In this paper, we consider a discrete-time stochastic SIR model, where the transmission rate and the true number of infectious individuals are random and unobservable. An advantage of this model is that it permits us to account for random fluctuations in infectiousness and for non-detected infections. However, a difficulty arises because statistical inference has to be done in a partial information setting. We adopt a nested particle filtering approach to estimate the reproduction rate and the model parameters. As a case study, we apply our methodology to Austrian Covid-19 infection data. Moreover, we discuss forecasts and model tests.

翻译：本文考虑一个离散时间随机SIR模型，其中传播率与真实感染人数均为随机且不可观测变量。该模型的优势在于能够解释感染性的随机波动及未检测感染病例。然而，统计推断需在部分信息框架下进行这一特性带来了技术挑战。我们采用嵌套粒子滤波方法估计再生率与模型参数。作为案例研究，我们将该方法应用于奥地利新冠肺炎感染数据，并进一步探讨预测与模型检验问题。