中文摘要：

研究现实复杂情形下（包含非线性传染率、有隔离措施、群外个体迁入、生育与死亡以及疾病可水平和垂直传播等）的SIRS型传染病模型。首先证明该传染病模型的无病平衡点与地方病平衡点的唯一存在性及渐近稳定性；然后从基本再生数以及折衷考虑人道主义、救治代价与疾病控制效果的原则，针对流行于人类的传染病，提出“优先隔离染病个体、提高疾病治愈率以及控制传染病垂直传播”的传染病综合控制策略；最后，数值仿真验证了模型的稳态特性以及综合控制策略的有效性。

英文摘要：

An SIRS infectious disease model under such real complex circumstances that the transmission rate of disease is non-linear; quarantine measures were partially taken for infectious individuals; immigrations, fertility and death of individuals were permitted; and finally diseases could be both directly and vertically transmitted, was studied. The disease-free and epidemic equilibriums were calculated and proved to be asymptotically stable with certain conditions. According to the basic reproductive number and a tradeoff among humanitarianism, costs of curing all infectious and control effect, a general strategy for controlling human being infectious disease, i.e., first quarantining infectious individuals, then raising the cure rate, and finally controlling vertical transmissions, was suggested. Finally, equilibriums of SIRS model and the effectiveness of general strategy were validated by numerical simulations.