We predict the future course of ongoing susceptible-infected-susceptible (SIS) epidemics on regular, Erd\H{o}s-R\'{e}nyi and Barab\'asi-Albert networks. It is known that the contact network influences the spread of an epidemic within a population. Therefore, observations of an epidemic, in this case at the population-level, contain information about the underlying network. This information, in turn, is useful for predicting the future course of an ongoing epidemic. To exploit this in a prediction framework, the exact high-dimensional stochastic model of an SIS epidemic on a network is approximated by a lower-dimensional surrogate model. The surrogate model is based on a birth-and-death process; the effect of the underlying network is described by a parametric model for the birth rates. We demonstrate empirically that the surrogate model captures the intrinsic stochasticity of the epidemic once it reaches a point from which it will not die out. Bayesian parameter inference allows for uncertainty about the model parameters and the class of the underlying network to be incorporated directly into probabilistic predictions. An evaluation of a number of scenarios shows that in most cases the resulting prediction intervals adequately quantify the prediction uncertainty. As long as the population-level data is available over a long-enough period, even if not sampled frequently, the model leads to excellent predictions where the underlying network is correctly identified and prediction uncertainty mainly reflects the intrinsic stochasticity of the spreading epidemic. For predictions inferred from shorter observational periods, uncertainty about parameters and network class dominate prediction uncertainty. The proposed method relies on minimal data and is numerically efficient, which makes it attractive either as a standalone inference and prediction scheme or in conjunction with other methods.
翻译:我们预测了常规网络、Erd\H{o}s-R\'{e}nyi和Barab\'asi-Albert网络上目前易感感染(SIS)流行病的未来趋势。已知接触网络会影响流行病在人口中的蔓延。因此,在人口一级对流行病的观察包含关于基本网络的信息。这种信息反过来有助于预测当前流行病的未来趋势。在预测框架中利用网络上SIS流行病的精确高维的不确定性模型,其精确高度的不确定性模型被一个低度的预测替代值模型所近似。代孕模型以出生和死亡过程的过程为基础;基础网络的影响则通过一个参数模型来描述有关出生率的信息。我们从实验中可以看出,在流行病到达一个不会消失的点后,这个模型的精确性模型的精确性模型的精确性模型和基本网络的预测性模型的精确性模型性模型性模型性模型性模型性模型性模型性模型性模型性模型性模型性模型性模型值和基础网络的精确性参数性模型性模型性模型性模型性模型性模型性模型性模型性模型性模型性,在预测的精确的预测性预测性数据性数据水平上,在预测性预测性预测性数据中可以直接反映的精确的预测性数据水平,在预测性数据性数据水平上, 。