Numerical Investigation of a Fractional-Order Dengue Fever Model via the Generalized Adams–Bashforth–Moulton Technique
DOI:
https://doi.org/10.70882/josrar.2026.v3i3.216Keywords:
Dengue fever, Fractional, Adam-Bashforth-Moulton, Transmission, Control, StrategiesAbstract
The rapid transmission and the increasing prevalence of Dengue fever make it a great public health challenge in the world, especially in tropical and subtropical regions. For this study, a fractional-order mathematical model was formulated to study the Dengue fever transmission dynamics and control. Important epidemiological parameters, including vaccination, treatment, and effective contact rates, were included in the model. Qualitative analysis confirmed that the model solutions exist, are unique, positive, and bounded, and that the basic reproduction number is computable to determine the conditions for the persistence and control of the disease. They found that higher vaccination and treatment coverage translates into decreased transmission and the reproduction number becoming less than 1, which is a good indicator of disease elimination. On the other hand, high contact rates were seen to be favorable for the spread and persistence of the infection. The analytical results were also supported with numerical simulations, contour plots, and surface plots, which showed that the prevalence of Dengue fever can only be reduced if intervention strategies are implemented in all aspects, such as vaccination, treatment, vector control, and reduction of transmission pathways. The results of this study help to understand the dynamics of Dengue transmission and offer valuable information to policy makers, health workers, and researchers for prevention, control, and potentially eradication of Dengue fever in endemic areas in the context of achieving sustainable solutions.
References
Abah, E., Bolaji, B., Atokolo, W., Amos, J., Acheneje, G. O., Omede, B. I., Omeje, D. (2024). Fractional mathematical model for the transmission dynamics and control of diphtheria. International Journal of Mathematical Analysis and Modelling, 7, ISSN: 2682-5694.
Abro, K., Atangana, A., & Gómez-Aguilar, J. F. (2021). An analytic study of bioheat transfer Pennes model via modern non-integer differential techniques. European Physical Journal Plus, 136. https://doi.org/10.1140/epjp/s13360-021-02136-x
Agahiu, N., Bolaji, B., Acheneje, G. O., & Atokolo, W. (2024). Approximate solution of fractional order mathematical model on the co-transmission of Zika and Chikungunya virus using Laplace-Adomian decomposition method. International Journal of Mathematics, 7(3), 47–81.
Ahmed, I., Goufo, E. F. D., Yusuf, A., Kumam, P., Chaipanya, P., & Nonlaopon, K. (2021). An epidemic prediction from analysis of a combined HIV-COVID-19 co-infection model via ABC fractional operator. Alexandria Engineering Journal, 60(3), 2979–2995.
Ali, Z., Zada, A., & Shah, K. (2017). Existence and stability analysis of three-point boundary value problem. International Journal of Applied and Computational Mathematics, 3, 651–664. https://doi.org/10.1007/s40819-017-0375-8
Ameh, P. O., Omede, B. I., & Bolaji, B. (2020). Dynamical analysis of a two-strain treatment model for anthrax in a population where it is deployed as a bioterrorism weapon. Journal of the Nigerian Society for Mathematical Biology, 3, 34–77.
Amos, J., Omale, D., Atokolo, W., Abah, E., Omede, B. I., Acheneje, G. O., & Bolaji, B. (2024). Fractional mathematical model for the transmission dynamics and control of Hepatitis C. FUDMA Journal of Sciences, 8(5), 451–463. https://doi.org/10.33003/fjs-2024-0805-2883
Atokolo, W. A., Aja, R. O., Omale, D., Ahman, Q. O., Acheneje, G. O., & Amos, J. (2024). Fractional mathematical model for the transmission dynamics and control of Lassa fever. Journal of Fractional Calculus and Applied Mathematics. https://doi.org/10.1016/j.fraope.2024.100110
Atokolo, W. A., Aja, R. O., Omale, D., Paul, R. V., Amos, J., & Ocha, S. O. (2023). Mathematical modeling of the spread of vector-borne diseases with influence of vertical transmission and preventive strategies. FUDMA Journal of Sciences, 7(6), 75–91. https://doi.org/10.33003/fjs-2023-0706-2174
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, Article 2297630.
Baskonus, H. M., & Bulut, H. (2015). On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method. Open Mathematics, 13, 1–9.
Bhatt, S., Gething, P. W., Brady, O. J., Messina, J. P., Farlow, A. W., Moyes, C. L., Drake, J. M., Brownstein, J. S., Hoen, A. G., Sankoh, O., et al. (2013). The global distribution and burden of dengue. Nature, 496(7446), 504–507.
