infective individuals produced by one infective individual introduced into a completely susceptible population. If , the disease-free equilibrium is globally asymptotically stable, while it is unstable and there exists a locally asymptotically stable endemic equilibrium when . A nonstandard finite difference scheme that replicates the dynamics of the continuous model is proposed. Numerical tests to support the theoretical analysis are provided.