Dynamics of COVID-19 mathematical model with stochastic perturbation

Zizhen Zhang; Anwar Zeb; Sultan Hussain; Ebraheem Alzahrani

doi:10.1186/s13662-020-02909-1

Dynamics of COVID-19 mathematical model with stochastic perturbation

Adv Differ Equ. 2020;2020(1):451. doi: 10.1186/s13662-020-02909-1. Epub 2020 Aug 28.

Authors

Zizhen Zhang¹, Anwar Zeb², Sultan Hussain², Ebraheem Alzahrani³

Affiliations

¹ School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, 233030 China.
² Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, 22060 Khyber Pakhtunkhwa Pakistan.
³ Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589 Saudi Arabia.

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: Extinction; Itô’s formula; Numerical analysis; Persistence; Stochastic COVID-19 model.