Asymptotic analysis of SIR epidemic model with nonlocal diffusion and generalized nonlinear incidence functional

Asymptotic analysis of SIR epidemic model with nonlocal diffusion and generalized nonlinear incidence functional

S Djilali, Y Chen, S Bentout – Mathematical Methods in the Applied Sciences

We aim in this research to determine the global stability of equilibrium states for an SIR epidemic model with nonlocal diffusion and nonlinear incidence function in a heterogeneous environment. For achieving this result, we consider that the model parameters are Lipschitz continuous functions. At the infection free‐equilibrium, the eigenvalue problem has a principal simple eigenvalue λ 0 λ _0 corresponding to
strictly positive eigenfunction which is expressed as λ 0= R 0− 1 λ _0= R _0-1. By a …