论文标题
带有随机传输的爵士模型
SIR Model with Stochastic Transmission
论文作者
论文摘要
易感感染的（SIR）模型是流行病学模型的基石。但是，该规范仅取决于两个参数，这意味着缺乏灵活性和复制在实践中观察到的挥发性繁殖数的困难。我们通过引入非线性随机传输来扩展经典的SIR模型，以获取随机的SIR模型。我们得出其确切的解决方案，并讨论了牛群免疫的条件。随机的SIR模型对应于无限大小的种群。当人口规模有限时，也存在抽样的不确定性。我们提出了一个状态空间框架，在该框架下，我们分析了流行病演变期间观察和随机流行病学不确定性的相对幅度。我们还强调，当SIR模型被离散时，牛群免疫概念的鲁棒性缺乏鲁棒性。
The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile reproduction numbers observed in practice. We extend the classic SIR model by introducing nonlinear stochastic transmission, to get a stochastic SIR model. We derive its exact solution and discuss the condition for herd immunity. The stochastic SIR model corresponds to a population of infinite size. When the population size is finite, there is also sampling uncertainty. We propose a state-space framework under which we analyze the relative magnitudes of the observational and stochastic epidemiological uncertainties during the evolution of the epidemic. We also emphasize the lack of robustness of the notion of herd immunity when the SIR model is time discretized.
