APPROXIMATE SOLUTION TO FRACTIONAL ORDER SOIL TRANSMITTED HELMINTH INFECTION MODEL USING LAPLACE ADOMIAN DECOMPOSITION METHOD
Keywords:
Fractional order, Caputo derivative, Laplace Adomian decomposition method.
Abstract
In this study, we proposed a fractional order compartmental model based on the Caputo derivative to describe the dynamics of soil-transmitted helminth infection. We employed the Laplace Adomian Decomposition Method (LADM) to derive series solutions for each equation within the system of non-linear differential equations that comprise the epidemiological model. Our findings indicate that the infinite series generated by LADM converges to the exact solution of the system. We performed numerical simulations of the fractional order compartmental deterministic model using MATLAB to validate the approximate results. Additionally, comparing the solutions of the fractional order model with the classical model reveals that the fractional order model offers greater flexibility, allowing the system to be adjusted to achieve various desired outcomes in different compartments by varying the fractional order to values such as 0.75, 0.8, 0.85, 0.9, 0.95, and 1.
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References
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Tefera, T., Biruksew, A., Mekonnen, Z., &Eshetu, T. (2014). Parasitic contamination of fruits and vegetables collected from selected local markets of Jimma Town, Southwest Ethiopia. International scholarly research notices, 2014(1), 382715.
Pullan, R. L., Smith, J. L., Jasrasaria, R., &Brooker, S. J. (2014). Global numbers of infection and disease burden of soil transmitted helminth infections in 2010. Parasites & vectors, 7, 1-19.
Chelkeba, L., Mekonnen, Z., Emana, D., Jimma, W., &Melaku, T. (2022). Prevalence of soil-transmitted helminths infections among preschool and school-age children in Ethiopia: a systematic review and meta-analysis. Global health research and policy, 7(1), 9.
Kurscheid, J., Laksono, B., Park, M. J., Clements, A. C., Sadler, R., McCarthy, J. S., ... & Gray, D. J. (2020). Epidemiology of soil-transmitted helminth infections in Semarang, Central Java, Indonesia.PLoS Neglected Tropical Diseases, 14(12), e0008907.
Lambura, A. G., Mwanga, G. G., Luboobi, L., &Kuznetsov, D. (2020). Mathematical Model for Optimal Control of Soil‐Transmitted Helminth Infection. Computational and Mathematical Methods in Medicine, 2020(1), 6721919
Oguntolu, F. A., Peter, O. J., Yusuf, A., Omede, B. I., Bolarin, G., &Ayoola, T. A. (2024). Mathematical model and analysis of the soil-transmitted helminth infections with optimal control. Modeling Earth Systems and Environment, 10(1), 883-897.
Truscott, J. E., Turner, H. C., Farrell, S. H., & Anderson, R. M. (2016). Soil-transmitted helminths: mathematical models of transmission, the impact of mass drug administration and transmission elimination criteria. Advances in parasitology, 94, 133-198.
Atokolo, W., Aja, R. O., Aniaku, S. E., Onah, I. S., &Mbah, G. C. (2022). Approximate solution of the fractional order sterile insect technology model via the Laplace–Adomian Decomposition Method for the spread of Zika virus disease. International Journal of Mathematics and Mathematical Sciences, 2022(1), 2297630.
Yunus, A. O., Olayiwola, M. O., Omoloye, M. A., &Oladapo, A. O. (2023). A fractional order model of lassa disease using the Laplace-adomian decomposition method. Healthcare Analytics, 100167.
Sahu, I., & Jena, S. R. (2023). SDIQR mathematical modelling for COVID-19 of Odisha associated with influx of migrants based on Laplace Adomian decomposition technique. Modeling Earth Systems and Environment, 9(4), 4031-4040.
