A Hand-Foot-and-Mouth Disease Model with Periodic Transmission Rate in Wenzhou, China

Abstract

We establish an SEIQRS epidemic model with periodic transmission rate to investigate the spread of seasonal HFMD in Wenzhou. The value of this study lies in two aspects. Mathematically, we show that the global dynamics of the HFMD model can be governed by its reproduction number $R_0$; if , the disease-free equilibrium of the model is globally asymptotically stable, which means that the disease will vanish after some period of time; while if $R_0>1$, the model has at least one positive periodic solution and is uniformly persistent, which indicates that HFMD becomes an endemic disease. Epidemiologically, based on the statistical data of HFMD in Wenzhou, we find that the HFMD becomes an endemic disease and will break out in Wenzhou. One of the most interesting findings is that, for controlling the HFMD spread, we must increase the quarantined rate or decrease the treatment cycle.