Paper title:

Analysis of Corona-Virus Mathematical Model in Asymptomatic and Symptomatic Cases with Vaccine using Homotopy Perturbation Method

Published in: Issue 1, (Vol. 17) / 2023
Publishing date: 2023-04-09
Pages: 20-27
Author(s): KOLAWOLE Mutairu Kayode, OLUWAROTIMI Aderonke O., ODEYEMI Kazeem Abidoye, POPOOLA Amos Oladele
Abstract. The impact of the emergence of Corona virus which affected all parts of the world cannot be over emphasized. COVID-19 has cost hundreds of thousands of human lives globally, presenting healthcare professionals with pressing challenges, and exposed the weaknesses of national health systems worldwide. Hence, there is a need for more vaccination of individuals which will in turn leads to the eradication of the deadly disease. In this paper, an investigation is carried out for the convergent solution of the model by making use of a reliable Homotopy Perturbation Method (HPM) in exploring the possible solution. Basic Reproduction number was computed using Next Generation Method, The Equilibriums points are determined and the model also explored the sensitivities aspect when the parameters are varied. Fractional model numerically using the Homotopy Perturbation Method (HPM) to obtain the iterative solution of the epidemic model scheme and presenting different forms of graphical results that can be useful to analyze the model. The numerical results show that the spread of the corona – virus disease is reduced by taking adequate and effective vaccines with time
Keywords: Covid-19, Basic Reproduction Number, Local Stability, Global Stability, Homotopy Perturbation Method

1. Ahmed, I., Modu, G. U., Yusuf, A., Kumam, P., & Yusuf, I. (2021). A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes. Results in physics, 21, 103776

2. Ayoola, T. A., Kolawole, M. K., & Popoola, A. O. (2022). Mathematical Model of COVID-19 Transmission Dynamics with Double Dose Vaccination. Tanzania Journal of Science, 48(2), 499-512.

3. Brauer, F., & Castillo-Chávez, C. (2001). Basic ideas of mathematical epidemiology. In Mathematical Models in Population Biology and Epidemiology (pp. 275-337). Springer, New York, NY.

4. Brauer, F. (2008). Compartmental models in epidemiology. In Mathematical epidemiology (pp. 19-79). Springer, Berlin, Heidelberg.

5. He, J.H (1999) Homotopy perturbation technique. Comput. Methods Appl. Mech. Eng. 178(3–4), 257–262 (1999) 21.

6. Heathcoat, H. W. (2000). The mathematics of infectious diseases. SIAM review, 42(4), 599-653.

7. Ivorra, B., Ferrández, M. R., Vela-Pérez, M., & Ramos, A. M. (2020). Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China. Communications in nonlinear science and numerical simulation, 88, 105303.

8. Anderson, R.M.; May, R.M. Population biology of infectious diseases: Part I. Nature 1979, 280, 361–367.

9. Anderson, R.M.; May, R.M. Population biology of infectious diseases: Part II. Nature 1979, 280, 455–461.

10. Khajanchi, S., Sarkar, K., Mondal, J., Nisar, K. S., & Abdelwahab, S. F. (2021). Mathematical modeling of the COVID-19 pandemic with intervention strategies. Results in Physics, 25, 104285.

11. Khan MA, Atangana A (2020). Modeling the dynamics of novel coronairus (2019- ncov) with fractional derivative. Alexandria Eng J 2020. j.aej.2020.02.033.

12. Kolawole, M. K., & Olayiwola, M. O. (2016). Behavioral Analysis of a Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) Epidemic Model with Saturated Incidence Rate Considering the saturation term for the infected individual, computing information system Development informatics & Allied Research Journal, 7. Computing Information Systems, Development Informatics & Allied Research Journal, 7(3), 47-62.

13. Z. Ma, J. Zhou, J. Wu, Modeling and Dynamics of Infectious Diseases, World Scientific Publishing, 2009.

14. A. Korobeinikon, G.C. Wake, Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models, Appl. Math. Lett. 15 (2002) 955–960.

15. Olayiwola, M. O., Kolawole, M. K., & Popoola, A. O. (2017). Variational Iteration Method For The Simulation Of The Effect Of Transmission Coefficient On The Susceptible-Exposed-Infected-Recovered-Susceptible (Seirs) Epidemic Model With Saturated Incidence Rate And Disease-Induced Death. Journal of science and arts, (2), 357-364.

16. W.H.O (World Health Organization) 2020 Emergencies, preparedness, response. Pneumonia of unknown Origin-China, Disease Outbreak News. 5. Available from: (Accessed on March 5, 2020).

Back to the journal content
Creative Commons License
This article is licensed under a
Creative Commons Attribution-ShareAlike 4.0 International License.
Home | Editorial Board | Author info | Archive | Contact
Copyright JACSM 2007-2024