Multi-channel Infectious Disease Dynamics Model Of Complex Networks Analysis

The focus of traditional homogeneous-mixing infection dynamics modeling is on es-tablishing the diferential-equations-based mathematical models of the spread of infectiousdiseases, studying disease spread, predicting the trends of the disease, finding out the keyfactors in the process of the spread, and preventing the disease by the optimal strategies.Although this method succeeds in explaining certain phenomena of epidemic spreading, thetraditional approach mainly deals with epidemic spreading in homogeneous mixing popu-lation. In fact, population-based epidemic spread is via social contact networks, therefore,it is more realistic to use models combining the theory of complex networks with epidemicdynamics than that of homogeneous-mixing-based dynamic models. Although the investi-gation of network-based infection dynamical models has been for about ten years, it lackssystematic dynamical theory analysis and proof. In this paper we mainly investigate themultiple routes of disease transmission models on complex networks.In chapter 1, we give an introduction to the development history of complex networks,the state of development of network-based infection dynamics and the main work in thisthesis.In chapter 2, we give a global analysis of an SIS dynamic model with both vectorinfection and network-contact infection. By investigating the local stability of the disease-free equilibrium, we obtain the threshold-basic reproduction number R0, which controls theprevalence of disease or not, and generalizes the results of infectious disease models only withvector infection or network-contact infection. Moreover, we study the existence, uniquenessand global behavior of equilibria (including disease-free and endemic equilibrium). Finally,we study the efects of various immunization schemes on networks on controlling disease,and perform a series of numerical simulations to confirm the theoretical analysis.In chapter 3, aiming at the phenomena of multiple modes of disease propagation onnetworks etc, we analyze an SIS model based on the spread along links of network andhomogeneous-mixing. Through mathematical analysis, we obtain the basic reproduction number R0by investigating the local stability of the disease-free equilibrium, and performsensitivity analysis of R0versus model parameters. Then, the existence and uniqueness andglobal stability of equilibria (disease-free and endemic equilibrium) are investigated in detail,and the efects of various immunization schemes on disease spread are discussed. The resultsof theoretical analysis are confirmed well by the numerical simulations.