The Analysis Of Two Types Of Mumps Transmission Models

Mumps is a worldwide pandemic of respiratory infectious disease controlled by vaccine,and of which the morality rate is low.But it can cause a variety of common complications,such as encephalitis,which severely threaten people's health,especially the growth of adolescents.In 2004-2016,Chinese accounted for 48.12%of global patients with mumps and China has the largest number of patients with mumps in the world.In mainland China,one dose of MuCV was introduced into the national expanded program on immunization(EPI)in 2008 for all children at 18-24 months of age.However,today,mumps is not eliminated and still popular in many provinces and cities of our country.Based on the characteristics of mumps in China,this paper formulates two different epidemic models and analyzes the stability of equilibrium points,then,some prevention strategies are introduced.This paper mainly consists of the following five parts.The first part briefly introduces the characteristics of mumps virus and mumps,summarizes the outbreaks and researches all around the world.Finally,the background and main content of this paper is presented.Part two is consist of the essential theory used in model analysis,such as RO and stability theory.In the third part,a SVEIQR epidemic model with contagious incubation period,vaccination rate for infants and vaccination rate for susceptible persons is formulated.We analyze the stability of equilibrium points in detail.It is shown that disease-free equilibrium P0 is globally asymptotically stable,if R0<1,and the endemic equi-librium P*is globally asymptotically stable in ?,if R0>1.Contagious incubation period is absolutely essential to mumps model,because ignoring the infectivity can make the theoretical value of RO smaller than actual value and the severity will be underestimated.According to the analysis of R0,we can reach the following conclu-sions:Increasing the vaccine coverage of infants and susceptible persons can correctly and effectively inhibit mumps transmission.We can increase the vaccination rate of susceptible persons to make R0<1,if the vaccination rate of infants is low.R0 is more sensitive to the transamination rate of ?1 than ?2,so we should reduce the exposure to patients with latent period.Taking into account the seriousness of mumps in China and recommendations made by some scholars,part four set up a S1V1V2S2EIsIaQR model including one-dose recipients,two-doses recipients and asymptomatic infection.We analyze the stability of equilibrium points in detail.It's clear from the model that two-doses of MMR vaccine is beneficial to the elimination of mumps.And it's best to make a second dose of MMR vaccine freely in mainland China.In order to make mump-s be better controlled by increasing the secondary vaccination rate,the secondary invalid vaccination rate ?2 should be reduced at the same time.Besides,reducing the transmission rate is also an effective method.It is easy for an asymptomatic infection to transmit to a susceptible person,but it is difficult to be discovered,so asymptomatic infection should take initiative to reduce ?2-It's equally important to reduce ?3,?1,because recipients are not all completely immune.And recipients should be self-protected and take initiative to reduce ?3,?4.The last part introduces main conclusions of this paper,mentions about some shortcomings and makes an outlook for the research.