Global Health Center, U.S. Centers for Disease Control and Prevention, Atlanta, GA, USA.
National Center for Immunization and Respiratory Diseases, U.S. Centers for Disease Control and Prevention, Atlanta, GA, USA.
J Math Biol. 2023 Mar 8;86(4):53. doi: 10.1007/s00285-023-01886-9.
Mixing among sub-populations, as well as heterogeneity in characteristics affecting their reproduction numbers, must be considered when evaluating public health interventions to prevent or control infectious disease outbreaks. In this overview, we apply a linear algebraic approach to re-derive some well-known results pertaining to preferential within- and proportionate among-group contacts in compartmental models of pathogen transmission. We give results for the meta-population effective reproduction number ([Formula: see text]) assuming different levels of vaccination in the sub-populations. Specifically, we unpack the dependency of [Formula: see text] on the fractions of contacts reserved for individuals within one's own subgroup and, by obtaining implicit expressions for the partial derivatives of [Formula: see text], we show that these increase as this preferential-mixing fraction increases in any sub-population.
在评估预防或控制传染病暴发的公共卫生干预措施时，必须考虑亚群之间的混合以及影响其繁殖数的特征的异质性。在本篇综述中，我们应用线性代数方法重新推导了与病原体传播的隔室模型中优先在组内和按比例在组间接触相关的一些著名结果。我们给出了在亚群中接种疫苗水平不同的情况下的元种群有效繁殖数([Formula: see text])的结果。具体来说，我们解析了[Formula: see text]对保留给自己亚群内个体的接触比例的依赖关系，并通过获得[Formula: see text]的偏导数的隐式表达式，我们表明在任何亚群中，这种优先混合的比例增加时，这些偏导数也会增加。
