With The Population Dynamics On The Network Behavior Of Infectious Disease Model

With the development of the society, it is remarkable to the characteristics of networkformed of the population structure, which based on regional diferences and populationfowing. The research of infectious disease models plays a signifcance role in practical basedon complex network.These models described by the occurring, evolution and environmental factor of infec-tious disease, which based on complex network. Establishing the mathematical model refectthe regular transformation of disease. The optimal strategy for preventing and controllingthe disease according to deeply research and analysis in order to provide the theory basisand data basis for infectious diseases.According to the actual situation from the transmission of infectious diseases, the impor-tant infuence for individuals on complex networks with the factors of population dynamics,such as birth, death, migration and time delay. On complex network, three models areestablished with using the theory and researching ways of dynamics of infectious disease,complex networks and qualitative and stability of diferential equations. The stability of thesystem researched by the deeply analysis and numerical simulation.Firstly, an SIS model with constant-inputting based on network is discussed. The basicreproduction number is calculated by the Jacobi matrix along to the disease-free equilib-rium of systems, and analyzed the stability of the disease-free equilibrium and the positiveequilibrium for the system. Finally, confrming the accuracy for the stability of system withnumerical simulation.Secondly, an SIS model with Logistic-inputting based on network is discussed. The basicreproduction number is calculated by the way of spectral radius for the system, and analyzedstability of the disease-free equilibrium and the positive equilibrium for the system. Finally,taking an example with the degree with2for confrming the accuracy for the stability ofsystem with numerical simulation.Thirdly, an SIR model with proportion-inputting and time delay based on network is discussed. The basic reproduction number is calculated by structuring a Θ function of thesystem. The infuence of stability is discussed for disease-free equilibrium with time delay.Furthermore, the stability of positive equilibrium is proved with structuring a Lyapunovfunction. Finally, confrming the accuracy for the stability of system and the stability oftime delay infuencing though numerical simulation.