Dynamics Models And Data Simulation Of Hand, Foot And Mouth Disease (HFMD) In China

Hand, foot and mouth disease (HFMD), an infectious disease caused by en-terovirus and Coxsackievirus, usually happens to children under age of five, with an especially high incidence being observed for those under three. It can result in herpes in such body parts as hands, feet and mouth and even other complications such as myocarditis, pulmonary edema, and aseptic meningoencephalitis in some children. Some severely affected patients may die due to the quick progress of the disease. There are over twenty types of enterovirus leading to HFMD, Coxsackievirus A16and EV71are the most common, and cause severe mortality in children. And there are more than one million children infected with HFMD every year in China. As a matter of fact, there is no effective vaccine or antiviral treatment specifically for HFMD, but if we can provide some preventive measures to control the HFMD, it will be very meaningful.This thesis has been divided into four chapters, the first chapter introduces the background of epidemic dynamics, etiology, epidemiology, diagnostication, research status and pre-knowledge of HFMD.In chapter two, an epidemic model with non-monotonic contact rate is devel-oped to explore the control of HFMD. By analyzing globally asymptotic stability of disease-free equilibrium, existence and global analysis of endemic equilibria, we establish the sufficient conditions for the extinction of the endemic disease. Mean-while, backward bifurcation, bistable states are investigated. Numerical simulations are presented to verify the theoretical result and then preventive measures of HFMD are proposed in the end. The huge infected population is the important reason that HFMD is still epidemic in China.In chapter three, we formulate a time-delay SEIQRS epidemic model with non-monotonic contact rate. Firstly, the existence of the disease-free equilibrium and the endemic equilibria is discussed. We further analyze the asymptotic behaviors of the dynamical model. With the help of Lyapunov functional methods we derive the sufficient conditions for the stability of these two equilibria in the end.In the fourth chapter, we concentrates on the HFMD data of China from2008to2012. We set up two mathematical models to fit those data with the goodness of fit and obtain the optimal parameter values of the model. By the Chi-square test of statistical inference, the optimal parameter values of the models are reasonable. We get the basic reproductive number of the disease for each year, and it is larger than1. Thus, we conclude that HFMD will persist in China under the current conditions. So we investigate the preventive measures to control the HFMD, the HFMD will be controlled quickly and the number of infections will decline rapidly in a period of time. Finally, we make use of the parameter values of the year2011and2012to simulate and forecast the number of patients of2013, and the predictive results inosculate well with the real-world situations.