3D-Chaotic discrete system of vector borne diseases using environment factor with deep analysis

Shaymaa H. Salih; Nadia M. G. Al-Saidi; Shaymaa H. Salih; Nadia M. G. Al-Saidi

doi:10.3934/math.2022219

AIMS Mathematics

2022, Volume 7, Issue 3: 3972-3987. doi: 10.3934/math.2022219

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3D-Chaotic discrete system of vector borne diseases using environment factor with deep analysis

Shaymaa H. Salih ¹,
Nadia M. G. Al-Saidi ^{2
,
,}

1.
Department of Mathematics, College of Science, Mustansiriyah University, Iraq
2.
Department of Applied Sciences, University of Technology, Iraq

Received: 08 October 2021 Accepted: 17 November 2021 Published: 13 December 2021
MSC : 37M20, 34H10

Vector-Borne Disease (VBD) is a disease that consequences as of an infection communicated to humans and other animals by blood-feeding anthropoids, like mosquitoes, fleas, and ticks. Instances of VBDs include Dengue infection, Lyme infection, West Nile virus, and malaria. In this effort, we formulate a parametric discrete-time chaotic system that involves an environmental factor causing VBD. Our suggestion is to study how the inclusion of the parasitic transmission media (PTM) in the system would impact the analysis results. We consider a chaotic formula of the PTM impact, separating two types of functions, the host and the parasite. The considered applications are typically characterized by chaotic dynamics, and thus chaotic systems are suitable for their modeling, with corresponding model parameters, that depend on control measures. Dynamical performances of the suggested system and its global stability are considered.
- differential operator,
- fractal chaotic system,
- fractal,
- locally fractional calculus,
- fractal dynamic system,
- difference system
Citation: Shaymaa H. Salih, Nadia M. G. Al-Saidi. 3D-Chaotic discrete system of vector borne diseases using environment factor with deep analysis[J]. AIMS Mathematics, 2022, 7(3): 3972-3987. doi: 10.3934/math.2022219

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Abstract

Vector-Borne Disease (VBD) is a disease that consequences as of an infection communicated to humans and other animals by blood-feeding anthropoids, like mosquitoes, fleas, and ticks. Instances of VBDs include Dengue infection, Lyme infection, West Nile virus, and malaria. In this effort, we formulate a parametric discrete-time chaotic system that involves an environmental factor causing VBD. Our suggestion is to study how the inclusion of the parasitic transmission media (PTM) in the system would impact the analysis results. We consider a chaotic formula of the PTM impact, separating two types of functions, the host and the parasite. The considered applications are typically characterized by chaotic dynamics, and thus chaotic systems are suitable for their modeling, with corresponding model parameters, that depend on control measures. Dynamical performances of the suggested system and its global stability are considered.

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