Inaba Hisashi, Nishiura Hiroshi
Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan.
Math Biosci. 2008 Nov;216(1):77-89. doi: 10.1016/j.mbs.2008.08.005.
In this paper, we develop the theory of a state-reproduction number for a multistate class age structured epidemic system and apply it to examine the asymptomatic transmission model. We formulate a renewal integral equation system to describe the invasion of infectious diseases into a multistate class age structured host population. We define the state-reproduction number for a class age structured system, which is the net reproduction number of a specific host type and which plays an analogous role to the type-reproduction number [M.G. Roberts, J.A.P. Heesterbeek, A new method for estimating the effort required to control an infectious disease, Proc. R. Soc. Lond. B 270 (2003) 1359; J.A.P. Heesterbeek, M.G. Roberts, The type-reproduction number T in models for infectious disease control, Math. Biosci. 206 (2007) 3] in discussing the critical level of public health intervention. The renewal equation formulation permits computations not only of the state-reproduction number, but also of the generation time and the intrinsic growth rate of infectious diseases. Subsequently, the basic theory is applied to capture the dynamics of a directly transmitted disease within two types of infected populations, i.e., asymptomatic and symptomatic individuals, in which the symptomatic class is observable and hence a target host of the majority of interventions. The state-reproduction number of the symptomatic host is derived and expressed as a measurable quantity, leading to discussion on the critical level of case isolation. The serial interval and other epidemiologic indices are computed, clarifying the parameters on which these indices depend. As a practical example, we illustrate the eradication threshold for case isolation of smallpox. The generation time and serial interval are comparatively examined for pandemic influenza.
在本文中，我们发展了多状态年龄结构流行系统的状态再生数理论，并将其应用于检验无症状传播模型。我们建立了一个更新积分方程组来描述传染病侵入多状态年龄结构宿主群体的过程。我们定义了年龄结构系统的状态再生数，它是特定宿主类型的净再生数，在讨论公共卫生干预的临界水平时，其作用类似于类型再生数[M.G. 罗伯茨，J.A.P. 赫斯特贝克，一种估算控制传染病所需努力的新方法，《英国皇家学会学报B》270 (2003) 1359；J.A.P. 赫斯特贝克，M.G. 罗伯茨，传染病控制模型中的类型再生数T，《数学生物科学》206 (2007) 3]。更新方程的形式不仅允许计算状态再生数，还能计算传染病的代时和内在增长率。随后，该基本理论被应用于捕捉两种感染人群（即无症状和有症状个体）中直接传播疾病的动态，其中有症状类别是可观察的，因此是大多数干预措施的目标宿主。推导了有症状宿主的状态再生数，并将其表示为一个可测量的量，进而讨论病例隔离的临界水平。计算了序列间隔和其他流行病学指标，明确了这些指标所依赖的参数。作为一个实际例子，我们说明了天花病例隔离的根除阈值。对大流行性流感的代时和序列间隔进行了比较研究。
