A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factors

Shahram Rezapour; Sina Etemad; Joshua Kiddy K. Asamoah; Hijaz Ahmad; Kamsing Nonlaopon; Shahram Rezapour; Sina Etemad; Joshua Kiddy K. Asamoah; Hijaz Ahmad; Kamsing Nonlaopon

doi:10.3934/math.2023161

AIMS Mathematics

2023, Volume 8, Issue 2: 3120-3162. doi: 10.3934/math.2023161

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Research article

A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factors

1.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
2.
Department of Mathematics, Kyuing Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
4.
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
5.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma RM, Italy
6.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 16 September 2022 Revised: 25 October 2022 Accepted: 01 November 2022 Published: 15 November 2022
MSC : 34A08, 65P99, 49J15

Malaria disease, which is of parasitic origin, has always been one of the challenges for human societies in areas with poor sanitation. The lack of proper distribution of drugs and lack of awareness of people in such environments cause us to see many deaths every year, especially in children under the age of five. Due to the importance of this issue, in this paper, a new five-compartmental $ (c_1, c_2) $-fractal-fractional $ \mathcal{SIR} $-$ \mathcal{SI} $-model of malaria disease for humans and mosquitoes is presented. We use the generalized Mittag-Leffler fractal-fractional derivatives to design such a mathematical model. In different ways, we study all theoretical aspects of solutions such as the existence, uniqueness and stability. A Newton polynomial that works in fractal-fractional settings is shown, which allows us to get some numerical trajectories. From the trajectories, we saw that an increase in antimalarial treatment in consideration to memory effects reduces the peak of sick individuals, and mosquito insecticide spraying minimizes the disease burden in all compartments.
- fractal-fractional hybrid operator,
- malaria,
- Newton polynomial,
- fixed point,
- stability
Citation: Shahram Rezapour, Sina Etemad, Joshua Kiddy K. Asamoah, Hijaz Ahmad, Kamsing Nonlaopon. A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factors[J]. AIMS Mathematics, 2023, 8(2): 3120-3162. doi: 10.3934/math.2023161

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Abstract

Malaria disease, which is of parasitic origin, has always been one of the challenges for human societies in areas with poor sanitation. The lack of proper distribution of drugs and lack of awareness of people in such environments cause us to see many deaths every year, especially in children under the age of five. Due to the importance of this issue, in this paper, a new five-compartmental $ (c_1, c_2) $-fractal-fractional $ \mathcal{SIR} $-$ \mathcal{SI} $-model of malaria disease for humans and mosquitoes is presented. We use the generalized Mittag-Leffler fractal-fractional derivatives to design such a mathematical model. In different ways, we study all theoretical aspects of solutions such as the existence, uniqueness and stability. A Newton polynomial that works in fractal-fractional settings is shown, which allows us to get some numerical trajectories. From the trajectories, we saw that an increase in antimalarial treatment in consideration to memory effects reduces the peak of sick individuals, and mosquito insecticide spraying minimizes the disease burden in all compartments.

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