The Effect of Double Dose of Vaccination on COVID-19 Infection in India: A Mathematical Study

ABSTRACT

In this paper, we have extended SEIR model of COVID-19 with the inclusion of single and double dose of vaccination compartments. The model is governed by seven dimensional system of ordinary differential equation. The seven compartmental model is analysed and based on the real cumulative numbers of COVID-19 reported cases in India, data has been fitted successfully. The three years time span of the data is taken from 1 January, 2021 to 31 December, 2023. We have investigated disease free equilibrium (DFE) points, basic reproduction number, stability analysis, parameter estimation, model fitting with real data, residual, effect of vaccination drive, sensitivity analysis and contour plots on and . It has been observed that the basic reproduction number is less than one which shows that the disease will be over in near future. Particularly, the study shows that, an increase in the vaccination rates (both first and second dose), reduces the number of infected individuals and increase the recovered individuals. Thus, it is evident that vaccination drive have ample power to reduce the disease burden in the population.

References

1. (2020). Coronavirus Pandemic (COVID-19). Our World in Data. https://ourworldindata.org/coronavirus.
2. Akinwande, N., Somma, S., Olayiwola, R., Ashezua, T., Gweryina, R., Oguntolu, F., Abdurahman, O., Kaduna, F., Adajime, T., Kuta, F., et al. (2023). Modelling the impacts of media campaign and double dose vaccination in controlling COVID-19 in Nigeria. Alexandria Engineering Journal, 80:167–190.
3. Akuka, P. N., Seidu, B., and Bornaa, C. (2022). Mathematical analysis of COVID-19 transmission dynamics model in Ghana with double-dose vaccination and quarantine. Computational and Mathematical Methods in Medicine, 2022.
4. Algarni, A. D., Hamed, A. B., Hamdi, M., Elmannai, H., and Meshoul, S. (2022). Mathematical covid-19 model with vaccination: a case study in saudi arabia. PeerJ Computer Science, 8:e959.
5. Asamoah, J. K. K., Jin, Z., Sun, G.-Q., and Li, M. Y. (2020). A deterministic model for Q fever transmission dynamics within dairy cattle herds: using sensitivity analysis and optimal controls. Computational and Mathematical methods in Medicine, 2020(1):6820608.
6. Ayoola, T. A., Kolawole, M. K., and Popoola, A. O. (2022). Mathematical model of COVID-19 transmission dynamics with double dose vaccination. Tanzania Journal of Science, 48(2):499–512.
7. Cao, Z., Zhang, Q., Lu, X., Pfeiffer, D., Jia, Z., Song, H., and Zeng, D. D. (2020). Estimating the effective reproduction number of the 2019-nCoV in China. medRxiv.
8. de Le´on, U. A.-P., Avila-Vales, E., and Huang, K.-l. (2022). Modeling COVID-19 dynamic using a two-strain model with vaccination. Chaos, Solitons & Fractals, 157:111927.
9. Diekmann, O., Heesterbeek, J., and Roberts, M. G. (2010). The construction of nextgeneration matrices for compartmental epidemic models. Journal of the royal society interface, 7(47):873–885.
10. Diekmann, O., Heesterbeek, J. A. P., and Metz, J. A. (1990). On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. Journal of mathematical biology, 28:365–382.
11. Feng, A., Obolski, U., Stone, L., and He, D. (2022). Modelling covid-19 vaccine breakthrough infections in highly vaccinated israel the effects of waning immunity and third vaccination dose. PLOS global public health, 2(11):e0001211.
12. Jacquez, J. A. and Simon, C. P. (1993). Qualitative theory of compartmental systems. Siam Review, 35(1):43–79.
13. James Peter, O., Ojo, M. M., Viriyapong, R., and Abiodun Oguntolu, F. (2022). Mathematical model of measles transmission dynamics using real data from Nigeria. Journal of Difference Equations and Applications, 28(6):753–770.
14. Khajanchi, S., Sarkar, K., and Mondal, J. (2020). Dynamics of the covid-19 pandemic in india. arXiv preprint arXiv:2005.06286.
15. Khoirunnisa, L. H. and Waluya, S. B. (2022). A Mathematical Model of COVID19 with Double Doses of Vaccination and Quarantine. Unnes Journal of Mathematics, 11(2):120–129.
16. Kobayashi, T. and Nishiura, H. (2022a). Prioritizing COVID-19 vaccination. Part 1: Final size comparison between a single dose and double dose. Mathematical Biosciences and Engineering, 19(7):7374–7387.
