Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale Andrea Doria 6, 95125, Catania, Italy.
J Math Biol. 2021 Sep 14;83(4):34. doi: 10.1007/s00285-021-01657-4.
Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible S, infected I, removed R and dead people D. In order to have a cross validation, a deterministic version of such a model is also devised which is represented by a system of ordinary differential equations with delays. In the second stochastic model two further compartments are added: the class A of asymptomatic individuals and the class L of isolated infected people. Effects such as social distancing measures are easily included and the consequences are analyzed. Numerical solutions are obtained with Monte Carlo simulations. Quantitative predictions are provided which can be useful for the evaluation of political measures, e.g. the obtained results suggest that strategies based on herd immunity are too risky. Finally, the models are calibrated on data referring to the second wave of infection in Italy.
提出了两个随机模型来描述 COVID-19 大流行的演变。在第一个模型中，人群被分为四个部分：易感者 S、感染者 I、移除者 R 和死亡者 D。为了进行交叉验证，还设计了一个这样的模型的确定性版本，它由一个带有时滞的常微分方程系统表示。在第二个随机模型中，又增加了两个部分：无症状个体的 A 类和隔离感染者的 L 类。很容易纳入社交距离措施等影响，并分析其后果。通过蒙特卡罗模拟获得数值解。提供了定量预测，这对于评估政治措施很有用，例如，得到的结果表明，基于群体免疫的策略风险太大。最后，根据意大利第二次感染的数据对模型进行了校准。
