Mathematical analysis and numerical simulations of the piecewise dynamics model of Malaria transmission: A case study in Yemen

K. A. Aldwoah; Mohammed A. Almalahi; Mansour A. Abdulwasaa; Kamal Shah; Sunil V. Kawale; Muath Awadalla; Jihan Alahmadi; K. A. Aldwoah; Mohammed A. Almalahi; Mansour A. Abdulwasaa; Kamal Shah; Sunil V. Kawale; Muath Awadalla; Jihan Alahmadi

doi:10.3934/math.2024216

AIMS Mathematics

2024, Volume 9, Issue 2: 4376-4408. doi: 10.3934/math.2024216

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Mathematical analysis and numerical simulations of the piecewise dynamics model of Malaria transmission: A case study in Yemen

1.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Al Madinah 42351, Saudi Arabia
2.
Department of Mathematics, Hajjah University, Hajjah, Yemen
3.
Department of Statistics, Taiz University, Taiz, Yemen
4.
Department of Statistics, BAMU University, Aurangabad, (M.S), India
5.
Department of Mathematics, University of Malakand, Chakdara Dir (Lower), 18000 Khyber Pakhtunkhawa, Pakistan
6.
Department of Computer Science and Mathematics, Lebanese American University, Byblos Lebanon
7.
Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia
8.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Received: 28 November 2023 Revised: 28 December 2023 Accepted: 02 January 2024 Published: 17 January 2024
MSC : 92B05, 34A12, 34D20, 65C20

This study presents a mathematical model capturing Malaria transmission dynamics in Yemen, incorporating a social hierarchy structure. Piecewise Caputo-Fabrizio derivatives are utilized to effectively capture intricate dynamics, discontinuities, and different behaviors. Statistical data from 2000 to 2021 is collected and analyzed, providing predictions for Malaria cases in Yemen from 2022 to 2024 using Eviews and Autoregressive Integrated Moving Average models. The model investigates the crossover effect by dividing the study interval into two subintervals, establishing existence, uniqueness, positivity, and boundedness of solutions through fixed-point techniques and fractional-order properties of the Laplace transformation. The basic reproduction number is computed using a next-generation technique, and numerical solutions are obtained using the Adams-Bashforth method. The results are comprehensively discussed through graphs. The obtained results can help us to better control and predict the spread of the disease.
- Malaria model,
- piecewise Caputo-Fabrizio fractional derivative,
- statistical analysis
Citation: K. A. Aldwoah, Mohammed A. Almalahi, Mansour A. Abdulwasaa, Kamal Shah, Sunil V. Kawale, Muath Awadalla, Jihan Alahmadi. Mathematical analysis and numerical simulations of the piecewise dynamics model of Malaria transmission: A case study in Yemen[J]. AIMS Mathematics, 2024, 9(2): 4376-4408. doi: 10.3934/math.2024216

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Abstract

This study presents a mathematical model capturing Malaria transmission dynamics in Yemen, incorporating a social hierarchy structure. Piecewise Caputo-Fabrizio derivatives are utilized to effectively capture intricate dynamics, discontinuities, and different behaviors. Statistical data from 2000 to 2021 is collected and analyzed, providing predictions for Malaria cases in Yemen from 2022 to 2024 using Eviews and Autoregressive Integrated Moving Average models. The model investigates the crossover effect by dividing the study interval into two subintervals, establishing existence, uniqueness, positivity, and boundedness of solutions through fixed-point techniques and fractional-order properties of the Laplace transformation. The basic reproduction number is computed using a next-generation technique, and numerical solutions are obtained using the Adams-Bashforth method. The results are comprehensively discussed through graphs. The obtained results can help us to better control and predict the spread of the disease.

