On The Application of Homotopy Perturbation Method in Simulating the Effect of Double Dose Vaccination on a Mathematical Model of Covid-19 Transmission Dynamics

Yıl 2023, Cilt: 20 Sayı: 1, 53 - 63, 01.05.2023

Mutairu Kolawole , Tawakalt A. Bosede Adedapo Alaje , Kehinde A. Bashiru Kehinde Adekunle Bashiru

Öz

In this research, the impact of first and second dose vaccination in a mathematical model of COVID-19 transmission dynamics with two vaccination classes is investigated. The homotopy perturbation method is applied to obtain the approximate solution of the mathematical model. The impact of the first and second dose vaccinations were analyzed on the susceptible and exposed classes. The results of the analysis reveal that the second dose vaccination strategy is important to control the spread of the COVID-19 virus which is endangering the global existence of human population.

Anahtar Kelimeler

Covid-19, Vaccination, HPM, Mathematical Modelling.

Kaynakça

• O. M. Ogunlaran, and S. C. Oukouomi Noutchie, “Mathematical model for an effective management of HIV infection,” Hindawi Publishing Corporation, vol. 2016, no. 4217548, pp. 6, 2016. http://dx.doi.org/10.1155/2016/4217548.
• S. Ahmad, A. Ullah, A. Akgül, and D. Baleanu, “Theoretical and numerical analysis of fractal fractional model of tumor-immune interaction with two different kernels,” Alexandria Engineering Journal, vol. 61, no. 7, pp. 5735- 5752, 2022.
• A. Akgül, M. Inc, A. Kilicman, and D. Baleanu, “A new approach for one-dimensional sine-Gordon equation,” Advances in Difference Equations, 2016. http://dx.doi.org/10.1186/s13662-015-0734-x.
• S. Balamuralitharan, and S. Geethamalini, “Solutions of epidemic of EIAV infection by HPM,” Journal of Physics: conf.series 1000, 012023, 2018.
• A. I. Alaje, M. O. Olayiwola, M. O. Ogunniran, J.A. Adedeji, and K. A. Adedokun, “Approximate Analytical Methods for the Solution of Fractional Order Integro-differential Equations,” Nigerian Journal of Mathematics and Applications, vol. 31, pp.175 – 190, 2021.
• S. A. Lauer, K. H. Grantz, Q Bi, F. K. Jones, Q. Zheng, H. R. Meredith, A.S. Azman, N.G. Reich, and J. Lessler “The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: estimation and application,” Ann. Internal Med., vol. 172, no. 9, pp. 577–582, 2020.
• Q. Li, X. Guan, and P. Wu, “Early transmission dynamics in Wuhan, China, of novel coronavirus–infected pneumonia,” New England Journal of Medicine, vol. 382, no. 13, pp. 1199–1207, 2020.
• C. Lai, T. Shih, W. Ko, H. Tang, and P. Hsueh, “Severe acute respiratory syndrome coronavirus the challenges,” International Journal of Antimicrobial Agents, vol. 55, no. 3, 2020.
• D. Rio, and P. N. Malani, “Covid-19. New insights on a rapidly changing epidemic,” JAMA, vol. 323, no. 14, pp. 1339-1340, 2020.
• O. A. Adegboye, A. I. Adekunle, and E. Gayawan, “Early transmission dynamics of novel coronavirus (COVID-19) in Nigeria,” Int. J. Environ. Res. Public Health, vol. 17, no. 3054, pp. 1–10, 2020.
• D. Kalyan, G. K. Ranjith, R. Madhusudhan, and K. Lakshminarayan, “Sensitivity and elasticity analysis of novel corona virus transmission model: A mathematical approach,” Sensors International, vol. 2, 1999.
• C. Xu, M. Farman, A. Hasan, A. Akgül, M. Zakarya, W. Albalawi, and C. Park, “Lyapunov stability and wave analysis of Covid-19 omicron variant of real data with fractional operator,” Alexandria Engineering Journal, vol. 61, no. 12, pp. 11787–802, 2022.
• G. Hussain, T. Khan, A. Khan, M. Inc, G. Zaman, K. Sooppy Nisar, and A. Akgül, “Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model,” Alexandria Engineering Journal, vol. 60, no. 4, pp. 4121- 4130, 2021.
• J. H. He, “Homotopy perturbation technique,” Comput. Methods. Appl. Mech. Eng., vol. 178, pp. 257, 1999.