Shatanawi Wasfi, Raza Ali, Arif Muhammad Shoaib, Abodayeh Kamaledin, Rafiq Muhammad, Bibi Mairaj
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402 Taiwan.
Adv Differ Equ. 2020;2020(1):505. doi: 10.1186/s13662-020-02960-y. Epub 2020 Sep 18.
The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus. The model adopts the form of a nonlinear stochastic susceptible-infected-treated-recovered system, and we investigate the stochastic reproduction dynamics, both analytically and numerically. We applied different standard and nonstandard computational numerical methods for the solution of the stochastic system. The design of a nonstandard computation method for the stochastic system is innovative. Unfortunately, standard computation numerical methods are time-dependent and violate the structure properties of models, such as positivity, boundedness, and dynamical consistency of the stochastic system. To that end, convergence analysis of nonstandard computational methods and simulation with a comparison of standard computational methods are presented.
当前的工作致力于研究和探索随机非线性数学大流行模型，以描述新型冠状病毒的动态。该模型采用非线性随机易感-感染-治疗-康复系统的形式，我们通过解析和数值方法研究随机繁殖动态。我们应用了不同的标准和非标准计算数值方法来求解随机系统。随机系统非标准计算方法的设计具有创新性。不幸的是，标准计算数值方法依赖于时间，并且违反了模型的结构特性，如随机系统的正性、有界性和动态一致性。为此，给出了非标准计算方法的收敛性分析以及与标准计算方法比较的模拟结果。
