Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues

Saima Rashid; Rehana Ashraf; Qurat-Ul-Ain Asif; Fahd Jarad; Saima Rashid; Rehana Ashraf; Qurat-Ul-Ain Asif; Fahd Jarad

doi:10.3934/mbe.2022539

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 11563-11594. doi: 10.3934/mbe.2022539

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Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues

1.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
2.
Department of Mathematics, Lahore College for Women University, Lahore, Pakistan
3.
Department of Physics, Government College University, Faisalabad 38000, Pakistan
4.
Department of Mathmatics, Cankaya 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

Academic Editor: Xiang-Sheng Wang

Received: 20 July 2022 Revised: 31 July 2022 Accepted: 02 August 2022 Published: 12 August 2022

In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existence-uniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of non-negative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-Baleanu-Caputo derivative incorporating fractional-order $ \alpha $ and fractal-dimension $ \wp $ have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.
- immune effector response model,
- fractal-fractional derivative operator,
- Brownian motion,
- ergodicity and stationary distribution
Citation: Saima Rashid, Rehana Ashraf, Qurat-Ul-Ain Asif, Fahd Jarad. Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11563-11594. doi: 10.3934/mbe.2022539

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Abstract

In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existence-uniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of non-negative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-Baleanu-Caputo derivative incorporating fractional-order $ \alpha $ and fractal-dimension $ \wp $ have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.

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