A periodic reaction-diffusion model of hospital infection with crowding effects

In this paper, we propose a periodic reaction-diffusion model of hospital infection with crowding effects. We introduce the basic reproduction number R₀ for this model and show that the infection-free periodic solution is globally asymptotically stable if R₀≤1, while the system admits a globally asymptotically stable positive periodic solution if R₀>1. We also obtain the asymptotic behavior of the basic reproduction number when the diffusion rates go to infinity and zero, respectively. Further, we numerically study the effects of diffusion rates, the outflow rate by patient crowding and other parameters on R₀ with and without seasonality, and found that the neglect of seasonality does overestimate the infection risk and the disease may be well controlled by avoiding overcrowding of patients rather than increasing the mobility of individuals or bacteria.