Numerical threshold stability of an unconditionally positivity-preserving numerical method for a nonlinear age-structured reaction-diffusion brucellosis model

This paper deals with numerical threshold stability of a nonlinear age-structured reaction-diffusion brucellosis model. An unconditionally positivity-preserving numerical scheme is established via a linearly implicit Euler method in time integration together with a center difference scheme in space discretization. A numerical basic reproduction number is proposed and denoted by R₀^Δt, which plays the same role in threshold stability analysis as the basic reproduction number of the model and converges to it as step-sizes vanishes. Namely, the numerical disease-free equilibrium is asymptotically stable if R₀^Δt < 1. Moreover, a unique space-independent coexistence equilibrium exists uniquely and is locally asymptotically stable while R₀^Δt > 1. Some numerical experiments are given in the end to confirm the efficiency of conclusions.