Farman, M., Saleem, M. U., Ahmad, A., & Ahmad, M. O. (2018). Analysis and numerical solution of SEIR epidemic model of measles with non-integer time fractional derivatives by using Laplace Adomian Decomposition Method. Ain Shams Engineering Journal, 9(4), 3391-3397.
Haq, F., Shah, K., Khan, A., &Shahzad, M. (2020). Numerical solution of fractional order epidemic model of a vector born disease by Laplace Adomian decomposition method. Punjab University Journal of Mathematics, 49(2).
AdewaleAdedokun, K., OyedunsiOlayiwola, M., AdedapoAlaje, I., OlarewajuYunus, A., OlalekanOladapo, A., &Oyeleye Kareem, K. (2024).A caputo fractional-order model of tuberculosis incorporating enlightenment and therapy using the Laplace-Adomian decomposition method. International Journal of Modelling and Simulation, 1-15.
Nave, O., Shemesh, U., &HarTuv, I. (2021). Applying Laplace Adomian decomposition method (LADM) for solving a model of Covid-19. Computer Methods in Biomechanics and Biomedical Engineering, 24(14), 1618-1628.
Haq, F., Shahzad, M., Muhammad, S., Wahab, H. A., &urRahman, G. (2017). Research Article Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases.
Yunus, A. O., Olayiwola, M. O., Adedokun, K. A., Adedeji, J. A., &Alaje, I. A. (2022). Mathematical analysis of fractional-order Caputo’s derivative of coronavirus disease model via Laplace Adomian decomposition method. Beni-Suef University Journal of Basic and Applied Sciences, 11(1), 144.
Lambura, A. G., Mwanga, G. G., Luboobi, L., &Kuznetsov, D. (2020). Modeling the effects of helminth infection on the transmission dynamics of Mycobacterium tuberculosis under optimal control strategies. Computational and Mathematical Methods in Medicine, 2020(1), 8869377.
Shah, K., &Bushnaq, S. (2017). Numerical treatment of fractional endemic disease model via Laplace Adomian decomposition method. Journal of science and arts, 17(2), 257.
Brooker, S., Clements, A. C., & Bundy, D. A. (2006). Global epidemiology, ecology and control of soil-transmitted helminth infections. Advances in parasitology, 62, 221-261.
XavierChristuRajan, V. (2017). Prevalence and Factors Influencing Soil Transmitted Helminths (STH) among School Age Children (5–14 Years Age) in a Rural Area of Coimbatore District (Doctoral dissertation, PSG Institute of Medical Sciences and Research, Coimbatore).
Tefera, T., Biruksew, A., Mekonnen, Z., &Eshetu, T. (2014). Parasitic contamination of fruits and vegetables collected from selected local markets of Jimma Town, Southwest Ethiopia. International scholarly research notices, 2014(1), 382715.
Pullan, R. L., Smith, J. L., Jasrasaria, R., &Brooker, S. J. (2014). Global numbers of infection and disease burden of soil transmitted helminth infections in 2010. Parasites & vectors, 7, 1-19.
Chelkeba, L., Mekonnen, Z., Emana, D., Jimma, W., &Melaku, T. (2022). Prevalence of soil-transmitted helminths infections among preschool and school-age children in Ethiopia: a systematic review and meta-analysis. Global health research and policy, 7(1), 9.
Kurscheid, J., Laksono, B., Park, M. J., Clements, A. C., Sadler, R., McCarthy, J. S., ... & Gray, D. J. (2020). Epidemiology of soil-transmitted helminth infections in Semarang, Central Java, Indonesia.PLoS Neglected Tropical Diseases, 14(12), e0008907.
Lambura, A. G., Mwanga, G. G., Luboobi, L., &Kuznetsov, D. (2020). Mathematical Model for Optimal Control of Soil‐Transmitted Helminth Infection. Computational and Mathematical Methods in Medicine, 2020(1), 6721919
Oguntolu, F. A., Peter, O. J., Yusuf, A., Omede, B. I., Bolarin, G., &Ayoola, T. A. (2024). Mathematical model and analysis of the soil-transmitted helminth infections with optimal control. Modeling Earth Systems and Environment, 10(1), 883-897.
