A Fractional-Order Nonlinear Model for The Transmission Dynamics of Ebola Virus Disease with Quarantine, Vaccination, and Condom Use

[1] Ahmad, M.D., Usman, M., Khan, A., & Imran, M. (2016). Optimal control analysis of Ebola disease with control strategies of quarantine and vaccination. Infectious Diseases of Poverty, 5(72). [2] World Health Organization . (2023). Ebola virus disease. Retrieved from https://www.who.int/news-room/fact-sheets/detail/ebola-virus-disease . [3] UK Health Security Agency. (2023). Ebola: overview, history, origins and transmission. Retrieved from https://www.gov.uk/government/publications/ebola-origins-reservoirs- transmission-and-guidelines/ebola-overview-history-origins-and-transmission. [4] Breman, J.G., Heymann, D.L, Loyd, G., McCormick, J.B., Miatudila, M., Murphy, F.A., ... & Johnson, K.M. (2016). Discovery and description of Ebola Zaire virus in 1976 and relevance to the West African epidemic during 2013 – 2016. Journal of Infectious Diseases, 214, 93–101. doi:10.1093/infdis/jiw207 [5] Otugene, V.B., Mbah, G.C.E, Owhenagbo, P., Idoko, P.I., Adedoyin, J.D., Enyejo, L.A., & Agina, P.C. (2024). Mathematical Analysis of Hepatitis B Virus Transmission Dynamics in the Absence of Therapy with Atangana-Baleanu Fractional-order SPQWXY Model. Journal of Advances in Mathematics and Computer Science, 39(11), 1–28. [6] Agina, P.C., Chukwuma, E.I., Chuka-Obidiegwu, B.E., Otugene, V.B., Ibeh, K.K., & Mbah, G.C.E. (2026). Local and Global Stability Analysis of the Disease-Free Equilibrium in a Fractional-Order Ebola Virus Transmission Model. International Journal of Applied Science and Mathematical Theory, 12(3), 30 – 48. [7] Olaniyi, S., Chuma, F.M., & Abimbade, S.F. (2025). “Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo sense,” Journal of the Nigerian Society of Physical Sciences, 7, 2025. DOI:10.46481/jnsps.2025.2304 [8] Pan, W., Li, T., & Ali, S. (2021). A fractional order epidemic model for the simulation of outbreaks of Ebola. Advances in Difference Equations, 161, 1- 21. [9] Andrawus, J., Abdulrahman, S., Singh, R.V.K., & Manga, S. S. (2022). Sensitivity analysis of a mathematical modeling of Ebola virus population dynamics in the presence of vaccine. Dutse Journal of Pure and Applied Sciences, 8. https://dx.doi.org/10.4314/dujopas.v8i2a.5 [10] Ahman, Q.O., Omale, D., Asogwa, C.C., Nnaji, D.U., & Mbah, G.C.E. (2021). Transmission dynamics of Ebola virus disease with vaccine, condom use, quarantine, isolation and treatment drug. African Journal of Infectious Diseases, 15(1), 10–23. [11] Agina, P.C., Chuka-Obidiegwu, B.E., Chukwuma, E.I., Ibeh, K.K., Otugene, V.B., & Mbah, G.C.E. (2026). An Approximate Solution of a Fractional-order Epidemic Model using the Homotopy Perturbation Method. International Journal of Applied Science and Mathematical Theory, 12(3). [12] Sidi-Ammi, M.R., Tahiri, M., & Torres, D.F.M. (2021). Global stability of a Caputo fractional SIRS model with general incidence rate. Mathematics in Computer Science ,15(9), 91-105. https://doi.org/10.1007/s11786-020-00467-z [13] Farman, M., Bin Rasheed, Q., Saleem, M.U., & Ahmad, A. (2020). Modelling and Analysis of the Fractional Order Ebola Virus Model with Caputo-Fabrizio Derivative. Punjab University Journal of Mathematics, 52(10), 25-45. [14] Yadav, P., Jahan, S., & Nisar, K.S. (2023). Fractional order mathematical model of Ebola virus under Atangana–Baleanu–Caputo operator. Results in Control and Optimization, 13. [15] Otugene, V.B., Agina, P.C., Ezeora, D.I., & Ibeh, K.K. (2026). Modeling Inflation Dynamics with Atangana-Baleanu Fractional Derivatives: A Memory-Driven Approach to Consumer Price Index Forecasting. Iconic Research and Engineering Journals, 9(9), 2000–2022. [16] Mouaouine, A., Boukhouima, A., Hattaf, K. & Yousfi, N. (2018). A fractional order SIR epidemic model with nonlinear incidence rate. Advances in Difference Equations, 2018(160). https://doi.org/10.1186/s13662-018-1613-z [17] Didigwu, N. Mbah, G. & Abonyi, M. (2021). Solution of Ebola virus disease transmission dynamics mathematical model using homotopy perturbation method. Academic Journal of Statistics and Mathematics, 7(1), 1–8. [18] Agina, P.C., Otugene, V. B., Adedoyin, J. D., Chukwuma, E.I., Chuka-Obidiegwu, B. E., Ezeora, D. I., & Mbah, G. C. E. (2025). Derivation of the basic reproduction number using the next generation matrix for a non-linear Ebola Virus transmission model. International Journal of Mathematical Analysis and Modelling, 8(2), 555-573. [19] Ndanusa, A., Abdulrahman, S., & Abdulmalik, A. (2015). A mathematical model for controlling the spread of Ebola virus disease in Nigeria. International Journal of Humanities and Management Sciences, 3(3). [20] Agina, P.C. & Echezona, G.N. (2022). Comparative analysis of the Gauss-Seidel and Jacobi methods for solving linear systems. COOU Journal of Physical Sciences, 5(1), 60–79. [21] Gupta, R., Gupta, R., & Verma, D. (2024). Solving general differential equations of fractional orders via Rohit transform. Kirkuk Journal of Science, 9(2), 1–16. doi: 10.32894/kujss.2024.146592.1137 [22] Podlubny, I. (1999). Fractional differential equations. California, CA: Academic Press. [23] Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J. (2006). Theory and applications of fractional differential equations. Amsterdam, Netherlands: Elsevier. [24] Rahimy, M. (2010). Applications of Fractional Differential Equations. Applied Mathematical Sciences, 4(50), 2453–2461. [25] Gorenflo, R., & Mainardi, F. (2008). Fractional calculus: Integral and differential equations of fractional order. Mathematical Physics, arXiv: 0805.3823, 223–276. https://doi.org/10.48550/arXiv.0805.3823 [26] Otugene, V.B., Agina, P.C., Edogbanya, H., & Digwo, D.C. (2022). Existence and uniqueness analysis of Atangana-Baleanu fractional order network model of Noro virus. International Journal of Mathematical Analysis and Modelling, 5(2), 63–75. [27] Dauhoo, M., Dumas, L., Gabriel, P., & Lafitte, P. (2018). An introduction to the basic reproduction number in Mathematical epidemiology. ESAIM: Proceedings and Surveys, 62, 123–138. [28] Jones, J. H. (2007). Notes On R0. Department of Anthropological Sciences, Stanford University. [29] Watmough, J. (2021). The Basic Reproduction Number. University of New Brunswick. ([email protected]). Fields-CQAM Thematic Program on Integrative Modelling of EID, Fields Institute. [30] Diekmann, O., Heesterbeek, J.A.P., & Metz, J.A.J. (1990). On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28, 365–382. [31] Driessche, P. & Watmough, J. (2008). Further Notes on the Basic Reproduction Number. 10.1007/978-3-540-78911-6_6.