Fractional-order dynamics of Chagas-HIV epidemic model with different fractional operators

Rahat Zarin; Amir Khan; Pushpendra Kumar; Usa Wannasingha Humphries; Rahat Zarin; Amir Khan; Pushpendra Kumar; Usa Wannasingha Humphries

doi:10.3934/math.20221041

AIMS Mathematics

2022, Volume 7, Issue 10: 18897-18924. doi: 10.3934/math.20221041

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Research article

Fractional-order dynamics of Chagas-HIV epidemic model with different fractional operators

1.
Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan
2.
Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan
3.
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
4.
Institute for the Future of Knowledge, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa

Received: 08 April 2022 Revised: 20 June 2022 Accepted: 29 June 2022 Published: 25 August 2022
MSC : 26A33, 34A08

In this research, we reformulate and analyze a co-infection model consisting of Chagas and HIV epidemics. The basic reproduction number $ R_0 $ of the proposed model is established along with the feasible region and disease-free equilibrium point $ E^0 $. We prove that $ E^0 $ is locally asymptotically stable when $ R_0 $ is less than one. Then, the model is fractionalized by using some important fractional derivatives in the Caputo sense. The analysis of the existence and uniqueness of the solution along with Ulam-Hyers stability is established. Finally, we solve the proposed epidemic model by using a novel numerical scheme, which is generated by Newton polynomials. The given model is numerically solved by considering some other fractional derivatives like Caputo, Caputo-Fabrizio and fractal-fractional with power law, exponential decay and Mittag-Leffler kernels.
- stability analysis,
- co-infection,
- reproduction number,
- fractional modeling
Citation: Rahat Zarin, Amir Khan, Pushpendra Kumar, Usa Wannasingha Humphries. Fractional-order dynamics of Chagas-HIV epidemic model with different fractional operators[J]. AIMS Mathematics, 2022, 7(10): 18897-18924. doi: 10.3934/math.20221041

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Abstract

In this research, we reformulate and analyze a co-infection model consisting of Chagas and HIV epidemics. The basic reproduction number $ R_0 $ of the proposed model is established along with the feasible region and disease-free equilibrium point $ E^0 $. We prove that $ E^0 $ is locally asymptotically stable when $ R_0 $ is less than one. Then, the model is fractionalized by using some important fractional derivatives in the Caputo sense. The analysis of the existence and uniqueness of the solution along with Ulam-Hyers stability is established. Finally, we solve the proposed epidemic model by using a novel numerical scheme, which is generated by Newton polynomials. The given model is numerically solved by considering some other fractional derivatives like Caputo, Caputo-Fabrizio and fractal-fractional with power law, exponential decay and Mittag-Leffler kernels.

References

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