Bolaji, B., Ani, F., Omede, B. I., Acheneje, G. O., & Ibrahim, A. (2024). A model for the control of transmission dynamics of human monkeypox disease in sub-Saharan Africa. Journal of the Nigerian Society of Physical Sciences, 6, 1800.
Bolaji, B., Odionyenma, U. B., Omede, B. I., Ojih, P., Abdullahi, B., & Ibrahim, A. (2023). Modelling the transmission dynamics of Omicron variant of COVID-19 in densely populated city of Lagos in Nigeria. Journal of the Nigerian Society of Physical Sciences, 5, 1055.
Brady, O. J., Gething, P. W., Bhatt, S., Messina, J. P., Brownstein, J. S., Hoen, A. G., Moyes, C. L., Farlow, A. W., Scott, T. W., & Hay, S. I. (2012). Refining the global spatial limits of dengue virus transmission by evidence-based consensus. PLoS Neglected Tropical Diseases, 6(8), e1760.
Chen, Y., Wong, K., & Zhao, L. (2023). Modeling the impact of vaccination strategies on hepatitis C and COVID-19 coinfection dynamics. Journal of Vaccine, 41(15), 2897–2905.
Chikaki, E., & Ishikawa, H. (2009). A dengue transmission model in Thailand considering sequential infections with all four serotypes. Journal of Infection in Developing Countries, 3(9), 711–722.
Das, R., Patel, S., & Kumar, A. (2024). Mathematical modeling of hepatitis C and COVID-19 coinfection in low- and middle-income countries: Challenges and opportunities. BMC Public Health, 24(1), 587.
Dengue Virus Net. (2018). Treatment of dengue. Retrieved from http://www.denguevirusnet.com/treatment.html
Dengue Virus Net. (2019). Dengue virus transmission. Retrieved from https://www.denguevirusnet.com/transmission.html
Diethelm, K. (1999). The Frac PECE subroutine for the numerical solution of differential equations of fractional order.
Emmanuel, L., Omale, D., Atokolo, W., Amos, J., Abah, E., Ojonimi, A., Onoja, T., Acheneje, G., & Bolaji, B. (2025). Fractional mathematical model for the dynamics of pneumonia transmission with control using fixed point theory. GPH-International Journal of Mathematics, 8(5), 55–86. https://doi.org/10.5281/zenodo.16364036
Garba S. M., Gumel .A. B. & Abubakar .M.R., (2008) “Backward Bifurcations in Dengue Transmission Dynamics”, Mathematical Biosciences 215 11.
Gubler, D. J. (1998). Dengue and dengue hemorrhagic fever. Clinical Microbiology Reviews, 11(3), 480–496.
Halstead, S. B., Nimmannitya, S., & Cohen, S. N. (1970). Observations related to pathogenesis of dengue hemorrhagic fever IV: Relation of disease severity to antibody response and virus recovered. Yale Journal of Biology and Medicine, 42(5), 311.
Jalija, E., Amos, J., Atokolo, W., Abah, E., Agbata, B. C., Acheneje, G. O., Shyamsunder, & Bolaji, B. (2026). Numerical solution of fractional order typhoid fever model via the generalized fractional Adams-Bashforth-Moulton approach. Network Modeling Analysis in Health Informatics and Bioinformatics, 15, 68. https://doi.org/10.1007/s13721-026-00743-1
Jalija, E., Amos, J., Atokolo, W., Omale, D., Abah, U., Alih, U., Alabi, P. A., & Bolaji, B. (2025). Numerical investigations on dengue fever model through singular and non-singular fractional operators. International Journal of Mathematical Analysis and Modelling, 8(1), 216–242.
Odiba, P. O., Acheneje, G. O., & Bolaji, B. (2024). A compartmental deterministic epidemiological model with nonlinear differential equations for analysing the co-infection dynamics between COVID-19, HIV, and monkeypox diseases. Healthcare Analytics, 5, 100311. https://doi.org/10.1016/j.health.2024.100311
Ojonimi, A. A., Amos, J., Atokolo, W., Omale, D., Emmanuel, L. M., Abah, E., Acheneje, G. O., & Bolaji, B. (2025). Numerical solution of fractional order Hepatitis B model via the generalized fractional Adams-Bashforth-Moulton approach. Journal of Science Research and Reviews, 2(5), 33–48. https://doi.org/10.70882/josrar.2025.v2i5.119
Omale, D., Akpa, M., & Atokolo, W. (2020). Global stability and sensitivity analysis of transmission dynamics of tuberculosis and its control: A case study of Ika General Hospital Ankpa, Kogi State, Nigeria. Academic Journal of Statistics and Mathematics, 6.
