Dynamical Behaviors of Nonlinear Coronavirus (COVID-19) Model with Numerical Studies
- Khaled A. Gepreel1,2, Mohamed S. Mohamed1,3, Hammad Alotaibi1, Amr M. S. Mahdy1,2,*
1 Department of Mathematics, College of Science, Taif University, Taif, 21944, Saudi Arabia
2 Department of Mathematics, Zagazig University, Zagazig, 44519, Egypt
3 Department of Mathematics, Al-Azher University, Nasr City, 11884, Egypt
* Corresponding Author: Amr M. S. Mahdy. Email:
,
(This article belongs to this Special Issue: Mathematical aspects of the Coronavirus Disease 2019 (COVID-19): Analysis and Control)
2 Department of Mathematics, Zagazig University, Zagazig, 44519, Egypt
3 Department of Mathematics, Al-Azher University, Nasr City, 11884, Egypt
* Corresponding Author: Amr M. S. Mahdy. Email:
(This article belongs to this Special Issue: Mathematical aspects of the Coronavirus Disease 2019 (COVID-19): Analysis and Control)
Received 19 June 2020; Accepted 05 October 2020; Issue published 12 January 2021
Abstract
The development of mathematical modeling of infectious diseases is a key research area in various fields including ecology and epidemiology. One aim of these models is to understand the dynamics of behavior in infectious diseases. For the new strain of coronavirus (COVID-19), there is no vaccine to protect people and to prevent its spread so far. Instead, control strategies associated with health care, such as social distancing, quarantine, travel restrictions, can be adopted to control the pandemic of COVID-19. This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods: the homotopy perturbation method (HPM) and the modified reduced differential transform method (MRDTM). We invoke a novel signal flow graph that is used to describe the COVID-19 model. Through our mathematical studies, it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus. The numerical simulation results are in reasonable agreement with the study predictions. The free equilibrium and stability point for the COVID-19 model are investigated. Also, the existence of a uniformly stable solution is proved.
Keywords
Nonlinear COVID-19 model; equilibrium point; stability; existence of uniformly stable; signal flow graph; homotopy perturbation method; reduced differential transform method
Cite This Article
K. A. Gepreel, M. S. Mohamed, H. Alotaibi and A. M., "Dynamical behaviors of nonlinear coronavirus (covid-19) model with numerical studies," Computers, Materials & Continua, vol. 67, no.1, pp. 675–686, 2021.
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