Assessing the spread of foot and mouth disease in mainland China by dynamical switching model

In mainland China, there are three prevalent serotypes of foot and mouth disease virus (FMDV) and they circulate in different susceptible animals, which respond to viral infection in various ways and present different prevalent features. Although powerful control measures are carried on regularly, the epidemic are still prevalent in livestock. Therefore it is essential to assess the disease trends of foot and mouth disease (FMD) in domestic animals in mainland China. The participation of contaminated environment in the transmission dynamics has been confirmed in laboratory research and it can alter the conditions for FMDV invasion and persistence. So environment transmission plays a key role in disease spreading process. In this paper, we establish a dynamical switching model with environment transmission to investigate the relevant internal force mechanism with respect to the threshold switching, effect of saturation of the quantity of FMDV in environment, and prevalent characteristics of the disease in mainland China. Through the dynamical analysis of the model, we understand that under different conditions, there may appear coexistence of one, two, three or even four steady states, and bistability might occur, showing that the development trend of epidemic not only depends on the model parameters, but also is associated with the initial condition. We further study the influence of key parameters on the dynamical behavior and classify the parameter space into several regions with different composition patterns. Applying the model to assess the development trend of FMD in livestock in mainland China, we find that under certain conditions, some of the serotypes persists and some may disappear, thus we can provide some suggestions for disease control of prevailing serotype.