Mohammed Wael W, Aly E S, Matouk A E, Albosaily S, Elabbasy E M
Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 2440, Saudi Arabia.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
Results Phys. 2021 Jul;26:104432. doi: 10.1016/j.rinp.2021.104432. Epub 2021 Jun 15.
COVID-19 has become a world wide pandemic since its first appearance at the end of the year 2019. Although some vaccines have already been announced, a new mutant version has been reported in UK. We certainly should be more careful and make further investigations to the virus spread and dynamics. This work investigates dynamics in Lotka-Volterra based Models of COVID-19. The proposed models involve fractional derivatives which provide more adequacy and realistic description of the natural phenomena arising from such models. Existence and boundedness of non-negative solution of the fractional model is proved. Local stability is also discussed based on Matignon's stability conditions. Numerical results show that the fractional parameter has effect on flattening the curves of the coexistence steady state. This interesting foundation might be used among the public health strategies to control the spread of COVID-19 and its mutated versions.
自2019年底首次出现以来，新冠病毒已成为全球大流行疾病。尽管已经公布了一些疫苗，但英国报告了一种新的突变版本。我们当然应该更加谨慎，并对病毒的传播和动态进行进一步调查。这项工作研究了基于Lotka-Volterra的新冠病毒模型中的动态。所提出的模型涉及分数阶导数，它能更充分、更现实地描述此类模型中出现的自然现象。证明了分数阶模型非负解的存在性和有界性。还基于马蒂尼翁稳定性条件讨论了局部稳定性。数值结果表明，分数阶参数对平缓共存稳态曲线有影响。这一有趣的发现可用于公共卫生策略中，以控制新冠病毒及其突变版本的传播。