Omale, D., Atokolo, W., .Akpa, M., (2020). Global stability and sensitivity analysis of transmission dynamics of tuberculosis and its control, A case study of Ika general hospital Ankpa, Kogi State, Nigeria. Acad. J. Stat. Math. 6, 5730-7151.
Omale, D., Ojih, P., Atokolo, W., Omale, A., Bolaji.B. (2021), Mathematical model for transmission dynamics of HIV and Tuberculosis co-infection in Kogi State, Nigeria. Journal of Mathematical Computational Science. 11, No. 5, 5580-5613. Available online at: https://doi.org/10.28919/jmcs/6080.
Omame, A.M., Abbas, M., Onyenegecha, C.P. (2022), "A fractional order model for the co-interaction of COVID-19 and hepatitis B virus." Journal of Mathematical Biology, pp. 112–118.
Omede, B. I., Bolarinwa Bolaji, Olumuyiwa, P. J., Ibrahim, A. A. and Oguntolu F. A (2023). Mathematical analysis on the vertical and horizontal transmission dynamics of HIV and Zika virus co-infection. Franklin open 6 100064. https://doi.org/10.1016/j.fraope.2023.100064. - Elsevier Journal .
Omede, B. I., Olumuyiwa, P. J., Atokolo, W., Bolaji, B. & Ayoola, T. A. (2023). A mathematical analysis of the two-strain tuberculosis model dynamics with exogenous re-infection. Healthcare Analytics 4, 100266. https://doi.org/10.1016/j.health.2023.100266 .
Omede, B.I., Israel, M., Mustapha, M. K., Amos, J., Atokolo, W., & Oguntolu, F. A. (2024). "Approximate solution to the fractional soil-transmitted helminth infection model using Laplace-Adomian Decomposition Method," International Journal of Mathematics, 07(04), pp. 16–40.
Omonu, G. U., Ameh, P.O., Omede, B.I, & Bolaji.B (2019), Mathematical modelling of Tuta Absoluta on Tomato plants. Journal of the Nigerian Society for Mathematical Biology. 2(1): 14-31.
Philip J., Omale D., Atokolo W., Amos J., Acheneje G.O., Bolaji B. (2024), Fractional mathematical model for the Transmission Dynamics and control of HIV/AIDs,FUDMA Journal of Sciences, Vol.8, No.6, pp.451-463, https://doi.org/10.33003/fjs-2024-0805-2883.
Samir Bhatt, Peter W. Gething, Oliver J. Brady, Jane P. Messina, Andrew W. Farlow, Catherine L. Moyes, John M. Drake, John S. Brownstein, Anne G. Hoen, Osman Sankoh, et al. (2013), The global distribution and burden of dengue, Nature 496 (7446) 504–507.
Shekhar, C. (2007). Deadly dengue: New vaccines promise to tackle this escalating global menace. Chemistry and Biology, 14(8), 871–872.
Smith, J., Johnson, A.B., & Lee, C. (2023), "Modeling the coinfection dynamics of hepatitis C and COVID-19: A systematic review," Journal of Epidemiology and Infection, 151(7), pp. 1350–1365.
Udoka, B. O., Nometa, I. & Bolaji, B. (2023). Analysis of a model to control the co-dynamics of Chlamydia and Gonorrhea using Caputo fractional derivative. Mathematical Modelling and Numerical Simulation with Applications, 2023, 3(2), 111–140. Available online at: https://doi.org/10.53391/mmnsa.1320175 - .
Ullah, A. Abdeljawad Z., Hammouch T. Z., Shah K. (2020). "A hybrid method for solving fuzzy Volterra integral equations of separable type kernels," Journal of King Saud University - Science, 33, https://doi.org/10.1016/j.jksus.2020.101246.
World Health Organization. (2017). Dengue vaccine research, immunization, vaccines and biologicals. Retrieved from https://www.who.int/immunization/research/development/dengue_vaccines/en/
World Health Organization. (2018). Epidemiology. Retrieved from https://www.who.int/denguecontrol/epidemiology/en/
World Health Organization. (2019). Dengue and severe dengue. Retrieved from https://www.who.int/news-room/fact-sheets/detail/dengue-and-severe-dengue
Yunus, A.O, M.O. Olayiwola, M.A. Omolaye, A.O. Oladapo, (2023). A fractional order model of lassa fever disease using the Laplace-Adomian decomposition method, Health Care Anal. 3 100167, www.elsevier.com/locate/health. Health Care Analytics.
Zhang, R. M. Li, (2022) bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations, Nonlinear Dynam. 108 http://dx.doi.org/10.1007/s11071-022-07207-x.
Zhang, R.F., Li, M.-C., J.Y. Gan, Q. Li, Z.-Z. Lan, (2022). Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method, Chaos Solitons Fractals 154.
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