Modeling enteric fever transmission dynamics: a comparative analysis of local and nonlocal boundary value approaches

This study delves into the transmission dynamics of enteric fever caused by Salmonella bacteria, employing a comparative analysis of local and nonlocal boundary value problem (BVP) formulations. Local BVPs model disease dynamics within specific regions, incorporating boundary conditions that reflect interactions with neighboring areas. In contrast, nonlocal BVPs account for global influences, such as long-range bacterial dispersal and large-scale health interventions. We develop mathematical formulations for both approaches, elucidating their key differences. Our analysis identifies the stability of disease-free and endemic equilibrium and determines the critical reproductive number. Sensitivity analyses highlight the relative importance of model parameters in transmission and control efforts. Numerical simulations suggest that a strategic combination of environmental sanitation and treatment is most effective in eradicating enteric fever. This comparative framework enhances understanding of the interplay between regional and global factors, informing targeted control measures for this infectious disease.