Modelling the effects of contaminated environments on HFMD infections in mainland China.

Hand-foot-mouth disease (HFMD) has spread widely in mainland China increasing in prevalence in most years with serious consequences for child health. The HFMD virus can survive for a long period outside the host in suitable conditions, and hence contaminated environments may play important roles in HFMD infection. A new mathematical model was proposed and used to investigate the roles that asymptomatic individuals and contaminated environments played in HFMD dynamics. The model includes both direct transmission between susceptible and infected individuals and indirect transmission via free-living infectious unites in the environment. Theoretical analysis shows that the disease goes to extinction if the basic reproduction number is less than unity, whilst otherwise the disease persists. By fitting the proposed model to surveillance data we estimated the basic reproduction number as 1.509. Numerical simulations show that increasing the rate of virus clearance and decreasing transmission rates can delay epidemic outbreaks and weaken the severity of HFMD. Sensitivity analysis indicated that the basic reproduction number is sensitive to the transmission rate induced by asymptomatic infectious individuals and parameters associated with contaminated environments such as the indirect transmission rate, the rate of clearance and the virus shedding rates. This implies that asymptomatic infectious individuals and contaminated environments contribute substantially to new HFMD infections, and so would be targets for effective control measures.