Analysis And Numerical Simulation Of Heterogeneous Epidemic Model

Heterogeneity has an important impact on spread of infection and assessment of control measures.In this paper,we study three types of infection with heterogeneity: HFMD,varicella and AIDS,then we build the infectious disease models with heterogeneous factors,and obtain numerical simulation of models,finally,we further evaluate the effectiveness of control measures.The main contents of this paper are as follows:First part,based on the different contact rates of newborns,preschool children,school children and adults,we propose an EV-71 HFMD model with age structured to study the effect of EV-71 inactivated vaccine in different age groups Then we calculate the control reproduction number under the condition of vaccination.The optimal vaccine allocation method among different age groups is analyzed,and the vaccine allocation strategy is obtained.Finally,we verify the reliability of the result by numerical simulation.Second part,in order to evaluate the effect of isolation and closure measures,according to the data of a varicella outbreak in X County of Xinjiang,we propose a two age groups varicella model based on the different contact rates between preschool children and school children.The implicit expression of the final size without control measures is obtained.And we estimate the unknown parameters in the model by using genetic algorithm,then we get the simulated image of the varicella outbreak.With the final size of the epidemic as a measure,we evaluate the effect of isolation and closure at different times.Third part,in order to explore the impact of media publicity on the spread of AIDS in MSM,we propose an AIDS model in MSM based on the different contact between fixed partners and non fixed partners,and we obtain the basic reproduction number of AIDS in MSM.Numerical explorations of the model suggest that improving the use of the condom with the fixed partners is more influential to the basic reproduction number and promoting the use of condom is more effective than other publicity strategies.