论文标题
一个用于预测COVID-19大流行传播的分数阶室模型
A fractional-order compartmental model for predicting the spread of the Covid-19 pandemic
论文作者
论文摘要
我们建议使用易感性，暴露，感染（无症状和有症状的），COVID-19-19-19的流行病的易感性，暴露，感染（无症状和症状），住院，恢复和死亡人数。我们研究所提出模型的性质和动力学。讨论了无病和地方性平衡点渐近稳定的条件。此外，我们研究了参数的敏感性，并使用田纳西州的数据（作为案例研究）来讨论模型参数的可识别性。模型中的非负参数是通过解决加利福尼亚，佛罗里达，佐治亚州，马里兰州，田纳西州，德克萨斯州，华盛顿和威斯康星州的经验数据的反问题获得的。基本的繁殖数被认为略高于一个临界值的临界价值，这表明诸如使用面罩，社交距离，接触式追踪以及甚至更长的家庭订单等更严格的措施需要强制执行以减轻病毒的传播。随着其中一些州的居住命令被撤销，我们看到案件的数量几乎立即增加，并且可能会继续增加，直到2020年底，除非采取更严格的措施。
We propose a time-fractional compartmental model (SEI$_A$I$_S$HRD) comprising of the susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized, recovered and dead population for the Covid-19 pandemic. We study the properties and dynamics of the proposed model. The conditions under which the disease-free and endemic equilibrium points are asymptotically stable are discussed. Furthermore, we study the sensitivity of the parameters and use the data from Tennessee state (as a case study) to discuss identifiability of the parameters of the model. The non-negative parameters in the model are obtained by solving inverse problems with empirical data from California, Florida, Georgia, Maryland, Tennessee, Texas, Washington and Wisconsin. The basic reproduction number is seen to be slightly above the critical value of one suggesting that stricter measures such as the use of face-masks, social distancing, contact tracing, and even longer stay-at-home orders need to be enforced in order to mitigate the spread of the virus. As stay-at-home orders are rescinded in some of these states, we see that the number of cases began to increase almost immediately and may continue to rise until the end of the year 2020 unless stricter measures are taken.
