Fouladi Somayeh, Kohandel Mohammad, Eastman Brydon
Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada.
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran.
Math Biosci Eng. 2022 Sep 1;19(12):12792-12813. doi: 10.3934/mbe.2022597.
The spread of SARS-CoV-2 in the Canadian province of Ontario has resulted in millions of infections and tens of thousands of deaths to date. Correspondingly, the implementation of modeling to inform public health policies has proven to be exceptionally important. In this work, we expand a previous model of the spread of SARS-CoV-2 in Ontario, "Modeling the impact of a public response on the COVID-19 pandemic in Ontario, " to include the discretized, Caputo fractional derivative in the susceptible compartment. We perform identifiability and sensitivity analysis on both the integer-order and fractional-order SEIRD model and contrast the quality of the fits. We note that both methods produce fits of similar qualitative strength, though the inclusion of the fractional derivative operator quantitatively improves the fits by almost 27% corroborating the appropriateness of fractional operators for the purposes of phenomenological disease forecasting. In contrasting the fit procedures, we note potential simplifications for future study. Finally, we use all four models to provide an estimate of the time-dependent basic reproduction number for the spread of SARS-CoV-2 in Ontario between January 2020 and February 2021.
截至目前，严重急性呼吸综合征冠状病毒2（SARS-CoV-2）在加拿大安大略省的传播已导致数百万例感染和数万人死亡。相应地，事实证明，运用模型为公共卫生政策提供依据极为重要。在这项工作中，我们扩展了之前关于SARS-CoV-2在安大略省传播的模型《模拟公众应对措施对安大略省COVID-19大流行的影响》，在易感人群 compartment 中纳入离散化的卡普托分数阶导数。我们对整数阶和分数阶SEIRD模型进行了可识别性和敏感性分析，并对比了拟合质量。我们注意到，两种方法产生的拟合在定性强度上相似，不过纳入分数阶导数算子在定量上使拟合效果提高了近27%，这证实了分数阶算子在现象学疾病预测方面的适用性。在对比拟合过程时，我们指出了未来研究可能的简化方向。最后，我们使用所有四个模型对2020年1月至2021年2月期间SARS-CoV-2在安大略省传播的时间依赖性基本再生数进行了估计。
