A Few Complex Network Infectious Disease Dynamics Model Analysis

Infectious diseases have serious efects on human society and healthy. Mathematicmodel is important and useful tool for human fighting with the epidemic disease. For betterunderstanding and analyzing the infectious disease, the epidemic model on complex networkis proposed. In this paper, three diferent epidemic model on complex network is analyzed,where contacts between humans are treated as a scale-free social network.In the chapter2, a sexually transmitted diseases model is proposed on complex networks.There are three groups in our model which are dangerous male, non-dangerous male andfemale. By mathematical analysis, we obtain the basic reproduction number for the existenceof endemic equilibrium and study the efects of various immunization schemes about diferentgroups. Furthermore, numerical simulations are taken to verify and reach more conclusions.In the chapter3, an epidemic disease model about the efect of awareness programsis proposed on complex networks. Two forms on increasing rate of awareness programs,which are a constant and the change with the number of infected individuals, are analyzed.Through dynamical analysis, the basic reproduction number R0is obtained and the stabil-ity of disease-free equilibrium and endemic equilibrium is proved. Furthermore, numericalsimulations about the model are taken to reach that, on the one hand, the two forms, whichare increasing rate of awareness programs, respectively, have advantages and disadvantageson preventing and controlling diseases, and they are complementary; on the other hand,awareness programs have more efects on nodes with smaller degrees.In the chapter4, an SIR model with birth and death on complex networks is analyzed,where infected individuals are divided into m groups according to their infection. Thebasic reproduction number R0is obtained and the efects of various immunization schemesis studied. Then it is established that the disease-free equilibrium is locally and globallyasymptotically stable in some conditions, otherwise disease-free equilibrium is unstable andthere exists an unique endemic equilibrium such that it is globally asymptotically stable.Our theoretical results are confirmed by numerical simulations and it is suggested that a promising way for the control of infectious diseases.