Spatio-temporal dynamical behavior of a nonlinear reaction-diffusion model with population variability

The spread of infectious diseases across regions is a global phenomenon, often complicated by the concurrent influence of multiple diseases within the same time frame. This paper explores the dynamics of disease transmission between two population groups, each affected by a distinct disease. The model incorporates transmission parameters dependent on spatial variables, while population dynamics are examined over both time and spatial dimensions. This spatially sensitive approach to model parameters enhances the applicability of findings to real-world scenarios. Our study is framed within a reaction-diffusion, multi-SIR population dynamics model. Initially, we investigate the well-posedness of the proposed model's solution via semigroup theory. Steady states are determined, and leveraging the disease-free steady state and the next-generation operator, we derive the basic reproduction number. Furthermore, we analyze the stability properties of these steady states through eigenvalue problems in partial differential equations. Finally, numerical simulations are performed to validate the proposed model with spatially dependent data, underscoring its relevance to spatially structured disease dynamics.