References

[1]	Malaria control and elimination, World Health Organization, 2021. Available from: https://www.who.int/news-room/fact-sheets/detail/Malaria.
[2]	E. Massad, G. Z. Laporta, J. E. Conn, L. S. Chaves, E. S. Bergo, E. A. G. Figueira, et al., The risk of malaria infection for travelers visiting the Brazilian Amazonian region: a mathematical modeling approach, Travel Med. Infect. Dis., 37 (2020), 101792. https://doi.org/10.1016/j.tmaid.2020.101792 doi: 10.1016/j.tmaid.2020.101792
[3]	S. Lai, J. Sun, N. W. Ruktanonchai, S. Zhou, J. Yu, I. Routledge, et al., Changing epidemiology and challenges of malaria in China towards elimination, Malar J., 18 (2019), 107. https://doi.org/10.1186/s12936-019-2736-8 doi: 10.1186/s12936-019-2736-8
[4]	R. M. Corder, G. A. Paula, A. Pincelli, M. U. Ferreira, Statistical modeling of surveillance data to identify correlates of urban Malaria risk: A population-based study in the Amazon Basin, PLoS One, 14 (2019), e0220980. https://doi.org/10.1371/journal.pone.0220980 doi: 10.1371/journal.pone.0220980
[5]	H. H. Hussien, F. H. Eissa, K. E. Awadalla, Statistical methods for predicting Malaria incidences using data from Sudan, Malaria Res. Treat., 2017 (2017), 4205957. https://doi.org/10.1155/2017/4205957 doi: 10.1155/2017/4205957
[6]	Malaria communication strategies: a guide for Malaria program managers, World Health Organization, 2019. Available from: https://www.mmv.org/Malaria-guidelines.
[7]	J. P. Daily, A. Minuti, N. Khan, Diagnosis, treatment, and prevention of Malaria in the US: A review, JAMA, 328 (2022), 460–471. https://doi.org/10.1001/jama.2022.12366 doi: 10.1001/jama.2022.12366
[8]	Q. Liu, W. Jing, L. Kang, J. Liu, M. Liu, Trends of the global, regional and national incidence of Malaria in 204 countries from 1990 to 2019 and implications for Malaria prevention, J. Travel Med., 28 (2021), taab046. https://doi.org/10.1093/jtm/taab046 doi: 10.1093/jtm/taab046
[9]	A. A. Kilbas, H. M. Shrivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam: Elsevier, 2006.
[10]	I. Podlubny, Fractional Differential Equations, San Diego: Academic Press, 1999.
[11]	M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl., 1 (2015), 73–85. http://dx.doi.org/10.12785/pfda/010201 doi: 10.12785/pfda/010201
[12]	A. Atangana, D. Baleanu, New fractional derivative with non-local and non-singular kernel, Therm. Sci., 20 (2016), 757–763.
[13]	W. Adel, Y. A. Amer, E. S. Youssef, A. M. Mahdy, Mathematical analysis and simulations for a Caputo-Fabrizio fractional COVID-19 model, Part. Differ. Equ. Appl. Math., 8 (2023), 100558. https://doi.org/10.1016/j.padiff.2023.100558 doi: 10.1016/j.padiff.2023.100558
[14]	A. El-Mesady, W. Adel, A. A. Elsadany, A. Elsonbaty, Stability analysis and optimal control strategies of a fractional-order monkeypox virus infection model, Phys. Scripta, 98 (2023), 095256. https://doi.org/10.1088/1402-4896/acf16f doi: 10.1088/1402-4896/acf16f
[15]	A. Elsonbaty, M. Alharbi, A. El-Mesady, W. Adel, Dynamical analysis of a novel discrete fractional lumpy skin disease model, Part. Differ. Equ. Appl. Math., 9 (2023), 100604. https://doi.org/10.1016/j.padiff.2023.100604 doi: 10.1016/j.padiff.2023.100604
