Analysis And Research On Two Kinds Of Vector Infectious Disease Models

Aiming at the problem of vector-borne infectious diseases that seriously affect human health,this paper is based on the warehouse model thought.Considering the factors such as the vertical transmission rate of the host and the vector,mutual contact rate,disease recovery rate,and media reports,two types of differential equation mathematical models are established.Through theoretical proofs and numerical simulations,the theoretical basis for development strategies to control the epidemic is provided.Furthermore,the research topics of the existing vector infectious diseases have been enriched.Firstly,a class of vector-borne infectious disease model with double vertical transmission is studied.The expression of the basic reproduction number is obtained by using the second generation generative matrix method.By constructing the positive definite Lyapunov function,using the La Salle invariant set principle,and applying the Bendixion criterion,the existence and stability of disease-free equilibrium point and endemic equilibrium point are proved.The validity of the conclusion is verified by simulation with Matlab software.It is concluded that the contact rate between the population and the vector is reduced or the medical level is improved,and the disease can be effectively controlled.Research and conclusions on diseases in which both the host and the vector have vertical transmission are enriched.Secondly,a class of vector-borne infectious disease model with double vertical transmission affected by the media is studied.The existence of equilibrium points are discussed.Using Hurwitz criterion and other methods,sufficient conditions for the stability of the equilibrium points are obtained,and the validity of the results is verified by numerical simulation.It is concluded that although the basic regeneration number is not affected by media factors,the extinction of disease is accelerated,and the proportion of patients and endemic vectors at the endemic equilibrium point is reduced.Studies and conclusions on the effects of media factors on vector-borne diseases have been enriched.Finally,through comparative analysis,dual vertical transmission compared to single vertical transmission of vector-borne diseases,the extinction of diseases takes longer,and it is more harmful to society.More attention should be paid to preventive measures in a timely manner.In addition,by comparing the actual effects of the presence or absence of media factors on the epidemic situation of vector-borne infectious disease,it is found that when media reports exit,the control of the disease is promoted,the extinction of infectious diseases is accelerated,and the harm of the epidemic is reduced.