Spatiotemporal dynamics of an age-space structured epidemic model with partial immunity, nonlinear infection rate, and combined transmission pathways from hosts and environment

To account for the complex challenges of spatial heterogeneity, inevitable human mobility, and dual transmission pathways (human-to-human and environment-to-human) in epidemic dynamics, we propose a novel age-space structured model incorporating partial immunity and nonlinear incidence. The model explicitly includes the infection age structure of both infected individuals and environmental pathogens to capture variations in infectivity during the transmission process. First, the well-posedness of the model solution is rigorously established using the Banach fixed-point theorem. Next, by applying the Laplace transform, we derive the next-generation operator ℒ , then the basic reproduction number is defined as its spectral radius. Furthermore, under a spatially homogeneous scenario, ℛ 0 is obtained in exact analytical form. The global asymptotic stability of the disease-free and endemic steady states is then established by analyzing the distribution of the roots of the characteristic equations and constructing appropriate Lyapunov functionals. Numerical simulations visually elucidate complex spatio-temporal-age dynamics and quantify the effectiveness of interventions. In particular, restricting the mobility of infected individuals and improving vaccine efficacy significantly curb transmission. Fitting to cholera case data from Somalia, we find that neglecting either age structure or spatial heterogeneity leads to significant biases in case number estimates, underscoring their indispensable role in accurate forecasting.