González-Guzmán J, Naulin R
Instituto de Matematicas, Universidad Católica de Valparaíso, Chile.
J Math Biol. 1994;33(2):211-23. doi: 10.1007/BF00160180.
In this paper a model of bovine brucellosis spread is analyzed. This model consider four epidemiological classes: susceptibles, aborting infectious, infectious carriers and immune by vaccination. The per capita death rates of susceptibles, aborting and carriers are interpreted as slaughtering rates and they are time variable in order to maintain the size of the herd constant. A description of the evolution of the disease at the beginning of the epizootiological outbreak is given by means of singular perturbation techniques. We obtain a threshold parameter for the outbreak of the disease and a description of the asymptotic behavior of the model by using a theorem of Markus on asymptotically autonomous systems.
本文分析了牛布鲁氏菌病传播模型。该模型考虑了四个流行病学类别：易感动物、流产感染动物、感染携带者以及通过接种疫苗产生免疫的动物。易感动物、流产感染动物和携带者的人均死亡率被解释为屠宰率，且它们是随时间变化的，以便使畜群规模保持恒定。利用奇异摄动技术给出了动物疫病流行爆发初期疾病演变的描述。我们通过使用马库斯关于渐近自治系统的一个定理，得到了疾病爆发的阈值参数以及模型渐近行为的描述。
