Analysis Of Two Measles Models Fitting Of The Measles Data In China

Measles is a highly contagious infectious disease caused by measles virus.In China,it is a very important public health problem.Although after large scale vaccination program,the incidence of measles is declining,but so far,it still can not be eradicated.In this thesis,we use SEIR models with nonlinear incidence to study the transmission dynamics of measles and consider two cases:with perfect immunization and with imperfect immunization.For perfect immunization model to calculate the basic reproductive number R0,it is concluded that when R0<1,disease-free equilibrium PO is globally asymptoti-cally stable.When R0>1,the disease-free equilibrium is unstable and an endemic equilibrium P*exists.And using the geometrical method we prove the stability of the endemic equilibrium.After calculating the basic reproductive number R0 and analyzing the dynamics behavior of the model,we use the model to simulate the annual data of measles cases of mainland China and predict the spread of measles in the next few years.After determining the parameters,we have carried on the sensitivity analysis to the basic reproductive number.The results show that we can improve the measles vaccination rates and reducing the failure rate and strengthen the protection consciousness to control measles.For the model with imperfect immunization,it is concluded that when R0<1,there is a global asymptotic stability of PO.When R0>1,the disease-free equilib-rium is unstable and an endemic equilibrium P*exists.And analysis system in the dynamic character of endemic equilibrium,under some conditions,it is showed there exists a Hopf bifurcation from an endemic equilibrium.Then through the numerical simulation verifies the correctness of the theory and the rationality of the model.Then use model to fit China measles are diseased annual data in 2004-2017,the dis-covery of model with imperfect immunization fitting degree better,we use this model to forecast.Through calculation we find in the present case R0>1,is temporarily unable to eliminate measles.The transmission mechanism of measles is very complicated and there are many influencing factors.Using the obtained results,we propose some control measures.