Local and Global Stability Analysis of the Disease-Free Equilibrium in A Fractional-Order Ebola Virus Transmission Model

1. Olaniyi, S., Chuma, F. M., and 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 2. Lolika, P. O., Helikumi, M., Jomah, S. A. S., Bakhet, M. Y. A., Galla, K. C., and Kheiralla, A. H. “Global Stability Analysis of a Fractional-Order Ebola Epidemic Model with Control Strategies,” Journal of Advances in Mathematics and Computer Science, 39(2), pp. 20-51, 2024. 3. Pan, W., Li, T., and Ali, S. “A fractional order epidemic model for the simulation of outbreaks of Ebola,”. Advances in Difference Equations, 161, pp. 1- 21, 2021. 4. Riaz, M., Khan, Z. A., Ahmad, S., and Ateya, A. A. “Fractional order dynamics in epidemic disease modeling with advanced perspectives of fractional calculus”, Fractal and fractional, 8(5), pp. 291, 2024. https://doi.org/10.3390/fractalfract8050291 5. Ali, Z., Rabiei, F., Rashidi, M. M., and Khodadadi, T. “A fractional-order mathematical model for COVID-19 outbreak with the effect of symptomatic and asymptomatic transmissions,” The European Physical Journal Plus, 137(395), 2022. https://doi.org/10.1140/epjp/s13360-022-02603-z 6. Mouaouine, A., Boukhouima, A., Hattaf, K. and Yousfi, N. “A fractional order SIR epidemic model with nonlinear incidence rate,” Advances in Difference Equations, 160, 2018. https://doi.org/10.1186/s13662-018-1613-z 7. Sidi-Ammi, M. R., Tahiri, M., and Torres, D. F. M. “Global stability of a Caputo fractional SIRS model with general incidence rate,” Mathematics in Computer Science ,15(9), pp. 91-105, 2021. https://doi.org/10.1007/s11786-020-00467-z 8. Abboubakar, H., Fandio, R., Sofack, B. S., and Fouda, H. P. E. “Fractional Dynamics of a Measles Epidemic Model,” Axioms, 11(8), pp. 363, 2022. https://doi.org/10.3390/axioms11080363 9. Alraqad, T., Almalahi, M. A., Mohammed, N., Alahmade, A., Khaled A. Aldwoah, K. A., and Saber, H. “Modeling Ebola Dynamics with a Φ-Piecewise Hybrid Fractional Derivative Approach,” Fractal and Fractional. 8(596), 2024. https://doi.org/10.3390/fractalfract8100596 10. Nandi, T. R., Saha, A. K., and Roy, S. “Analysis of a fractional order epidemiological model for tuberculosis transmission with vaccination and reinfection,” Scientific Reports, 14(28290), 2024. https://doi.org/10.1038/s41598-024-73392-x 11. Farman, M., Bin Rasheed, Q., Saleem, M. U., and Ahmad, A. “Modelling and Analysis of the Fractional Order Ebola Virus Model with Caputo-Fabrizio Derivative,” Punjab University Journal of Mathematics, 52(10), pp. 25-45, 2020. 12. Hasan, A., Akgul, A., Farman, M., Chaudhry, F., Sultan, M., and De la Sen, M. “Epidemiological Analysis of Symmetry in Transmission of the Ebola Virus with Power Law Kernel,” Symmetry, 15, 2023. https://doi.org/10.3390/sym15030665 13. Yadav, P., Jahan, S., and Nisar, K. S. “Fractional order mathematical model of Ebola virus under Atangana–Baleanu–Caputo operator,” Results in Control and Optimization, 13, 2023. 14. Agina, P.C., Otugene, V. B., Adedoyin, J. D., Chukwuma, E.I., Chuka-Obidiegwu, B. E., Ezeora, D. I., and Mbah, G. C. E. “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), pp. 555-573, 2025. E- ISSN 2489-009X , 15. Aguegboh, N. S., Nwokoye, N. R., Onyiaji, N. E., Amanso, O. R. and Oranugo, D. O. “A Fractional Order Model for the Transmission Dynamics of Measles with Vaccination,” Open Access Library Journal, 7, e6670, 2020. https://doi.org/10.4236/oalib.1106670 16. Almeida, R., Martins, N., and Silva, C. J. “Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models,” Axioms, 10, 238, 2021. https://doi.org/10.3390/axioms 10040238 17. Shekari, P., Jajarmi, A., Torkzadeh, L., and Nourim, K. “Fractional-order modeling of human behavior in infections: analysis using real data from Liberia,” Computer Methods in Biomechanics and Biomedical, 6, pp. 1–15, 2025. doi: 10.1080/10255842.2024.2448559. 