Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanism
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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023183?viewType=HTML |
| _version_ | 1797953854147395584 |
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| author | Saima Rashid Fahd Jarad |
| author_facet | Saima Rashid Fahd Jarad |
| author_sort | Saima Rashid |
| collection | DOAJ |
| description | 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 ρ and fractal-dimension τ. 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. |
| first_indexed | 2024-04-10T23:09:46Z |
| format | Article |
| id | doaj.art-24dd3ee4ba644174afc634491f6e445e |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T23:09:46Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-24dd3ee4ba644174afc634491f6e445e2023-01-13T06:25:47ZengAIMS PressAIMS Mathematics2473-69882023-01-01823634367510.3934/math.2023183Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanismSaima Rashid0Fahd Jarad11. Department of Mathematics, Government College University, Faisalabad, Pakistan2. 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 ArabiaRecent 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 ρ and fractal-dimension τ. 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.https://www.aimspress.com/article/doi/10.3934/math.2023183?viewType=HTMLebola virus diseasefractal-fractional differential operatorsextinctionqualitative analysisstochastic analysis |
| spellingShingle | Saima Rashid Fahd Jarad Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanism AIMS Mathematics ebola virus disease fractal-fractional differential operators extinction qualitative analysis stochastic analysis |
| title | Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanism |
| title_full | Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanism |
| title_fullStr | Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanism |
| title_full_unstemmed | Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanism |
| title_short | Stochastic dynamics of the fractal-fractional Ebola epidemic model combining a fear and environmental spreading mechanism |
| title_sort | stochastic dynamics of the fractal fractional ebola epidemic model combining a fear and environmental spreading mechanism |
| topic | ebola virus disease fractal-fractional differential operators extinction qualitative analysis stochastic analysis |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023183?viewType=HTML |
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