Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference

Xuan Leng, Asad Khan () and Anwarud Din ()
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Xuan Leng: School of Science, Hunan City University, Yiyang 413000, China
Asad Khan: School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China
Anwarud Din: Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Mathematics, 2023, vol. 11, issue 8, 1-18

Abstract: When an individual with confirmed or suspected COVID-19 is quarantined or isolated, the virus can linger for up to an hour in the air. We developed a mathematical model for COVID-19 by adding the point where a person becomes infectious and begins to show symptoms of COVID-19 after being exposed to an infected environment or the surrounding air. It was proven that the proposed stochastic COVID-19 model is biologically well-justifiable by showing the existence, uniqueness, and positivity of the solution. We also explored the model for a unique global solution and derived the necessary conditions for the persistence and extinction of the COVID-19 epidemic. For the persistence of the disease, we observed that R s 0 > 1 , and it was noticed that, for R s < 1 , the COVID-19 infection will tend to eliminate itself from the population. Supplementary graphs representing the solutions of the model were produced to justify the obtained results based on the analysis. This study has the potential to establish a strong theoretical basis for the understanding of infectious diseases that re-emerge frequently. Our work was also intended to provide general techniques for developing the Lyapunov functions that will help the readers explore the stationary distribution of stochastic models having perturbations of the nonlinear type in particular.

Keywords: stochastic model; air; environmental noise; persistence; numerical simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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