异质群体si -流行病模型的聚集和渐近分析

V. M. Veliov;A. Widder
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引用次数: 4

摘要

本文研究了一个简单的流行病学模型,该模型只涉及易感和感染者,其中考虑了人群在易感/传染性方面的异质性。基于该模型的显式聚合,对该疾病的渐近行为进行了全面分析。将结果与模型的同质版本的结果进行比较,以突出异质性对渐近线的影响。此外,所进行的分析揭示了在哪些情况下,关于人群异质性的不完整信息足以确定疾病的长期结果。数值模拟被用来强调,对于给定的流行水平,从长远来看,异质性影响下的疾病演变可能与同质模型“预测”的有质的不同。此外,研究表明,在封闭种群中,种群生存的指标是存在不同于基本繁殖数的异质性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Aggregation and asymptotic analysis of an SI-epidemic model for heterogeneous populations
The paper investigates a version of a simple epidemiological model involving only susceptible and infected individuals, where the heterogeneity of the population with respect to susceptibility/infectiousness is taken into account. A comprehensive analysis of the asymptotic behaviour of the disease is given, based on an explicit aggregation of the model. The results are compared with those of a homogeneous version of the model to highlight the influence of the heterogeneity on the asymptotics. Moreover, the performed analysis reveals in which cases incomplete information about the heterogeneity of the population is sufficient in order to determine the long-run outcome of the disease. Numerical simulation is used to emphasize that, for a given level of prevalence, the evolution of the disease under the influence of heterogeneity may in the long run qualitatively differ from the one ‘predicted’ by the homogeneous model. Furthermore, it is shown that, in a closed population, the indicator for the survival of the population is in the presence of heterogeneity distinct from the basic reproduction number.
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