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研究一类具有一般形式非线性饱和传染率染病年龄结构SIS流行病传播数学模型动力学性态,得到疾病绝灭和持续生存的阈值条件――基本再生数。当基本再生数小于或等于1时,仅存在无病平衡点,且在其小于1的情况下,无病平衡点全局渐近稳定,疾病将逐渐消除;当基本再生数大于1时,存在不稳定的无病平衡点和唯一的局部渐近稳定的地方病平衡点,疾病将持续存在。已有的两类模型可视为本模型的特例,其相关结论可作为本文的推论。
This paper studies the dynamic behavior of a mathematical model with general form of non-linear saturated infection rate of age-affected SIS epidemic and obtains the threshold condition of extinction and continuous survival of disease - basic regeneration number. When the number of basic regeneration is less than or equal to 1, there is only disease-free equilibrium, and if it is less than 1, the disease-free equilibrium will be globally asymptotically stable and the disease will be gradually eliminated; when the number of basic regeneration is greater than 1, Stable disease-free balances and the only locally asymptotically stable endemic balance will continue to exist. The two existing models can be considered as special cases of this model, and the related conclusions can be used as inferences in this paper.