Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanism

Saima Rashid; Fahd Jarad; Saima Rashid; Fahd Jarad

doi:10.3934/math.2023183

AIMS Mathematics

2023, Volume 8, Issue 2: 3634-3675. doi: 10.3934/math.2023183

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Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanism

Saima Rashid ^{1
,
,},
Fahd Jarad ^{2,3,4
,
,}

1.
Department of Mathematics, Government College University, Faisalabad, Pakistan
2.
Department of Mathematics, Çankaya University, Ankara, Turkey
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
4.
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

Received: 11 August 2022 Revised: 08 October 2022 Accepted: 11 October 2022 Published: 24 November 2022
MSC : 46S40, 47H10, 54H25

Recent Ebola virus disease infections have been limited to human-to-human contact as well as the intricate linkages between the habitat, people and socioeconomic variables. The mechanisms of infection propagation can also occur as a consequence of variations in individual actions brought on by dread. This work studies the evolution of the Ebola virus disease by combining fear and environmental spread using a compartmental framework considering stochastic manipulation and a newly defined non-local fractal-fractional (F-F) derivative depending on the generalized Mittag-Leffler kernel. To determine the incidence of infection and person-to-person dissemination, we developed a fear-dependent interaction rate function. We begin by outlining several fundamental characteristics of the system, such as its fundamental reproducing value and equilibrium. Moreover, we examine the existence-uniqueness of non-negative solutions for the given randomized process. The ergodicity and stationary distribution of the infection are then demonstrated, along with the basic criteria for its eradication. Additionally, it has been studied how the suggested framework behaves under the F-F complexities of the Atangana-Baleanu derivative of fractional-order $ \rho $ and fractal-dimension $ \tau $. The developed scheme has also undergone phenomenological research in addition to the combination of nonlinear characterization by using the fixed point concept. The projected findings are demonstrated through numerical simulations. This research is anticipated to substantially increase the scientific underpinnings for understanding the patterns of infectious illnesses across the globe.
- Ebola virus disease,
- fractal-fractional differential operators,
- extinction,
- qualitative analysis,
- stochastic analysis
Citation: Saima Rashid, Fahd Jarad. Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanism[J]. AIMS Mathematics, 2023, 8(2): 3634-3675. doi: 10.3934/math.2023183

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Abstract

Recent Ebola virus disease infections have been limited to human-to-human contact as well as the intricate linkages between the habitat, people and socioeconomic variables. The mechanisms of infection propagation can also occur as a consequence of variations in individual actions brought on by dread. This work studies the evolution of the Ebola virus disease by combining fear and environmental spread using a compartmental framework considering stochastic manipulation and a newly defined non-local fractal-fractional (F-F) derivative depending on the generalized Mittag-Leffler kernel. To determine the incidence of infection and person-to-person dissemination, we developed a fear-dependent interaction rate function. We begin by outlining several fundamental characteristics of the system, such as its fundamental reproducing value and equilibrium. Moreover, we examine the existence-uniqueness of non-negative solutions for the given randomized process. The ergodicity and stationary distribution of the infection are then demonstrated, along with the basic criteria for its eradication. Additionally, it has been studied how the suggested framework behaves under the F-F complexities of the Atangana-Baleanu derivative of fractional-order $ \rho $ and fractal-dimension $ \tau $. The developed scheme has also undergone phenomenological research in addition to the combination of nonlinear characterization by using the fixed point concept. The projected findings are demonstrated through numerical simulations. This research is anticipated to substantially increase the scientific underpinnings for understanding the patterns of infectious illnesses across the globe.

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