A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factors
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 t...
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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.2023161?viewType=HTML |
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| author | Shahram Rezapour Sina Etemad Joshua Kiddy K. Asamoah Hijaz Ahmad Kamsing Nonlaopon |
| author_facet | Shahram Rezapour Sina Etemad Joshua Kiddy K. Asamoah Hijaz Ahmad Kamsing Nonlaopon |
| author_sort | Shahram Rezapour |
| collection | DOAJ |
| description | 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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| first_indexed | 2024-04-10T23:14:26Z |
| format | Article |
| id | doaj.art-6afbfdb53c6d4934b817ebb9c2863c91 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T23:14:26Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-6afbfdb53c6d4934b817ebb9c2863c912023-01-13T01:58:00ZengAIMS PressAIMS Mathematics2473-69882023-01-01823120316210.3934/math.2023161A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factorsShahram Rezapour0Sina Etemad1Joshua Kiddy K. Asamoah2Hijaz Ahmad3Kamsing Nonlaopon4. 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, Taiwan1. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran4. Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana5. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma RM, Italy6. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandMalaria 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. https://www.aimspress.com/article/doi/10.3934/math.2023161?viewType=HTMLfractal-fractional hybrid operatormalarianewton polynomialfixed pointstability |
| spellingShingle | 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 AIMS Mathematics fractal-fractional hybrid operator malaria newton polynomial fixed point stability |
| title | A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factors |
| title_full | A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factors |
| title_fullStr | A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factors |
| title_full_unstemmed | A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factors |
| title_short | A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factors |
| title_sort | mathematical approach for studying the fractal fractional hybrid mittag leffler model of malaria under some control factors |
| topic | fractal-fractional hybrid operator malaria newton polynomial fixed point stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023161?viewType=HTML |
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