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This paper is concerned with a reaction–diffusion system on a growing domain describing the spatial spreading of bacterial and viral diseases induced by fecal–oral transmission. We introduce a threshold parameterby means of the eigenvalue problem to explore the stability of the disease-free and endemic equilibria. By overcoming the difficulty induced by the time-dependent diffusion rates, we are further able to investigate the asymptotic behavior of solutions to the reaction–diffusion system. Compared to the model counterpart with fixed domain, biological impacts of a growing domain on the spreading of infectious diseases are obtained. We conclude that the growth of the domain is detrimental to the prevention and control of infectious diseases.

The asymptotic behavior of bacterial and viral diseases model on a growing domain