Dynamics of fecal–oral periodic propagation model in heterogeneous environments

The transmission of fecal–oral infectious diseases exhibits seasonal and periodic variations, especially the transmission risk of the disease increases in areas where water sources are contaminated. In this paper, we established and studied a fecal–oral model incorporating spatial heterogeneity and temporal periodicity. By employing methods including the spectral radius of the next-generation operator and the principal eigenvalue, we analyzed the basic reproduction number [Formula: see text] of the model and its associated properties. Additionally, we investigated the existence and attractiveness of positive T-periodic solutions and obtained the asymptotic behavior of the model. The dynamical results indicated that when [Formula: see text], the infectious diseases will exhibit periodic changes and eventually become endemic diseases, while when [Formula: see text], the diseases will be controlled and eventually disappear. Finally, numerical simulations and epidemiological explanations echoed our theoretical results.