Abstract
Substantial and increasing outbreaks of EV71-related hand, foot and mouth disease (HFMD) have occurred recently in mainland China with serious consequences for child health. The HFMD pathogens can survive for long periods outside the host in suitable conditions, and hence indirect transmission via free-living pathogens in the environment cannot be ignored. We propose a novel mathematical model of both periodic direct transmission and indirect transmission followed by incorporation of an impulsive vaccination strategy. By applying Floquet theory and the comparison theorem of impulsive differential equations, we obtained a threshold parameter which governs the extinction or the uniform persistence of the disease. The rate, frequency and timing of pulse vaccination were found to affect the basic reproduction number and the number of infected individuals significantly. In particular, frequent vaccination with a high coverage rate leads to declines in the basic reproduction number. Moreover, for a given rate of vaccination or frequency, numerical studies suggested that there was an optimal time (September, just before the start of new school terms) when the basic reproduction number and hence new HFMD infections could be minimised. Frequent high intensity vaccinations at a suitable time (e.g. September) and regular cleaning of the environment are effective measures for controlling HFMD infections.
Highlights
Hand, Foot and Mouth Disease (HFMD) was first diagnosed in New Zealand in 1957 [12], and has subsequently been reported across the AsiaPacific region where it is endemic
Our model considers a subgroup of recessive infected individuals to investigate the impact of asymptomatic individuals and contaminated environments on HFMD transmission
We proposed and analysed a HFMD model with periodic transmission rates and impulsive vaccination for seasonal outbreaks
Summary
Foot and Mouth Disease (HFMD) was first diagnosed in New Zealand in 1957 [12], and has subsequently been reported across the AsiaPacific region where it is endemic. Recent outbreaks of HFMD in many areas were caused by EV71 which induced a variety of neurological diseases including aseptic meningitis, encephalitis, and poliomyelitislike paralysis [19]. Enterovirus 71 (EV71) is a major cause of HFMD in children in China and may even be fatal. It accounts for the majority of cases worldwide [6], and up to 13.8 million cases were reported between 2008 and 2015 [8]. An EV71 vaccine has been successfully developed Evidence suggests that it consistently elicits immunogenicity and provides protection against mild-to-severe diseases caused by EV71 for at least one year in infants and young children [43]. The vaccine efficacy against EV71-associated HFMD is 97.4% [21]
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