Alves D, Haas V J, Caliri A
Laboratório Interdisciplinar de Computação Científica, Faculdades COC, Rua Abrahão Issa Hallack, 980 -, 14096-160 Ribeirão Preto, SP -, Brazil ; Departamento de Física e Química, FCFRP -, Universidade de São Paulo, Av. do Café S/N -, 14040-903 Ribeirão Preto, SP -, Brazil.
J Biol Phys. 2003 Mar;29(1):63-75. doi: 10.1023/A:1022567418081.
An important issue in theoretical epidemiology is the epidemic thresholdphenomenon, which specify the conditions for an epidemic to grow or die out.In standard (mean-field-like) compartmental models the concept of the basic reproductive number, R(0), has been systematically employed as apredictor for epidemic spread and as an analytical tool to study thethreshold conditions. Despite the importance of this quantity, there are nogeneral formulation of R(0) when one considers the spread of a disease ina generic finite population, involving, for instance, arbitrary topology ofinter-individual interactions and heterogeneous mixing of susceptible andimmune individuals. The goal of this work is to study this concept in ageneralized stochastic system described in terms of global and localvariables. In particular, the dependence of R(0) on the space ofparameters that define the model is investigated; it is found that near ofthe `classical' epidemic threshold transition the uncertainty about thestrength of the epidemic process still is significantly large. Theforecasting attributes of R(0) for a discrete finite system is discussedand generalized; in particular, it is shown that, for a discrete finitesystem, the pretentious predictive power of R(0) is significantlyreduced.
理论流行病学中的一个重要问题是流行阈值现象，它规定了流行病增长或消亡的条件。在标准（类平均场） compartmental 模型中，基本再生数(R(0))的概念已被系统地用作流行病传播的预测指标和研究阈值条件的分析工具。尽管这个量很重要，但当考虑疾病在一般有限人群中的传播时，例如涉及个体间相互作用的任意拓扑结构以及易感个体和免疫个体的异质混合时，(R(0))并没有通用的公式。这项工作的目标是在一个用全局和局部变量描述的广义随机系统中研究这个概念。特别地，研究了(R(0))对定义模型的参数空间的依赖性；发现在“经典”流行阈值转变附近，流行病过程强度的不确定性仍然很大。讨论并推广了离散有限系统中(R(0))的预测属性；特别地，表明对于离散有限系统，(R(0))的虚假预测能力显著降低。
