Dynamic Analysis Of Several Types Of Edge-based Modeling On Complex Networks

Infectious disease is a kind of disease caused by various pathogens,which can spread between people and people,animals and animals,or people and animals.It not only endangers the health and survival of individuals,but also brings great economic burden to the whole society.In recent years,with the deep research of the complex network,the network provides new theories,tools and methods for the research of the field of communication dynamics.These new theories,tools and methods are helpful to establish the reasonable dynamic model of infectious disease transmission,so as to better understand the process of infectious disease transmission and predict the epidemic scale of infectious disease.In this paper,the mathematical models are established by using the edge-based model theory,and analyze its dynamics.The main research results are as follows:1.The SEIR model with recovery rate in latent period is established and analyzed.The dynamic model of infectious diseases without recovery rate in latent period is briefly introduced,and the dynamic model of infectious diseases with recovery rate in latent period is established by using the edge-based model theory.We obtain the accurate expression of the basic reproduction number and the final size.The large-scale simulations are performed to compare the SEIR model with or without recovery rate in latent period,and analyze the influence of the recovery rate in latent period?and the length of latent period 1/?on the epidemic spreading.We found that our model predictions agree well with the ensemble averages of the stochastic simulations on ER random network and SF scale-free network.We also found that the recovery rate in latent period?and the length of the latent period 1/?not only effect the basic reproduction number but also effect the final size.2.The SIR model on one-way-coupled networks is established and analyzed.The one-way-coupled networks is briefly introduced,and the SIR model on one-way-coupled networks is established by using the edge-based model theory.We obtain the accurate expression of the basic reproduction number and the final size.The large-scale simulations are performed to analyze the influence of infection rate on disease transmission.We found that the basic reproduction number R₀ of the whole network is the maximum of the basic reproduction numbers of the two subnetworks;R₀ is not only dependent of the cross-infection rate?₁and?₂but also dependent of the internal-infection rate?₃.We also found that the final size of layer A is only related to?₁and?₃,but not to?₂;the final size of layer B is only related to?₂,but not to?₁and?₃.3.The SIR model with social-support is established and analyzed.The SIS model with social-support is briefly introduced,and the SIR model with social-support is established by using the edge-based model theory.We obtain the accurate expression of the basic reproduction number and the final size.The large-scale simulations are performed to analyze the influence of various parameters in the model on disease transmission.We found that when the social support level c=0,the simulation results of our model agree well with the standard SIR model.