[16]	W. Li, Y. Guan, J. Cao, F. Xu, A note on global stability of a degenerate diffusion avian influenza model with seasonality and spatial Heterogeneity, Appl. Math. Lett., 148 (2024), 108884. https://doi.org/10.1016/j.aml.2023.108884 doi: 10.1016/j.aml.2023.108884
[17]	W. Li, J. Ji, L. Huang, L. Zhang, Global dynamics and control of malicious signal transmission in wireless sensor networks, Nonlinear Anal, Hybrid Syst., 48 (2023), 101324. https://doi.org/10.1016/j.nahs.2022.101324 doi: 10.1016/j.nahs.2022.101324
[18]	A. Atangana, S. I. Araz, New concept in calculus: Piecewise differential and integral operators, Chaos Solit. Fract., 145 (2021), 110638. https://doi.org/10.1016/j.chaos.2020.110638 doi: 10.1016/j.chaos.2020.110638
[19]	M. B. Jeelani, A. S. Alnahdi, M. S. Abdo, M. A. Almalahi, N. H. Alharthi, K. Shah, A generalized fractional order model for COV-2 with vaccination effect using real data, Fractals, 31 (2023), 2340042. https://doi.org/10.1142/S0218348X2340042X doi: 10.1142/S0218348X2340042X
[20]	A. Atangana, J. F. Gómez-Aguilar, Fractional derivatives with no-index law property: Application to chaos and statistics, Chaos Solit. Fract., 114 (2018), 516–535. https://doi.org/10.1016/j.chaos.2018.07.033 doi: 10.1016/j.chaos.2018.07.033
[21]	R. T. Alqahtani, S. Ahmad, A. Akgül, On Numerical analysis of bio-ethanol production model with the effect of recycling and death rates under fractal fractional operators with three different kernels, Mathematics, 10 (2022), 1102. https://doi.org/10.3390/math10071102 doi: 10.3390/math10071102
[22]	S. R. Khirsariya, S. B. Rao, Solution of fractional Sawada-kotera-ito equation using Caputo and Atangana-Baleanu derivatives, Math. Meth. Appl. Sci., 46 (2023), 16072–16091. https://doi.org/10.1002/mma.9438 doi: 10.1002/mma.9438
[23]	A. Khan, J. F. Gómez-Aguilar, T. S. Khan, H. Khan, Stability analysis and numerical solutions of fractional order HIV/AIDS model, Chaos Solit. Fract., 122 (2019), 119–128. https://doi.org/10.1016/j.chaos.2019.03.022 doi: 10.1016/j.chaos.2019.03.022
[24]	K. A. Aldwoah, M. A. Almalahi, K. Shah, Theoretical and numerical simulations on the hepatitis B virus model through a piecewise fractional order, Fractal Fract., 7 (2023), 844. https://doi.org/10.3390/fractalfract7120844 doi: 10.3390/fractalfract7120844
[25]	M. A. Almalahi, S. K. Panchal, W. Shatanawi, M. S. Abdo, K. Shah, K. Abodayeh, Analytical study of transmission dynamics of 2019-nCoV pandemic via fractal fractional operator, Results Phys., 24 (2021), 104045. https://doi.org/10.1016/j.rinp.2021.104045 doi: 10.1016/j.rinp.2021.104045
[26]	M. Sinan, H. Ahmad, Z. Ahmad, J. Baili, S. Murtaza, M. A. Aiyashi, et al., Fractional mathematical modeling of Malaria disease with treatment & insecticides, Results Phys., 34 (2022), 105220. https://doi.org/10.1016/j.rinp.2022.105220 doi: 10.1016/j.rinp.2022.105220
[27]	S. Rezapour, S. Etemad, J. K. Asamoah, H. Ahmad, K. Nonlaopon, A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of Malaria under some control factors, AIMS Math., 8 (2023), 3120–3162. https://doi.org/10.3934/math.2023161 doi: 10.3934/math.2023161
