The Applied Research Of Dynamic Systems On Several Specific Problems Of Transmission

In the paper, taking the transmission of animal disease as the research background, We estab-lish multiple dynamic models of infectious disease. Based on dynamical system theory, we study the dynamic behavior of disease transmission and the impact of risk factors on disease transmission, and we evaluate the effectiveness of risk management measures. We focused on the Bacteria in the environment, Population migration, Immunity, Culling and other factors on disease transmission. These results are significant not only in mathematical theory but also in many applied fields. The main work in this dissertation is listed as follows:In chapter2, we propose a new deterministic model which incorporates general incidences, various stages of infection and a general shedding rate of the pathogen to analyze the dynamics of animal diseases. Under the biologically motivated assumptions, we derive the basic reproduction number Rq, analyze the uniqueness of the endemic equilibrium, and prove the global asymptotically stability of the equilibria. Some specific examples are used to illustrate the utilization of our results, an example is given to illustrate that conditions for the uniqueness of equilibrium are sufficient rather than necessary.In chapter3, we construct a susceptible-infectious-brucella in the environment (SIB) dynamic model with general incidences and shedding rate of the pathogen. Under the biologically motivated assumptions, we analyze the existence of the endemic equilibrium, and we show that, if R0≤1, disease-free equilibrium is globally asymptotically stable, the endemic equilibrium is globally asymptotically stable if Rq>1.In chapter4, Based on cross-infection between populations and migration between patches, we study two meta-population dynamics model, the basic reproduction number R0is given, and we analyze the uniqueness of the endemic equilibrium and prove the global Stability of equilibria.In chapter5, we establish a dynamic model for the sheep-human transmission of brucellosis. We first determine the basic reproduction number R0and analyze the global stability of the disease-free and endemic equilibrium. Using the reported human brucellosis data, we carry out numerical simulations and make sensitivity analysis of the basic reproduction number in terms of some pa-rameters. The results show that brucellosis cannot be eradicated even though disinfection rate and vaccination rate of adult sheep are100%. Vaccinating and disinfecting both young and adult sheep are effective strategies to control brucellosis in Inner Mongolia of China. In chapter6, given the characteristics of the brucellosis infection in Changling County of Jilin Province, we propose a dynamic model for the sheep brucellosis transmission. We first determine the basic reproduction number Ro and discuss the stability of the disease free equilibrium and the existence of the endemic equilibrium. Secondly, using the reported sheep brucellosis data, we carry out numerical simulations and make sensitivity analysis of the basic reproduction number in terms of some parameters. The results show that brucellosis cannot be eradicated if we only take measures on young sheep and breeding rams, and both vaccinating ewes and young sheep (4-6months) and culling infected breeding rams are effective and feasible strategies to control brucellosis in Changling County.In chapter7, based on the reported data and characteristics of the rabies infection in Guang-dong Province, we establish a mathematical model for the dog-human transmission of rabies. We first determine the basic reproduction number R0and discuss the stability of disease-free equilib-rium and persistence of the disease. By carrying out sensitivity analysis of the basic reproduction number in terms of some parameters, we find that the domestic dog vaccination rate, the recruit-ment rate of domestic dogs, and the quantity of stray dogs play important roles in the transmission of rabies. This study suggests that rabies control and prevention strategies should include public education and awareness about rabies, increase of the domestic dog vaccination rate and reduction of the stray dog population.