Dynamics of COVID-19 mathematical model with stochastic perturbation
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(2020) 2020:451
RESEARCH
Open Access
Dynamics of COVID-19 mathematical model with stochastic perturbation Zizhen Zhang1 , Anwar Zeb2* , Sultan Hussain2 and Ebraheem Alzahrani3 *
Correspondence: [email protected] 2 Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Khyber Pakhtunkhwa, Pakistan Full list of author information is available at the end of the article
Abstract Acknowledging many effects on humans, which are ignored in deterministic models for COVID-19, in this paper, we consider stochastic mathematical model for COVID-19. Firstly, the formulation of a stochastic susceptible–infected–recovered model is presented. Secondly, we devote with full strength our concentrated attention to sufficient conditions for extinction and persistence. Thirdly, we examine the threshold of the proposed stochastic COVID-19 model, when noise is small or large. Finally, we show the numerical simulations graphically using MATLAB. Keywords: Stochastic COVID-19 model; Itô’s formula; Extinction; Persistence; Numerical analysis
1 Introduction There are many people who are currently alert of the outburst of COVID-19, which was recognized in China in December of 2019. As of this conformation, each continent has been influenced by this profoundly infectious disease, with about million cases analyzed in more than 200 nations around the world. The reason for this episode is another infection, known as the extremely intense respiratory disorder coronavirus 2 (SARS-CoV-2). On February 12, 2020, WHO named this disease coronavirus. The rapid spread of coronavirus COVID-19 is of great interest and has the attention of governments, medical doctors and public/private health organizations because of its high rate of spreading and the significant number of deaths that occurred specially in China, Italy, Iran, USA, UK, Turkey, Pakistan, and India. In the meantime, many doctors, mathematicians, pharmacists, biologists and chemists are trying to study the behavior of COVID-19, which is a pandemic initiated from China [1]. Actually, this virus was initiated from Wuhan, China. This is a vector transmission because its required source is in the form of human-to-human spread. It means the vector for this disease is people; so far all the governments restricted the people to keep distance from each other but the public is careless in this situation. On the mathematical side, the authors applied modified SIR (susceptible, infected and recovered), SEIR (susceptible, exposed, infected and recovered) and SIRS (susceptible, infected and recovered, susceptible) models to determine the actual number of infected by COVID-19, and specific burdens on isolation wards and intensive care units, similarly, using different scenarios for how to control the quick spread of this viral disease. Nesteruk [2], studied the © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as
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