[28]	A. I. Abioye, O. J. Peter, H. A. Ogunseye, F. A. Oguntolu, T. A. Ayoola, A. O. Oladapo, et al., A fractional-order mathematical model for Malaria and COVID-19 co-infection dynamics, Health. Anal., 4 (2023), 100210. https://doi.org/10.1016/j.health.2023.100210 doi: 10.1016/j.health.2023.100210
[29]	M. M. Ibrahim, M. A. Kamran, M. M. Naeem Mannan, S. Kim, I. H. Jung, Impact of awareness to control Malaria disease: A mathematical modeling approach, Complexity, 2020 (2020), 8657410. https://doi.org/10.1155/2020/8657410 doi: 10.1155/2020/8657410
[30]	S. Olaniyi, M. Mukamuri, K. O. Okosun, O. A. Adepoju, Mathematical analysis of a social hierarchy-structured model for Malaria transmission dynamics, Results Phys., 34 (2022), 104991. https://doi.org/10.1016/j.rinp.2021.104991 doi: 10.1016/j.rinp.2021.104991
[31]	F. Al Basir, T. Abraha, Mathematical modelling and optimal control of malaria using awareness-based interventions, Mathematics, 11 (2023), 1687. https://doi.org/10.3390/math11071687 doi: 10.3390/math11071687
[32]	S. Muhammad, O. J. Algahtani, S. Saifullah, A. Ali, Theoretical and numerical aspects of the Malaria transmission model with piecewise technique, AIMS Math., 8 (2023), 28353–28375. https://doi.org/10.3934/math.20231451 doi: 10.3934/math.20231451
[33]	Series of Statistical Yearbook for the years (2000–2021), Central Statistical Organization, Ministry of Planning and International Cooperation, Republic of Yemen.Sana'a, 2021.
[34]	T. Lancet, Malaria in 2022: A year of opportunity, Lancet, 399 (10335), 1573–173. https://doi.org/10.1016/S0140-6736(22)00729-2
[35]	Z. Luo, X. Jia, J. Bao, Z. Song, H. Zhu, M. Liu, et al., A combined model of SARIMA and prophet models in forecasting AIDS incidence in henan province, China. Int. J. Environ. Res. Public Health, 19 (2022), 5910. https://doi.org/10.3390/ijerph19105910 doi: 10.3390/ijerph19105910
[36]	L. Onambele, S. Guillen-Aguinaga, L. Guillen-Aguinaga, W. Ortega-Leon, R. Montejo, R. Alas-Brun, et al., Trends, projections, and regional disparities of maternal mortality in Africa (1990–2030): An ARIMA forecasting approach, Epidemiologia, 4 (2023), 322–351. https://doi.org/10.3390/epidemiologia4030032 doi: 10.3390/epidemiologia4030032
[37]	M. A. K. Fatmawati, E. Bonyah, Z. Hammouch, E. M. Shaiful, A mathematical model of tuberculosis (TB) transmission with children and adults groups: A fractional model, AIMS Math., 5 (2020), 2813–2842. http://dx.doi.org/10.3934/math.2020181 doi: 10.3934/math.2020181
[38]	S. Chatterjee, A. Sarkar, S. Chatterjee, M. Karmakar, R. Paul, Studying the progress of COVID-19 outbreak in India using SIRD model, Indian J. Phys., 95 (2021), 1941–1957. https://doi.org/10.1007/s12648-020-01766-8 doi: 10.1007/s12648-020-01766-8
[39]	T. Mathevet, M. L. Lepiller, A. Mangin, Application of time-series analyses to the hydrological functioning of an Alpine karstic system: the case of Bange-L'Eau-Morte, Hydrol. Earth Syst. Sci., 8 (2004), 1051–1064. https://doi.org/10.5194/hess-8-1051-2004 doi: 10.5194/hess-8-1051-2004
[40]	P. Van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48. https://doi.org/10.1016/S0025-5564(02)00108-6 doi: 10.1016/S0025-5564(02)00108-6

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