Truscott, J. E., Turner, H. C., Farrell, S. H., & Anderson, R. M. (2016). Soil-transmitted helminths: mathematical models of transmission, the impact of mass drug administration and transmission elimination criteria. Advances in parasitology, 94, 133-198.
Atokolo, W., Aja, R. O., Aniaku, S. E., Onah, I. S., &Mbah, G. C. (2022). Approximate solution of the fractional order sterile insect technology model via the Laplace–Adomian Decomposition Method for the spread of Zika virus disease. International Journal of Mathematics and Mathematical Sciences, 2022(1), 2297630.
Yunus, A. O., Olayiwola, M. O., Omoloye, M. A., &Oladapo, A. O. (2023). A fractional order model of lassa disease using the Laplace-adomian decomposition method. Healthcare Analytics, 100167.
Sahu, I., & Jena, S. R. (2023). SDIQR mathematical modelling for COVID-19 of Odisha associated with influx of migrants based on Laplace Adomian decomposition technique. Modeling Earth Systems and Environment, 9(4), 4031-4040.
Farman, M., Saleem, M. U., Ahmad, A., & Ahmad, M. O. (2018). Analysis and numerical solution of SEIR epidemic model of measles with non-integer time fractional derivatives by using Laplace Adomian Decomposition Method. Ain Shams Engineering Journal, 9(4), 3391-3397.
Haq, F., Shah, K., Khan, A., &Shahzad, M. (2020). Numerical solution of fractional order epidemic model of a vector born disease by Laplace Adomian decomposition method. Punjab University Journal of Mathematics, 49(2).
AdewaleAdedokun, K., OyedunsiOlayiwola, M., AdedapoAlaje, I., OlarewajuYunus, A., OlalekanOladapo, A., &Oyeleye Kareem, K. (2024).A caputo fractional-order model of tuberculosis incorporating enlightenment and therapy using the Laplace-Adomian decomposition method. International Journal of Modelling and Simulation, 1-15.
Nave, O., Shemesh, U., &HarTuv, I. (2021). Applying Laplace Adomian decomposition method (LADM) for solving a model of Covid-19. Computer Methods in Biomechanics and Biomedical Engineering, 24(14), 1618-1628.
Haq, F., Shahzad, M., Muhammad, S., Wahab, H. A., &urRahman, G. (2017). Research Article Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases.
Yunus, A. O., Olayiwola, M. O., Adedokun, K. A., Adedeji, J. A., &Alaje, I. A. (2022). Mathematical analysis of fractional-order Caputo’s derivative of coronavirus disease model via Laplace Adomian decomposition method. Beni-Suef University Journal of Basic and Applied Sciences, 11(1), 144.
Lambura, A. G., Mwanga, G. G., Luboobi, L., &Kuznetsov, D. (2020). Modeling the effects of helminth infection on the transmission dynamics of Mycobacterium tuberculosis under optimal control strategies. Computational and Mathematical Methods in Medicine, 2020(1), 8869377.
Shah, K., &Bushnaq, S. (2017). Numerical treatment of fractional endemic disease model via Laplace Adomian decomposition method. Journal of science and arts, 17(2), 257.
Published
2024-06-13
How to Cite
Omede, B., Israel, M., Mustapha, M., Amos, J., Atokolo, W., & Oguntolu, F. (2024). APPROXIMATE SOLUTION TO FRACTIONAL ORDER SOIL TRANSMITTED HELMINTH INFECTION MODEL USING LAPLACE ADOMIAN DECOMPOSITION METHOD. GPH - International Journal of Mathematics, 7(04), 16-40. https://doi.org/10.5281/zenodo.11630908
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Copyright (c) 2024 Benjamin Idoko Omede
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