Age structural model of the hand foot mouth disease in Thailand

Abstract

The hand foot mouth disease (HFMD) is a virulent disease caused by virus of the enteroviruses serotypes, whose symptoms include soreness inside or around the mouth, and rashes or blisters on the hands, feet or legs. Most cases are seen in infant and children. The severity of HFMD outbreaks has thus constituted serious threat to general public health. In this work, the transmission model of the HFMD is formulated. Specifically, the population is divided into two subclasses, namely, those under the age of ten, and those over the age of ten. Two SEIR models, one for each subclasses, are then formed. This model is then analyzed through the use of standard dynamical systems method, where two equilibriums of the model, namely the disease-free equilibrium, and the endemic equilibrium, are firstly determined. Stability analyses of the respective equilibriums are then conducted. Results show that the disease-free equilibrium will be stable if the basic reproduction number is less than one, while the endemic equilibrium is stable when the basic reproduction number exceeds unity. These results can be used in controlling the epidemics of the HFMD.