Kumar Pushpendra, Erturk Vedat Suat, Murillo-Arcila Marina
Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab 151001, India.
Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Atakum 55200, Samsun, Turkey.
Results Phys. 2021 May;24:104213. doi: 10.1016/j.rinp.2021.104213. Epub 2021 Apr 20.
The most dangerous disease of this decade or COVID-19 is yet not over. The whole world is facing this threat and trying to stand together to defeat this pandemic. Many countries have defeated this virus by their strong control strategies and many are still trying to do so. To date, some countries have prepared a vaccine against this virus but not in an enough amount. In this research article, we proposed a new SEIRS dynamical model by including the vaccine rate. First we formulate the model with integer order and after that we generalize it in Atangana-Baleanu derivative sense. The high motivation to apply Atangana-Baleanu fractional derivative on our model is to explore the dynamics of the model more clearly. We provide the analysis of the existence of solution for the given fractional SEIRS model. We use the famous Predictor-Corrector algorithm to derive the solution of the model. Also, the analysis for the stability of the given algorithm is established. We simulate number of graphs to see the role of vaccine on the dynamics of the population. For practical simulations, we use the parameter values which are based on real data of Spain. The main motivation or aim of this research study is to justify the role of vaccine in this tough time of COVID-19. A clear role of vaccine at this crucial time can be realized by this study.
这十年最危险的疾病——新型冠状病毒肺炎（COVID-19）尚未结束。全世界都面临着这一威胁，并齐心协力抗击这场大流行病。许多国家通过强有力的防控策略战胜了这种病毒，还有许多国家仍在努力。迄今为止，一些国家已研制出针对这种病毒的疫苗，但数量不足。在这篇研究文章中，我们通过纳入疫苗接种率提出了一个新的SEIRS动力学模型。首先，我们建立了整数阶模型，之后在阿坦加纳-巴莱努导数意义下对其进行了推广。在我们的模型中应用阿坦加纳-巴莱努分数阶导数的主要动机是更清晰地探究模型的动态变化。我们对给定的分数阶SEIRS模型的解的存在性进行了分析。我们使用著名的预估-校正算法来求解该模型。此外，还对给定算法的稳定性进行了分析。我们模拟了大量图表以观察疫苗在人群动态变化中的作用。在实际模拟中，我们使用了基于西班牙真实数据的参数值。这项研究的主要动机或目的是证明疫苗在COVID-19这一艰难时期所起的作用。通过这项研究可以明确疫苗在这一关键时期所起的作用。
