论文标题
确切可解决的SIR模型，其扩展以及它们在敏感大流行预测中的应用
Exactly solvable SIR models, their extensions and their application to sensitive pandemic forecasting
论文作者
论文摘要
经典的流行动力学SIR模型完全通过四倍体解决，包括在一系列不完整的伽马函数中扩展的时间积分变换。该模型还被推广到任意时间依赖的感染率，并在控制参数取决于时间$ t $的累积感染时明确解决。数值结果是通过比较提供的。还考虑了SIR进行相互作用区域的自主和非自主概括，包括两个或多个相互作用区域的不可分割性。将简单的SIR模型降低到一个变量，使我们进入了广义的逻辑模型Richards模型，我们用来将其拟合墨西哥的COVID-19数据最多可容纳134天。预测各种配件引起的预测场景。就这些模型在鲁棒性方面的适用性批评了当前的大流行暴发。最后，我们获得了离散版本的理查兹模型的分叉图，显示了分叉与混乱的时期。
The classic SIR model of epidemic dynamics is solved completely by quadratures, including a time integral transform expanded in a series of incomplete gamma functions. The model is also generalized to arbitrary time-dependent infection rates and solved explicitly when the control parameter depends on the accumulated infections at time $t$. Numerical results are presented by way of comparison. Autonomous and non-autonomous generalizations of SIR for interacting regions are also considered, including non-separability for two or more interacting regions. A reduction of simple SIR models to one variable leads us to a generalized logistic model, Richards model, which we use to fit Mexico's COVID-19 data up to day number 134. Forecasting scenarios resulting from various fittings are discussed. A critique to the applicability of these models to current pandemic outbreaks in terms of robustness is provided. Finally, we obtain the bifurcation diagram for a discretized version of Richards model, displaying period doubling bifurcation to chaos.
