In this paper, we develop a discrete time stochastic model under partial information to explain the evolution of Covid-19 pandemic. Our model is a modification of the well-known SIR model for epidemics, which accounts for some peculiar features of Covid-19. In particular, we work with a random transmission rate and we assume that the true number of infectious people at any observation time is random and not directly observable, to account for asymptomatic and non-tested people. We elaborate a nested particle filtering approach to estimate the reproduction rate and the model parameters. We apply our methodology to Austrian Covid-19 infection data in the period from May 2020 to June 2022. Finally, we discuss forecasts and model tests.
翻译：在本文中,我们根据部分信息开发了一个离散时间随机模型,以解释Covid-19大流行病的演变情况。我们的模型是对众所周知的SIR流行病模型的修改,该模型反映了Covid-19的一些特殊特征。特别是,我们使用随机传输率开展工作,我们假设任何观察时间的传染人口的真实数量都是随机的,而不是直接可见的,以说明无症状和未检测的人。我们详细设计了一个嵌巢式粒子过滤法,以估计生殖率和模型参数。我们用我们的方法对2020年5月至2022年6月期间的奥地利Covid-19感染数据进行了应用。最后,我们讨论了预测和模型测试。
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