Seasonal Dynamics Analysis Of Measles In China

Measles,a highly contagious infection caused by the measles virus,is a major public-health problem in China.The reported measles cases decreased dramatically from 2004 to 2012 due to the mandatory measles vaccine program started in 2005 and the goal of e-liminating measles by 2012.However,after reaching its lowest level in 2012,measles has resurged again since 2013.Since the monthly data of measles cases exhibit a seasonally fluctuating pattern,based on the measles model in Earn et al.(Science 287(2000),667-670)we propose a susceptible,exposed,infectious,and recovered(SEIR)model with periodic transmission rate to investigate the seasonal measles epidemics and the effect of vaccination.We calculate the basic reproduction number R0,analyze the dynamical behavior of the model,and use the model to simulate the monthly data of measles cases reported in China.We also carry out some sensitivity analysis of R0 in the terms of various model parameters which shows that measles can be controlled and eventually eradicated by increasing the immunization rate,improving the effective vaccine management,and enhancing the awareness of people about measles.This thesis consists of four chapters.The first chapter introduces the background of measles,the epidemic of measles in China,the fundamental concepts of epidemic dynamics,and the general method to calculate the basic reproductive number.In chapter two,a measles dynamic model with periodic transmission rates is pro-posed.we calculate the basic reproduction number.Further,by using qualitative and stable theory of differential equations,sufficient conditions of local and global stability are derived for the disease free equilibrium when R0<1.Finally,the existence of the positive periodic solutions of the system is proved when R0>1.In chapter three,dynamic models of measles are investigated with numerical simula-tion and sensitivity analysis.We also use the model to simulate the reported measle data in China.In chapter four,we arrive at a conclusion by summarizing the current work and setting the research targets afterwards.