| Paper title: |
Conceptual Analysis of a Fractional Order Epidemic model of Measles Capturing Logistic growth using Laplace Adomian Decomposition Method |
| DOI: | https://doi.org/10.4316/JACSM.202301004 |
| Published in: | Issue 1, (Vol. 17) / 2023 |
| Publishing date: | 2023-04-09 |
| Pages: | 28-34 |
| Author(s): | BASHIRU Kehinde A., K. KOLAWOLE Mutairu, OJURONGBE Taiwo A., ADEKUNLE Hammed O., ADEBOYE Nureni O., AFOLABI Habeeb A. |
| Abstract. | Measles is a highly contagious, dangerous virus-borne disease. Prior to the advent of the measles vaccine and widespread immunization in 1963, severe outbreaks occurred every 2-3 years. Mathematical model of measles with logistic growth and enlightenment to go for vaccination was proposed and presented, the disease-free and endemic equilibria were obtained and their stabilities were investigated, basic reproduction number was generated using next generation matrix. Laplace-Adomian decomposition was utilized to carry out the numerical simulation in order to investigate the impact of the parameters of the model. The results were presented graphically and it was established that both enlightenments to go for vaccination and vaccination itself are effective methods are the measure to eradicate transmission of the disease measles in the population |
| Keywords: | Vaccination, Disease Free Equilibrium, Endemic Equilibrium, Laplace Adomian Decomposition Method |
| References: | 1. Mugoša, Boban, et al. "Measles outbreak, Montenegro January–July 2018: Lessons learned." Journal of medical virology 94.2 (2022): 514-520. 2. Nuwahereze, D., Onuorah, M. O., Abdulahi, B. M., & Kabandana, I. (2022). Standard Incidence Model of Measles with two Vaccination Strategies. World Scientific News, 170, 149-171. 3. El Hajji, M., & Albargi, A. H. (2022). A mathematical investigation of an “SVEIR” epidemic model for the measles transmission. Math. Biosc. Eng, 19, 2853-2875. 4. Hove-Musekwa, S. D., Nyabadza, F., Chiyaka, C., Das, P., Tripathi, A., & Mukandavire, Z. (2011). Modelling and analysis of the effects of malnutrition in the spread of cholera. Mathematical and computer modelling, 53(9-10), 1583-1595. 5. Gastanaduy, P. A., Banerjee, E., DeBolt, C., Bravo-Alcántara, P., Samad, S. A., Pastor, D., & Durrheim, D. N. (2018). Public health responses during measles outbreaks in elimination settings: Strategies and challenges. Human vaccines & immunotherapeutics, 14(9), 2222-2238. 6. Huang, J., Ruan, S., Wu, X., & Zhou, X. (2018). Seasonal transmission dynamics of measles in China. Theory in Biosciences, 137(2), 185-195. 7. Akingbade, J. A., Adetona, R. A., & Ogundare, B. S. (2018). Mathematical model for the study of transmission and control of measles with immunity at initial stage. Malaya Journal of Matematik (MJM), 6(4, 2018), 823-834. 8. Sowole, S. O., Ibrahim, A., Sangare, D., & Lukman, A. O. (2020). Mathematical model for measles disease with control on the susceptible and exposed compartments. Open Journal of Mathematical Scineces, 4(1), 60-75. 9. Aldila, Dipo, and Dinda Asrianti. A Deterministic Model of Measles with Imperfect Vaccination and Quarantine Intervention. Journal of Physics: Conference Series 1218 (2019). 10. Nwafor, E. U., Okoro, C. J., Inyama, S. C., Omame, A., & Mbachu, H. I. Analysis of a Mathematical Vaccination Model of an Infectious Measles Disease. FUTO Journal Series, 5(1), 168-188. 11. Nwafor, E. U., Okoro, C. J., Inyama, S. C., Omame, A., & Mbachu, H. I. Analysis of a Mathematical Vaccination Model of an Infectious Measles Disease. FUTO Journal Series, 5(1), 168-188. 12. Jaharuddin, and Toni Bakhtiar. Control Policy Mix in Measles Transmission Dynamics Using Vaccination, Therapy, and Treatment. International Journal of Mathematics and Mathematical Sciences (2020). 13. Paul, R. V., Atokolo, W., Saka, S. A., & Joseph, A. O. (2021). Modeling the Transmission Dynamics of Measles in the Presence of Treatment as Control Strategy. 14. Kiymaz, O. “An algorithm for solving initial value problems using Laplace Adomian Decomposition Method”, Appl. Math. Sci., 3 (30), 2009, pp. 1453–1459. 15. Diekmann O, Heesterbeek JAP, Metz JAJ (1990) On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28: 365–382.https://doi.org/10.1007/BF00178324. 16. Nthiiri, J. K. (2016). Mathematical modelling of typhoid fever disease incorporating protection against infection. 17. Onuorah, M., Ni, a., & Kuta, F. A. Stability analysis of endemic equilibrium of a lassa fever model Onuorah, M.o, Akinwande Ni 2, Faruk Adamu Kuta3 & Abubakar, U.Y 4. Journal of science, technology, mathematics and education (jostmed), 163. |
| Back to the journal content | |
