Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel.
Gonda Brain Research Center and Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel.
Phys Rev E. 2016 Aug;94(2-1):022409. doi: 10.1103/PhysRevE.94.022409. Epub 2016 Aug 11.
A goal of many epidemic models is to compute the outcome of the epidemics from the observed infected early dynamics. However, often, the total number of infected individuals at the end of the epidemics is much lower than predicted from the early dynamics. This discrepancy is argued to result from human intervention or nonlinear dynamics not incorporated in standard models. We show that when variability in infection rates is included in standard susciptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) models the total number of infected individuals in the late dynamics can be orders lower than predicted from the early dynamics. This discrepancy holds for SIS and SIR models, where the assumption that all individuals have the same sensitivity is eliminated. In contrast with network models, fixed partnerships are not assumed. We derive a moment closure scheme capturing the distribution of sensitivities. We find that the shape of the sensitivity distribution does not affect R_{0} or the number of infected individuals in the early phases of the epidemics. However, a wide distribution of sensitivities reduces the total number of removed individuals in the SIR model and the steady-state infected fraction in the SIS model. The difference between the early and late dynamics implies that in order to extrapolate the expected effect of the epidemics from the initial phase of the epidemics, the rate of change in the average infectivity should be computed. These results are supported by a comparison of the theoretical model to the Ebola epidemics and by numerical simulation.
许多传染病模型的目标是根据观察到的早期感染动力学来计算传染病的结果。然而，通常情况下，传染病结束时的感染总人数比早期动力学预测的要低得多。这种差异被认为是由于标准模型中未包含的人为干预或非线性动力学造成的。我们表明，当在标准的易感-感染-易感（SIS）和易感-感染-恢复（SIR）模型中包含感染率的可变性时，晚期动力学中的感染总人数可以比早期动力学预测的低几个数量级。这种差异适用于 SIS 和 SIR 模型，其中消除了所有个体都具有相同敏感性的假设。与网络模型不同，不假设固定的伙伴关系。我们推导出了一个捕捉敏感性分布的矩闭合方案。我们发现，敏感性分布的形状不会影响 R_{0}或传染病早期阶段的感染人数。然而，敏感性的广泛分布会减少 SIR 模型中的去除个体总数和 SIS 模型中的稳态感染分数。早期和晚期动力学之间的差异意味着，为了从传染病的初始阶段推断出传染病的预期效果，应该计算平均传染性的变化率。这些结果得到了埃博拉疫情的理论模型比较和数值模拟的支持。
