Yang Christine K, Brauer Fred
Harvard Graduate School of Education, Harvard University, Cambridge, MA 02138, USA.
Math Biosci Eng. 2008 Jul;5(3):585-99. doi: 10.3934/mbe.2008.5.585.
We consider age-of-infection epidemic models to describe multiple- stage epidemic models, including treatment. We derive an expression for the basic reproduction number R0 in terms of the distributions of periods of stay in the various compartments. We find that, in the model without treatment, R0 depends only on the mean periods in compartments, and not on the form of the distributions. In treatment models, R0 depends on the form of the distributions of stay in infective compartments from which members are removed for treatment, but the dependence for treatment compartments is only on the mean stay in the compartments. The results give a considerable simplification in the calculation of the basic reproduction number.
我们考虑感染年龄流行模型来描述多阶段流行模型，包括治疗情况。我们根据在各个隔室中的停留时间分布推导出基本再生数(R_0)的表达式。我们发现，在没有治疗的模型中，(R_0)仅取决于隔室中的平均停留时间，而不取决于分布的形式。在治疗模型中，(R_0)取决于因治疗而被移出的感染隔室中的停留时间分布形式，但对于治疗隔室的依赖性仅在于隔室中的平均停留时间。这些结果在基本再生数的计算中带来了相当大的简化。
