Structure Preserving Algorithm for Fractional Order Mathematical Model of COVID-19

• Published in: Computers, materials & continua materials & continua, 2022, Vol.71 (2), p.2141-2157
• Main Authors: Iqbal, Zafar, Aziz-ur Rehman, Muhammad, Ahmed, Nauman, Raza, Ali, Rafiq, Muhammad, Khan, Ilyas, Sooppy Nisar, Kottakkaran
• Format: Article
• Language: English
• Subjects: Algorithms; Coronaviruses; COVID-19; Finite difference method; Infectious diseases; Mathematical models; Routh-Hurwitz criterion; Stability analysis
• ISSN: 1546-2226; 1546-2218; 1546-2226
• DOI: 10.32604/cmc.2022.013906

In this article, a brief biological structure and some basic properties of COVID-19 are described. A classical integer order model is modified and converted into a fractional order model with as order of the fractional derivative. Moreover, a valued structure preserving the numerical design, coined as Grunwald–Letnikov non-standard finite difference scheme, is developed for the fractional COVID-19 model. Taking into account the importance of the positivity and boundedness of the state variables, some productive results have been proved to ensure these essential features. Stability of the model at a corona free and a corona existing equilibrium points is investigated on the basis of Eigen values. The Routh–Hurwitz criterion is applied for the local stability analysis. An appropriate example with fitted and estimated set of parametric values is presented for the simulations. Graphical solutions are displayed for the chosen values of (fractional order of the derivatives). The role of quarantined policy is also determined gradually to highlight its significance and relevancy in controlling infectious diseases. In the end, outcomes of the study are presented.