Several Dynamic Models For Brucellosis With Indirect Transmission And The Analysis Of Its Stability

Brucellosis is a zoonosis, the source of the zoonosis is animal and caused by bacteria. It can be found in a variety of animals all around the world, it has high pathogenic, easy recurrence and other characteristics. Although the disease is not transmitted from person to person but because its main carrier is closely related to humans, domestic animals(cattle, sheep, pigs, etc), therefore there is a serious threat to our daily lives. Brucella is a certain resistance to the outside environment, under the right conditions can live for a long time, thus indirectly caused by Brucella infection also has a bigger threat. However, due to its lower death rates and the symptoms are not apparent, so the indirect infection of brucellosis are few research, and for non-major source of contagion pet and wildlife, the researchs are almost none. In this paper, we do the following researchs:1. According to wildlife survival status assumed its growth obedience Logistic growth, established a epidemic model for Brucellosis in wildlife with indirect transmission, calculated the basic reproduct number, analysis the dynamics behavior and make some numerical simulations, found that the affecting of indirect transmission is large.2. According to the features of the brucellosis spread from animal to human, considered some control measures, established an animal-livestock dynamics model, calculated the disease outbreak threshold value--basic reproduction number, proved that the disease-free equilibrium point and the endmic equilibrium point in each population are global stable, then the numerical simulation validation the results. The result explain that the key to prevention and control of brucellosis is in livestock, only control brucellosis in livestock to control brucellosis in human.3. The feeding of pets increased the probability for human infect brucellosis, so we established a livestock-pet-human dynamics model for brucellosis, calculated there are two basic reproduction numbers, through constructed Lyapunov function, constructed Dulac function and the nature of limit system, proved disease- free equilibrium point and endemic equilibrium points are global stable. The through numerical simulation descipt that only both control the brucellosis in livestock and pet, the disease in human will go to extinct.4. Wildlife is an important carrier for brucellosis, the epidemics caused by wildlife in recent years growing fast. Considering direct transmission of livestock and wildlife are standard incidence and considering the hunting rate of wild animals as an infected item, established a livestock-wildlife- human model for brucellosis. Then through dynamic analysis shows that global stability of the equilibrium point. Numerical simulation and parameter sensitivity analysis illustrates the reduction of indirect transmission can reduce the number of wild animals and human patients, and hunting of wildlife can reduce human brucellosis patients while keeping the number of wild animals has drastically reduced or even extinction, put an end to the killing of wildlife-you can completely cut off people this transmission also said protecting wild animals is to protect ourselves. Forbidding the killing of wildlife can completely cut off the transmission, that is, protecting wild animals is to protect ourselves.