Mathematical Modeling And Dynamic Analysis For Transmission Of Varicella

Research on the dynamics of infectious diseases based on differential equations has played a positive role in the prediction of epidemic trends of various infectious diseases and the guidance of prevention and control strategies.The outbreak and development of the varicella epidemic is one of the public health problems that are easily overlooked.If not handled properly,severe or even death cases such as pneumonia and encephalitis will occur.Vaccination of susceptible people is one of the effective ways to prevent varicella outbreaks.In response to the varicella epidemic in China,biomathematicians have established transmission dynamics models based on its transmission route and mode of transmission to explore the epidemic trend and control measures of varicella in individual regions of China and even the nationwide.Generally,for highly infectious diseases,a higher vaccination ratio is often required to achieve the mass immunity barrier.Multiple doses of vaccination are a common method to increase the coverage of immunity.For the varicella epidemic that continues to spread in my country,the impact of multiple doses of vaccine immunization is not well understood and needs to be further studied.On the other hand,because varicella infections are mostly infants and preschool children,the characteristics of distribution with age are very obvious.Therefore,considering the influence of the age structure of the population on the transmission of varicella,dynamic modeling is useful for understanding the rules of varicella transmission and analyzing effective prevention and control measures.Based on the above two points,this paper carried out the dynamic modeling of varicella transmission and related research for the two factors of "two doses of vaccine immunity" and "age structure".The mainly includes the following contents.Chapter one mainly introduces the research background and significance of varicella disease,and the current research status at home and abroad.Chapter two mainly introduces ordinary differential equations and some related theories of infectious disease dynamics.Chapter three formulates a varicella transmission model with two doses of vaccination in consideration and analyze the stability for the model.First,the Hurwitz criterion is used to prove that the disease-free equilibrium is locally asymptotically stable.Then the Lyapunov function is constructed to prove that the disease-free equilibrium is globally asymptotically stable when basic reproduction number not more than one.while the unique equilibrium is locally asymptotically stable when more basic reproduction number than one.Numerical simulation results show that two doses of vaccination are more conducive to the control of varicella epidemic.Through the sensitivity analysis of the parameters,when the vaccine effective rate is low,the vaccination rate of two doses is increased,and the value of the basic reproductive number is reduced,thereby achieving the effect of disease control.Chapter four formulates a SIRV varicella transmission model with age-structured and analyze the stability for the equilibrium.When the basic reproduction number not more than one,the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function;When the basic reproduction number more than one,the disease-free equilibrium is unstable,the model uniformly persistent,and there is a globally asymptotically stable endemic equilibrium.