Dynamical behavior of a stochastic highly pathogenic avian influenza A (HPAI) epidemic model via piecewise fractional differential technique

Maysaa Al-Qureshi; Saima Rashid; Fahd Jarad; Mohammed Shaaf Alharthi; Maysaa Al-Qureshi; Saima Rashid; Fahd Jarad; Mohammed Shaaf Alharthi

doi:10.3934/math.2023089

AIMS Mathematics

2023, Volume 8, Issue 1: 1737-1756. doi: 10.3934/math.2023089

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Dynamical behavior of a stochastic highly pathogenic avian influenza A (HPAI) epidemic model via piecewise fractional differential technique

1.
Department of Mathematics, King Saud University, P.O.Box 22452, Riyadh 11495, Saudi Arabia
2.
Department of Mathematics, Saudi Electronic University, Riyadh, Saudi Arabia
3.
Department of Mathematics, Government College university, Faislabad, pakistan
4.
Department of Mathematics, Çankaya University, Ankara, Turkey
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
6.
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
7.
Department of Mathematics and Statistics, College of Science, Taif University, P.O.Box 11099, Taif 21944, Saudi Arabia

Received: 11 August 2022 Revised: 05 October 2022 Accepted: 11 October 2022 Published: 24 October 2022
MSC : 46S40, 47H10, 54H25

In this research, we investigate the dynamical behaviour of a HPAI epidemic system featuring a half-saturated transmission rate and significant evidence of crossover behaviours. Although simulations have proposed numerous mathematical frameworks to portray these behaviours, it is evident that their mathematical representations cannot adequately describe the crossover behaviours, particularly the change from deterministic reboots to stochastics. Furthermore, we show that the stochastic process has a threshold number $ {\bf R}_{0}^{s} $ that can predict pathogen extermination and mean persistence. Furthermore, we show that if $ {\bf R}_{0}^{s} > 1 $, an ergodic stationary distribution corresponds to the stochastic version of the aforementioned system by constructing a sequence of appropriate Lyapunov candidates. The fractional framework is expanded to the piecewise approach, and a simulation tool for interactive representation is provided. We present several illustrated findings for the system that demonstrate the utility of the piecewise estimation technique. The acquired findings offer no uncertainty that this notion is a revolutionary viewpoint that will assist mankind in identifying nature.
- HPAI epidemic model,
- Atangana-Baleanu operator,
- piecewise numerical scheme,
- ergodicity and stationary distribution,
- extinction
Citation: Maysaa Al-Qureshi, Saima Rashid, Fahd Jarad, Mohammed Shaaf Alharthi. Dynamical behavior of a stochastic highly pathogenic avian influenza A (HPAI) epidemic model via piecewise fractional differential technique[J]. AIMS Mathematics, 2023, 8(1): 1737-1756. doi: 10.3934/math.2023089

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Abstract

In this research, we investigate the dynamical behaviour of a HPAI epidemic system featuring a half-saturated transmission rate and significant evidence of crossover behaviours. Although simulations have proposed numerous mathematical frameworks to portray these behaviours, it is evident that their mathematical representations cannot adequately describe the crossover behaviours, particularly the change from deterministic reboots to stochastics. Furthermore, we show that the stochastic process has a threshold number $ {\bf R}_{0}^{s} $ that can predict pathogen extermination and mean persistence. Furthermore, we show that if $ {\bf R}_{0}^{s} > 1 $, an ergodic stationary distribution corresponds to the stochastic version of the aforementioned system by constructing a sequence of appropriate Lyapunov candidates. The fractional framework is expanded to the piecewise approach, and a simulation tool for interactive representation is provided. We present several illustrated findings for the system that demonstrate the utility of the piecewise estimation technique. The acquired findings offer no uncertainty that this notion is a revolutionary viewpoint that will assist mankind in identifying nature.

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