Dynamical analysis for a reaction-diffusion HFMD model with nonsmooth saturation treatment function

Abstract

In this paper, we propose a new reaction-diffusion model to investigate the spatial spread of hand, foot and mouth disease (HFMD). To reflect the actual factors which are limited medical resources for treatment and intensive treatment strategies which depend on a certain threshold, we also consider a continuous and nonsmooth treatment function in our model. First, existences of equilibria are determined by discussing the relation of parameters. Second, for the local stability of equilibria, the effect of the spatial diffusion including the variation of the size of the space domain and the diffusion coefficients of susceptible and infectious individuals on the stability is studied and Turing instability is demonstrated. Third, spatially homogeneous Hopf bifurcation and spatially homogeneous Hopf bifurcation are also studied by analyzing the corresponding characteristic equation. Finally, we use the model to fit the reported cases of HFMD in Guangxi Province, China from January, 2016 to May, 2019. Our results containing theoretical analysis and numerical simulations show that reducing the threshold Ic with respect to intensive treatment and reducing the range of activities of infectious individuals can effectively control the spread of HFMD.