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

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 parameter Θ 0 ρ by 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. [ABSTRACT FROM AUTHOR]