Kouidere Abdelfatah, Youssoufi Lahcen El, Ferjouchia Hanane, Balatif Omar, Rachik Mostafa
LAMS, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sik, Hassan II University of Casablanca, Morocco.
Laboratory of Dynamical Systems, Mathematical Engineering Team (INMA), Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco.
Chaos Solitons Fractals. 2021 Apr;145:110777. doi: 10.1016/j.chaos.2021.110777. Epub 2021 Feb 12.
As of November 14, 2020, the number of people infected with the COVID-19 disease has reached more than 54 million people worldwide and more than 1323196 people have died, according to the World Health Organization. This requires many countries to impose a health emergency or quarantine, which has had positive results in reducing the spread of the COVID-19 pandemic, and it has also had negative economic, social and health effects. So, we suggest a mathematical model for the dynamics of how COVID-19 disease is spread, as well as a mathematical modeling for the dynamics of diabetes, then highlight the negative effect of quarantine has on the health of diabetics. Pontryagin's maximum principle is used to characterize the optimal controls, and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using MATLAB.
根据世界卫生组织的数据，截至2020年11月14日，全球感染新冠病毒疾病的人数已超过5400万人，死亡人数超过1323196人。这使得许多国家实施了卫生紧急状态或检疫措施，这些措施在减少新冠疫情传播方面取得了积极成果，但同时也产生了负面的经济、社会和健康影响。因此，我们提出了一个关于新冠病毒疾病传播动态的数学模型，以及一个关于糖尿病动态的数学模型，然后突出检疫措施对糖尿病患者健康的负面影响。利用庞特里亚金极大值原理来刻画最优控制，并通过迭代方法求解最优性系统。最后，使用MATLAB进行了一些数值模拟以验证理论分析。
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