Research On Population Heterogeneous Infectious Disease Model And Prevention And Control Strategy

Population heterogeneity has an important impact on spread of infection and assessment of control measures.In this paper,we study two infectious diseases with heterogeneity:measles and tuberculosis,then we build the infectious disease model with heterogeneous factors,and the analysis and numerical simulation of the model is carried out,finally,we further evaluate the effectiveness of control measures.The research content of this paper is as follows:First part,to study the effect of measles vaccine in different age groups and the impact of important parameters such as mortality on vaccine control strategies,according to the characteristics of measles and contact heterogeneity in different age groups,a SEIR measles dynamics model with age structure is established,two types of mortality are defined,and the effective reproduction number of the model under vaccination conditions was calculated.Using the gradient descent method to obtain the optimal vaccine distribution ratio of measles intensive vaccine in the 4^th and 5^th age groups?10¹9 years old?and optimal vaccine allocation ratio in the 3^th,4^th,and 5^th age groups?5-19 years old?.In the case of the same vaccine amount,the vaccines in the 4^th and 5^th age groups were more effectively reduced Rv than the 3^th,4^th,and 5^thage groups.Numerical simulations show that the optimal vaccine allocation ratio of two types of mortality models and the reduction of Rv is basically consistent.It shows that the two types of mortality have little effect on the optimal vaccine strategy.Second part,to study the impact of migration between two regions with different population densities on the spread of tuberculosis and assess the effect of vaccination in two regions,the dynamic model of tuberculosis in two regions was established,and the effective reproduction number Rv is calculated.Combined with the survey data,numerical simulations show that high-density migration to low-density areas will reduce the scale of infection.Conversely,migration from low density to high density areas will increase the scale of infection.,but tuberculosis can't be eliminated by migration.Vaccination of a local population in high-density areas can reduce Rv to less than one,which can eliminate tuberculosis.Third part,to study the impact of immigrants to Guangdong on the spread of local tuberculosis,we establish a dynamics model of SEIR tuberculosis including local and immigrant population in Guangdong.The heterogeneity of contact between the two types of population was considered.The effective reproduction number Rv of the model was calculated.The optimal immune planning model was established.The optimal gradient method was used to solve the optimal vaccine allocation ratio of vaccine to local population and immigrant population in Guangdong.Numerical simulations showed that the application of vaccine at the optimal vaccine allocation rate can effectively control the tuberculosis outbreak.