18. Raza, A., Farman, M., Akgul, A., Iqbal, M.S., and Ahmad, A. “Simulation and numerical solution of fractional order Ebola virus model with novel technique,” AIMS Bioengineering, 7(4), pp. 194–207, 2020. 19. Rosa, S., and Ndairou, F. “Optimal Control Applied to Piecewise Fractional Ebola Model,” Mathematics, 12(7), 2024. https://doi.org/10.3390/math12070985 20. Alwell, U., Uwakwe, J. I., Onyegbuchulem, C. A., and Mbah, G. C. E. “Mathematical Modelling Of Covid-19 Transmission Dynamics In Nigeria With Control Through Vaccination, Treatment, And Awareness Campaigns,” Nigerian Journal of Technology, 44(4), pp. 1 – 13, 2025. https://doi.org/10.4314/njt.2025.369 21. Statista, “Africa: mortality rate 2000 – 2027 / Statista”. Retrieved from https://www.statista.com/statistics/1227851/crude-death-rate-in-africa/ , August 2024. 22. Madubueze, C. E., Kimbir, A. R., and Aboiyar, T. “Global stability of Ebola virus disease model with contact tracing and quarantine,” Applications and Applied Mathematics, 13 (1), pp. 382 – 403, 2018. 23. Ahman, Q. O., Omale, D., Asogwa, C. C., Nnaji. D. U., and Mbah, G. C. E. “Transmission dynamics of Ebola virus disease with vaccine, condom use, quarantine, isolation and treatment drug,” African Journal of Infectious Diseases, 15 (1), pp. 10 – 23, 2021. https: //doi.org/10.21010/ajidv15i1.2 24. Mbah, G. C. E., Onah, I. S., Ahman, Q. O., Collins, O. C., Asogwa, C. C., and Okoye, C. “Mathematical modeling approach of the study of Ebola virus disease transmission dynamics in a developing country,” African Journal of Infectious Diseases, 17 (1), pp. 10 – 26, 2023. https://doi.org/10.21010/Ajidv17il.2 25. Gomes, M. F. C., Piontti, A. P., Rossi, L., Chao, D., Longini, I., Hallorans, M. E., and Vespignani, A. “Assessing the international spreading risk associated with the 2014 West African Ebola outbreak,” PLOS Currents Outbreak, Sep 2(6), 2014. doi: 10.1371/currents.outbreaks.cd818f63d40e24aef769dda7df9e0da5. 26. Legrand, J., Grais, R. F., Boelle, P. Y., Valleron, A. J., and Flahault, A. “Understanding the dynamics of Ebola epidemics,” Epidemiology & Infection, 135(5), pp. 610 – 621, 2007. doi:10.1017/S0950268806007217 27. Rivers, C. M., Lofgren, E. T., Marathe, M., Eubank, S., and Lewis, B. L. “Modeling the impact of interventions on an epidemic of Ebola in Sierra Leone and Liberia,” PLOS Currents, 6(6), 2014. doi:10.1371/currents.outbreaks.fd38dd85078565450b0be3fcd78f5ccf 28. Otugene, V. B., Mbah, G. C. E, Owhenagbo, P., Idoko, P. I., Adedoyin, J. D., Enyejo, L. A., and Agina, P. C. “Mathematical Analysis of Hepatitis B Virus Transmission Dynamics E- ISSN 2489-009X , in the Absence of Therapy with Atangana-Baleanu Fractional-order SPQWXY Model,” Journal of Advances in Mathematics and Computer Science, 39(11), pp. 1–28, 2024. 29. Otugene, V. B., Agina, P. C., Edogbanya, H., and Digwo, D. C. “Existence and uniqueness analysis of Atangana-Baleanu fractional order network model of Noro virus,” International Journal of Mathematical Analysis and Modelling, 5(2), pp. 63–75, 2022. 30. Mbah, G. C. E, Onwuamaegbu, P. C., and Okoye, C. “Mathematical model on prostate cancer growth and its control,” International Journal of Multidisciplinary Research and Development, 4(11): 68–81, 2017 31. Kamgang, J. C., and Sallet, G. “Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium ,” Mathematical Biosciences, 213(1), pp. 1–12, 2008. 32. Riobello, R. N. “On some new mathematical models for infective diseases: analysis, equilibrium, positivity and vaccination controls,” A Thesis Presented to The Faculty of Science and Technology, University of Basque Country, Leioa, 2015. 33. Agina, P. C. and Echezona, G. N. “Comparative analysis of the Gauss-Seidel and Jacobi methods for solving linear systems” COOU Journal of Physical Sciences, 5(1), pp. 60–79, 2022.