Analysis of a general multi-group reaction-diffusion epidemic model with nonlinear incidence and temporary acquired immunity

Considering the individual differences, spatial environment and the temporary acquired immunity, a general multi-group reaction-diffusion epidemic model with nonlinear incidence and temporary acquired immunity is proposed in this paper. The well-posedness of the solution including the existence of global solutions and the ultimate boundedness of the solutions are obtained, and then we define the basic reproduction number Ro. Further, the threshold dynamics of the disease are obtained in terms of R-0. Moreover, by constructing suitable Lyapunov functions, we obtain the endemic steady state is globally asymptotically stable in homogeneous space and heterogeneous case when R-0 > 1. Based on theoretical analysis, we conclude that the existence of immunity loss rate and the difference of diffusion rate may bring great difficulties to control the disease. Finally, we find the spatial heterogeneity cannot always enhance the infectious risk of the disease and simply increasing the diffusion coefficient cannot effectively control the spread of the disease via some numerical simulations. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.