Stochastic epidemic model for the dynamics of novel coronavirus transmission

Tahir Khan; Fathalla A. Rihan; Muhammad Bilal Riaz; Mohamed Altanji; Abdullah A. Zaagan; Hijaz Ahmad; Tahir Khan; Fathalla A. Rihan; Muhammad Bilal Riaz; Mohamed Altanji; Abdullah A. Zaagan; Hijaz Ahmad

doi:10.3934/math.2024608

AIMS Mathematics

2024, Volume 9, Issue 5: 12433-12457. doi: 10.3934/math.2024608

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Research article

Stochastic epidemic model for the dynamics of novel coronavirus transmission

1.
Department of Mathematical Sciences, UAE University, Al-Ain, P.O. Box 15551, United Arab Emirates
2.
IT4Innovations, VSB – Technical University of Ostrava, Ostrava, Czech Republic
3.
Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
4.
Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia
5.
Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia
6.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina 42210, Saudi Arabia
7.
Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Mishref, Kuwait
8.
Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey

Received: 22 February 2024 Accepted: 21 March 2024 Published: 29 March 2024
MSC : 26A33, 34A08, 34A12

Stochastic differential equation models are important and provide more valuable outputs to examine the dynamics of SARS-CoV-2 virus transmission than traditional models. SARS-CoV-2 virus transmission is a contagious respiratory disease that produces asymptomatically and symptomatically infected individuals who are susceptible to multiple infections. This work was purposed to introduce an epidemiological model to represent the temporal dynamics of SARS-CoV-2 virus transmission through the use of stochastic differential equations. First, we formulated the model and derived the well-posedness to show that the proposed epidemiological problem is biologically and mathematically feasible. We then calculated the stochastic reproductive parameters for the proposed stochastic epidemiological model and analyzed the model extinction and persistence. Using the stochastic reproductive parameters, we derived the condition for disease extinction and persistence. Applying these conditions, we have performed large-scale numerical simulations to visualize the asymptotic analysis of the model and show the effectiveness of the results derived.
- stochastic differential equations,
- existence analysis,
- Itô formula,
- Lyapunov function,
- extinction,
- persistence,
- Milstein's higher order scheme,
- numerical simulations
Citation: Tahir Khan, Fathalla A. Rihan, Muhammad Bilal Riaz, Mohamed Altanji, Abdullah A. Zaagan, Hijaz Ahmad. Stochastic epidemic model for the dynamics of novel coronavirus transmission[J]. AIMS Mathematics, 2024, 9(5): 12433-12457. doi: 10.3934/math.2024608

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Abstract

Stochastic differential equation models are important and provide more valuable outputs to examine the dynamics of SARS-CoV-2 virus transmission than traditional models. SARS-CoV-2 virus transmission is a contagious respiratory disease that produces asymptomatically and symptomatically infected individuals who are susceptible to multiple infections. This work was purposed to introduce an epidemiological model to represent the temporal dynamics of SARS-CoV-2 virus transmission through the use of stochastic differential equations. First, we formulated the model and derived the well-posedness to show that the proposed epidemiological problem is biologically and mathematically feasible. We then calculated the stochastic reproductive parameters for the proposed stochastic epidemiological model and analyzed the model extinction and persistence. Using the stochastic reproductive parameters, we derived the condition for disease extinction and persistence. Applying these conditions, we have performed large-scale numerical simulations to visualize the asymptotic analysis of the model and show the effectiveness of the results derived.

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