Dynamics analysis of a spatially extended SIS epidemic model with nonlocal disease transmission

Infectious diseases that permit reinfection, such as various bacterial and viral pathogens, present enduring public health challenges characterized by recurrent outbreaks and complex spatial heterogeneity. To elucidate the mechanisms underlying these dynamics, we develop and analyze a Susceptible-Infectious-Susceptible (SIS) epidemic model with saturating incidence rate and nonlocal disease transmission.We analyze the system across three frameworks: a non-spatial ordinary differential equation (ODE) model, a spatially explicit system with local disease transmission, and a system incorporating nonlocal disease transmission. For the ODE model, bifurcation analysis identifies a Hopf bifurcation, which implies that disease control requires reducing transmission significantly below the outbreak threshold. In the spatially extended model, diffusion-driven Turing instability gives rise to stationary infection patterns, representing the spontaneous emergence of localized endemic hotspots. Furthermore, the inclusion of nonlocal transmission reveals a complex dual role, while the integral averaging effect tends to suppress pattern amplitude, the nonlocal interaction range serves as a critical parameter that can drive the system into spatiotemporal chaos. Overall, the results demonstrate how synergistic infection, behavioral feedback, and heterogeneous transmission pathways interact to produce rich epidemic dynamics, providing a theoretical foundation for understanding reinfection-driven diseases and mechanistic insights for their control.