| Brucellosis is a serious zoonotic disease caused by brucella and is widely prevalent in many regions and countries.It not only poses a threat to the health of animal and human,but also brings huge economic losses to the livestock industry.Epidemic dynamic plays an important role in predict-ing the law of disease transmission and in evaluating intervening measures.Considering the strong seasonality of brucellosis transmission,a deterministic brucellosis model in a periodic environment will be established and its dynamic will be analyzed.In addition,the spread of brucellosis must be affected by random factors.In this thesis,we will also establish a stochastic brucellosis model in a periodic environment and analyze extinction probability.The specific content of this thesis is arranged as follows.In Chapter 1,we introduce the research background of this thesis,and expound the main work and the main theoretical knowledge involved.According to the transmission law of brucellosis,a deterministic brucellosis model in a periodic environment is established in Chapter 2.We use the next generation operator method to give the basic regeneration numberR0of the time-dependent model,and analyze the dynamic of the model.WhenR0<1,the disease-free periodic solution of the model is globally asymptotically stable.And whenR0>1,the disease is uniformly persistent,and there is at least one positive periodic solution of the model.Finally,numerical simulation is used to verify the rationality of the conclusions and to evaluate the influence of seasonal drivers on the periodic outbreak of brucellosis.Based on the sensitivity analysis,to control the spread of brucellosis more effectively,the detection rate,disinfection rate and vaccination coverage should be further expanded.In Chapter 3,considering the influence of environmental stochastic factors on the transmission of brucellosis,we establish a brucellosis model in a periodic environment based on a continuous-time Markov chain.We present the state transition rate of Markov chain and the multitype branching pro-cess approximation near the disease-free periodic solution.And we derive the offspring probability generation function and the backward Kolmogorov differential equation.Furthermore,we deduce the probability of disease extinction.Based on the analysis of extinction probability,we derive the analytical expressions of the mean and variance of extinction time.These approximations suggest that the probability of disease outbreak is also periodic and depends on the time when the infec-tious individuals are introduced and the number of initially infectious individuals.We compare the deterministic model with the stochastic model by numerical simulations and simulate the disease out-break probability.The results show that the outbreak probability estimated by the branching process approximation is in good agreement with the results of Monte Carlo simulation.In Chapter 4,we summarize the work of this thesis,point out the shortcomings and propose the next research plans. |
