Research On Vector-borne Epidemic Models With Asymptomatic Infectors

In recent years,the research on vector-borne diseases such as malaria,leishman,dengue fever and zika has attracted extensive attention from many researchers at home and abroad.This paper focuses on the dynamics of vector-borne models with seasonal effects,media coverage,and control strategies,especially the effects of asymptomatic infection on disease transmission.The main research content can be summarized as follows:In the first part(corresponding to chapters 2),a dynamic model of malaria virus transmission between humans and mosquitoes with seasonal changes,asymptomatic infections and media saturation effects is proposed.Through the next-generation matrix,the comparison theorem of ordinary differential equation,the threshold conditions that determine the local and global asymptotic stability of the disease-free periodic solution of this model and the persistence of the disease are obtained.In the second part(corresponding to chapters 3),a dynamic model of the transmission of malaria parasites between humans and mosquitoes with asymptomatic infections and vector control is proposed.The existence and stability of the diseasefree equilibrium and endemic equilibrium of this model,the persistence of this disease are discussed,respectively.Further,using the sensitivity method to study the impact of key parameters in the model on the transmission of the disease.In additonal,using the Pontryagin maximum principle to get the best strategy to control the spread of disease.Finally,the numerical simulations verify the accuracy of the main theoretical results.In the third part(corresponding to chapters 4),a dynamical model for the spread of Leishmania protozoa between the vector sandfly,canine host and human host is established.The next generation matrix method is used to obtain the exact expression of the basic reproduction number of the sandfly-canidae model and sandfly-humans model,respectively.Furthermore,the existence and stability of the disease-free equilibrium point of the two types of sub-models are given using the Routh-Horwitz criterion.In addition,the influence of the main parameters of the model on disease transmission and control was discussed through sensitivity analysis.