Dynamic Properties Of Disease Transmission Model On Complex Networks

With the development of human history,from the earlier Black Death and smallpox virus to Covid-19 in recent years,infectious diseases have brought great disasters and incalculable losses to human society.Therefore,it is of great practical significance to explore the transmission mechanism of infectious diseases and put for-ward effective control strategies to reduce the harm of infectious diseases to society.In this paper,two kinds of infectious disease transmission models are proposed con-sidering asymptomatic individuals,mutant individuals and isolated individuals,and their dynamic properties such as the existence of equilibrium point,basic reproductive number and stability are analyzed respectively.The specific contents are as follows.（1）Considering the existence of asymptomatic individuals,mutant individuals and isolated individuals,as well as the fact that susceptible individuals directly become im-mune in other ways,the infectious disease transmission models of SAIVR and SIVQR on the uniform network are established respectively.（2）The existence of equilibrium point and basic reproductive number of SAIVR and SIVQR epidemic models are analyzed by differential equation theory and next generation matrix method respectively.The research shows that the basic reproduc-tion numbers of SAIVR model and SIVQR model are related to the parameters in the propagation model,and the correctness of theoretical analysis is verified.（3）Routh-Hurwitz criterion and Lyapunov stability are used to analyze the local asymptotic stability and global asymptotic stability at the equilibrium point for SAIVR and SIVQR epidemic models,respectively.The research shows that the condition for local asymptotic stability of the two epidemic models is₀<1,and the simulation results are consistent with the theoretical results.（4）In both kinds of infectious disease models,the problem of minimum popu-lation loss caused by the spread of infectious diseases is considered.An infectious disease spread model with control is established,an optimal control problem is put for-ward,Hamilton function is constructed,and the optimal control strategy of the model is studied by using Pontryagin extreme principle.