System Research On Transmission Mechanism And Control Of Some Infectious Diseases

In this thesis, several system dynamics models are formulated based on the occurance and transmission patterns of some infectious diseases such as vector-borne diseases, herpes, avian influenza,etc, and are systemically studied. The transmission mechanisms for these diseases are revealed. The results obtained in this thesis can be applied to guide the control of these diseases.This thesis consists of three parts:the first part (contains Chapter 2 and Chapter 3) mainly concerns the vector-borne diseases and herpes; the second part (contains Chapter 4 and Chapter 5) mainly focus on avian influenza with different treatment rules; the third part (contains Chapter 6 and Chapter 7) formulate and study the age-structured epidemic models with isolation or infectiousness in latent period.This thesis contains seven chapters. The main results and innovations in this disser-tation can be summarized as the following:In chapter 1, the background, significance of the theory and practices, research on-goings at Home and Abroad, main contents and methods in this dissertation are briefly introduced.In chapter 2, a vector-borne systematic epidemic model with nonlinear incidence is formulated and studied. The model can describe the dynamic of many diseases spreading by vectors such as malaria, dengue, West Nile Fever and so on. We get the conditions ensuring that the system exhibits backward bifurcation and analyze the stability of the endemic equilibrium. Our results imply that a nonlinear incidence make the models more complex dynamic behavior. It is not enough to make the disease die out that the basic reproductive number is smaller than 1.In Chapter 3, an herpes systematic epidemic model with nonlinear incidence rate is formulated and investigated. We get the expression of the basic reproductive number which decide the spread of the diseases. If the basic reproductive number is smaller than 1, the disease-free equilibrium is globally asymptotically stable and the disease dies out. If the basic reproductive number is bigger than 1, the endemic equilibrium is globally asymptotically stable and the disease persists.In Chapter 4, an avian systematic epidemic model with saturation treatment is es-tablished and studied. We obtain the basic reproductive number of the model and the stability conditions of the infection-free equilibrium. By using the Bendixson-Dulac the-orem, the global asymptotic stability of the endemic equilibrium is proved.In Chapter 5, we develop a mathematical model for the spread of the avian influenza when drug resources and treatment capacity are limited. Moreover we assume the treat-ment rate is proportional to the number of infections when the capacity of treatment is not reach and otherwise, adopt a constant treatment. We analyze the existence and the stability of equilibria under different conditions.In Chapter 6, an age-structured epidemic model with isolation is proposed and an-alyzed. We get the expression of the basic reproductive number and proved globally stability results for the disease-free equilibrium. At last we get the locally stability con-ditions of the endemic equilibrium.Chapter 7, an age-structured HIV/AIDS epidemic model with infectivity in incuba-tive period is formulated and studied. By using the theory and methods of differential and integral equation, the explicit expression of the basic reproductive number was obtained, it is showed that the disease-free equilibrium is locally and globally asymptotically stable if the basic reproductive number is smaller than 1, at least one endemic equilibrium ex-ists if the basic reproductive number is bigger than 1, the stability conditions of endemic equilibrium are also given.