Study On The Transmission Dynamics Of Infectious Diseases In Heterogeneous Metapopulations

With the advancement of technology,as people's travel methods become more and more convenient,we must consider the impact of migration on the spread of infectious diseases.Therefore,in this paper,the factor of migration is taken into account when building a mathematical model,making the model more realistic.This will make the prevention and control of infectious diseases more effective in reality.In the past study of infectious disease model with migration,in order to make the calculation convenient,some limitations be imposed on the model,such as approximating the adjacency matrix???,which will make the migration rate have an impact on the number of infected individuals at the endemic equilibrium.Therefore,in this paper,we mainly improve the previous study of infectious disease transmission model,that is,the migration model with the adjacency matrix not approximating.The conditions for the outbreak or extinction of infectious diseases are discussed by using the qualitative theory of differential equations.In the first chapter,the main research basis and significance of this paper are clarified under the background of the study of infectious disease transmission in heterogeneous metapopulation networks.In the second chapter,the SIS infectious disease model on heterogeneous metapopulation without birth and death is studied.We consider the threshold condition of disease outbreak in the global coupled network.The research shows that when R₀?27?1and the adjacency matrix is irreducible,disease will not break out.On the contrary,the model will have a unique endemic equilibrium,and the disease will break out in an all-round way.Finally,the theoretical research results of the above model are verified by numerical simulation,that is,the number of susceptible individuals and infected individuals will increase with the increase of degree when the model is in a stable state.There was a positive correlation between mobility and the number of infected individuals at the endemic equilibrium.In the third chapter,we mainly study the SIS infectious disease model on the heterogeneous metapopulation with birth and death.We calculate the threshold conditions of the model for the global coupled network and the star network respectively,and prove the global asymptotic stability of the disease-free equilibrium by constructing Lyapunov function.Then,we further verify the existence,uniqueness and global asymptotic stability of the endemic equilibrium.Finally,through numerical simulation,it is found that the increase of node degree will promote the increase of the number of individuals in stable state.When _cR?29?1,with the increase of mobility,the number of infected individuals is also increasing,and the impact of the migration of infected individuals is far greater than that of susceptible individuals.In this paper,we mainly consider the migration model on the heterogeneous metapopulation network.Through the analysis of the non approximate adjacency matrix,we get a series of results,which provide guidance value in the prevention and control of infectious diseases.That is to say,we should especially consider the influence of network structure and migration in the transmission model of infectious diseases.