Research On A Few Kinds Dynamic Model Of Infectious Diseases

The spread of infection is typical emergencies of public health and major public safety problem that the human facing in the21st century. Quantitative analysis research on the law of epidemic disease is the key work of prevention and control, a dynamic model of infectious diseases has become important tools for analysing and controlling the spread of the disease. The mathematical model of differential equations can reflect the dynamic characteristics of infectious diseases, better reflect popular rule from the mechanism of disease spread, and hence it is good for people to understand some overall condition of the popular process. Many of these questions are boils down to research on periodic solution of dynamics model of infectious diseases. Therefore, research on periodic solution of differential equations which describe the process of an infectious disease has important practical significance.This thesis respectively discuss several types of infectious disease model with delay or impulsive effect. By means of the comparison theorem of impulsive differential equation and Floquet multiplier theory method, several kinds of the sufficient conditions of the systems existing infection-free periodic solutions and global attractive or the global asymptotic sta-bility of that have been obtained, and some examples are explained the feasibility of each chapter. The full text structures are as follows:In chapter1, we simply introduce research background and meaning of infectious dis-eases, two kinds of basic dynamics model of infectious diseases, development history and research status of the dynamics of infectious disease, and puts forward some problems which will be discussed in our paper, and give the necessary prior knowledge.In chapter2,through the model improvement, establish an SEIR model for diseases with two pathogen strains, delay and impulsive. Base on the comparison theorem of impulsive differential equation, a globally attractive condition for the infection-free periodic solution of the system was given. By constructing the Liapunov functions, we prove the permanence of system.In chapter3, an SIR epidemic model with generalized Logistic death rate and stage-structured is formulated. Using the discrete dynamical system determined by the the stro-boscopic map, an infection-free periodic solution of the model under impulsive vaccination is obtained. Base on Floquet Multiplier theory and the comparison theorem of impulsive differential equation, the analysis of global asymptotic stability of the infection-free periodic solution is given.In chapter4, base on the control strategy of using insect viruses to control pests and classification of species, a stage-structured delay pest model based on biological control with impulsive is formulated. Utilize Floquet theory and the comparison theorem of impulsive differential equation, a global attractive condition for the pest-eradication periodic solution of the investigated system is proved which provides reliable theory basis for pest control.In chapter5, as this paper’s conclusion, we have carried on the subtotal to the paper and proposed several questions which were worth further studying.