论文标题
SARS-COV-2(COVID-19)疾病的分数最佳控制模型
Fractional Optimal Control Model of SARS-CoV-2 (COVID-19) Disease in Ghana
论文作者
论文摘要
研究重点是分数差分方程带来的最佳控制问题,实际上已广泛应用。但是,由于它们仍然是开放式且具有挑战性的,因此分数数学建模和最佳控制问题的许多问题需要额外的研究。使用Atangana Baleanu Caputo Sense中定义的分数衍生物,我们改变了文献中提出的整数模型。我们证明了溶液的存在,唯一性,平衡点,基本繁殖数和平衡点的局部稳定性。将操作员的数值方法付诸实践,以获得数值模拟,以备份分析结论。将部分最佳控制纳入模型中,以确定控制疾病的最有效的干预策略。利用加纳在2020年3月至2021年3月的几个月中的实际数据,该模型已验证。模拟的结果表明,分数算子显着影响每个隔室,并且当v> 0.6时,人口的发病率上升。对最有效的控制技术的检查发现,社会排斥和疫苗接种都是停止疾病发展的非常有效的方法。
Research focus on optimal control problems brought on by fractional differential equations has been extensively applied in practice. However, because they are still open-ended and challenging, a number of problems with fractional mathematical modeling and problems with optimal control require additional study. Using fractional-order derivatives defined in the Atangana Baleanu Caputo sense, we alter the integer-order model that has been proposed in the literature. We prove the solution's existence, uniqueness, equilibrium points, fundamental reproduction number, and local stability of the equilibrium points. The operator's numerical approach was put into practice to obtain a numerical simulation to back up the analytical conclusions. Fractional optimum controls were incorporated into the model to identify the most efficient intervention strategies for controlling the disease. Utilizing actual data from Ghana for the months of March 2020 to March 2021, the model is validated. The simulation's results show that the fractional operator significantly affected each compartment and that the incidence rate of the population rose when v>0.6. The examination of the most effective control technique discovered that social exclusion and vaccination were both very effective methods for halting the development of the illness.