Analysis of a degenerate reaction–diffusion anthrax model with spatial heterogeneity

Abstract

To investigate the impact of spatial heterogeneity on anthrax transmission, we develop a novel degenerate reaction–diffusion model for anthrax. Despite the lack of compactness of the solution map, the asymptotic smoothness is confirmed by examining its contractility. We establish two thresholds, s(J) obtained by an auxiliary system and R0 defined by next generation operator, corresponding to the extinction and persistence of anthrax, respectively. Additionally, we investigate the steady-state bifurcation at the disease-free equilibrium by bifurcation theory. Our numerical simulations reveal the effects of heterogeneity on the transmission of anthrax and discover a phenomenon of spatial synchronization, which maintains the invariance of the basic reproduction number. Notably, we demonstrate that synchronization is the underlying mechanism for this invariance. In summary, our findings provide valuable insights for advancing the understanding of infectious disease transmission dynamics.