Modelling seasonal HFMD infections with the effects of contaminated environments in mainland China

Hand-foot-mouth disease (HFMD) has spread widely in mainland China and exhibited an increasing trend in prevalence in recent years with serious consequences for child health. The HFMD virus can survive for a long period outside the host in suitable conditions, and hence indirect transmission via free-living virus in the environment can not be ignored. We then propose a novel mathematical model to represent both direct transmission and indirect transmission, and also periodic transmission and vaccination rates. We obtain a threshold value, the basic reproduction number which governs whether nor not HFMD infection dies out by applying the persistence theory of periodic systems. Theoretical results indicate that the disease goes to extinction if the basic reproduction number is less than unity and otherwise the disease uniformly persists. By fitting the proposed model to reported data on symptomatic cases of endemic HFMD in mainland China we estimate the basic reproduction number as 1.74. Numerical simulations show that the asymptotic infected individuals and contaminated environments are essential factors substantially contributing to HFMD new infections, and hence they should not be ignored. Sensitivity analysis indicates that the basic reproduction number is sensitive to the transmission rate induced by asymptomatic infectious individuals, vaccination rate and parameters associated with contaminated environments such as the indirect transmission rate and the rate of clearance. Our finding suggests that enhancing vaccination strategy and the frequent cleaning of the environment and enhancing individual sanitation (e.g. regular hand-washing) are effective measures in controlling HFMD infections.