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 [Formula: see text], 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 [Formula: see text]. Moreover, a unique space-independent coexistence equilibrium exists uniquely and is locally asymptotically stable while [Formula: see text]. Some numerical experiments are given in the end to confirm the efficiency of conclusions.