Asymptotically Autonomous Epidemic Models
Asymptotically Autonomous Epidemic Models
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发表时间：
1994-07
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通讯作者：
C. Castillo-Chavez;H. Thieme
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作者：
C. Castillo-Chavez;H. Thieme
考虑模拟传染病传播的微分方程系统，它可以重写为更小的渐近自治系统，其限制系统比原始系统更容易处理。使用最近开发的技术，表明原始系统的渐近动力学与简化系统的渐近动力学相同，即收敛到无病平衡或地方性平衡。这些模型描述了非致命性传播疾病。第一个模型考虑了发病率对易感者、感染者和被移除个体的数量的复杂依赖性，这是由于根据感知风险的行为变化而引起的。第二种模型添加了具有完全交叉免疫的多种感染因子。第三个模型考虑标准发生率，但去除期的分布长度。
Differential equation systems modeling the spread of infectious diseases are considered which can be rewritten as smaller asymptotically autonomous systems with limiting systems that are easier to handle than the original ones. Using recently developed techniques, it is shown that the asymptotic dynamics of the original systems are the same as the ones of the reduced systems, namely convergence to the disease-free or an endemic equilibrium. The models describe non-lethal sexually transmitted diseases. The first model considers a complex dependence of the incidence on the numbers of susceptible, infective, and removed individuals caused by change of behavior according to the perceived risk. The second model adds multiple strains of the infective agent with total cross-immunity. The third model considers a standard incidence, but a distributed length of the removal period.