17. Kobayashi, T. and Nishiura, H. (2022b). Prioritizing COVID-19 vaccination. Part 2: Real-time comparison between single-dose and double-dose in Japan. Math. Biosci. Eng, 19:7410–7424.
18. Korobeinikov, A. and Rezounenko, A. (2018). Stability of a retrovirus dymanic model. arXiv preprint arXiv:1812.11456.
19. Kuddus, M. A., Mohiuddin, M., and Rahman, A. (2021). Mathematical analysis of a measles transmission dynamics model in bangladesh with double dose vaccination. Scientific reports, 11(1):16571.
20. Kuddus, M. A., Paul, A. K., and Theparod, T. (2024). Cost-effectiveness analysis of COVID-19 intervention policies using a mathematical model: an optimal control approach. Scientific Reports, 14(1):494.
21. Kurmi, S. and Chouhan, U. (2022). A multicompartment mathematical model to study the dynamic behaviour of COVID-19 using vaccination as control parameter. Nonlinear Dynamics, pages 1–17.
22. Legesse, F. M., Rao, K. P., Keno, T. D., et al. (2023). Modeling and optimal control analysis applied to real cases of covid-19 pandemic with double dose vaccination in ethiopia. Journal of Applied Mathematics, 2023.
23. Liu, Y., Gayle, A. A., Wilder-Smith, A., and Rockl¨ov, J. (2020). The reproductive number of COVID-19 is higher compared to SARS coronavirus. Journal of Travel Medicine, 27(2). taaa021.
24. Marques, C., Forattini, O., and Massad, E. (1994). The basic reproduction number for dengue fever in Sao Paulo state, Brazil: 1990–1991 epidemic. Transactions of the Royal Society of Tropical Medicine and Hygiene, 88(1):58–59.
25. Martcheva, M. (2015). An introduction to mathematical epidemiology, volume 61. Springer.
26. Mukandavire, Z., Liao, S., Wang, J., Gaff, H., Smith, D. L., and Morris, J. G. (2011). Estimating the reproductive numbers for the 2008–2009 cholera outbreaks in Zimbabwe. Proceedings of the National Academy of Sciences, 108(21):8767–8772.
27. Mukandavire, Z., Smith, D. L., and Morris Jr, J. G. (2013). Cholera in Haiti: reproductive numbers and vaccination coverage estimates. Scientific Reports, 3(1):1–8.
28. Nishiura, H., Mizumoto, K., Villamil-G´omez, W. E., and Rodr´ıguez-Morales, A. J. (2016). Preliminary estimation of the basic reproduction number of Zika virus infection during Colombia epidemic, 2015-2016. Travel Medicine and Infectious Disease, 14(3):274– 276.
29. Ojo, M. and Akinpelu, F. (2017). Lyapunov functions and global properties of seir epidemic model. International journal of Chemistry, mathematics and Physics (IJCMP),1(1).
30. Omar, O. A., Alnafisah, Y., Elbarkouky, R. A., and Ahmed, H. M. (2021). COVID-19 deterministic and stochastic modelling with optimized daily vaccinations in Saudi Arabia. Results in Physics, 28:104629.
31. Parino, F., Zino, L., Calafiore, G. C., and Rizzo, A. (2023). A model predictive control approach to optimally devise a two-dose vaccination rollout: a case study on COVID-19 in Italy. International journal of robust and nonlinear control, 33(9):4808–4823.
32. Paul, A. K. and Kuddus, M. A. (2022). Mathematical analysis of a COVID-19 model with double dose vaccination in Bangladesh. Results in Physics, 35:105392.
33. Peter, O., Ibrahim, M., Akinduko, O., and Rabiu, M. (2017). Mathematical model for the control of typhoid fever. IOSR J. Math, 13(4):60–66.
34. Peter, O. J., Panigoro, H. S., Abidemi, A., Ojo, M. M., and Oguntolu, F. A. (2023). Mathematical model of COVID-19 pandemic with double dose vaccination. Acta biotheoretica, 71(2):9.
35. Sharbayta, S. S., Desta, H. D., Abdi, T., et al. (2022). Mathematical modelling of COVID-19 transmission dynamics with vaccination: A case study in Ethiopia. Discrete Dynamics in Nature and Society, 2023.
36. Sharma, A., Sharma, G., and Singh, F. (2023). Computational models to study the infectious disease COVID-19: a review. International Journal of Mathematical Modelling and Numerical Optimisation, 13(4):405–441.
37. Theparod, T., Kreabkhontho, P., and Teparos, W. (2023). Booster Dose Vaccination and Dynamics of COVID-19 Pandemic in the Fifth Wave: An Efficient and Simple Mathematical Model for Disease Progression. Vaccines, 11(3):589.
38. Tilahun, G. T., Demie, S., and Eyob, A. (2020). Stochastic model of measles transmission dynamics with double dose vaccination. Infectious Disease Modelling, 5:478–494.
39. Tithi, S. K., Paul, A. K., and Kuddus, M. A. (2023). Mathematical investigation of a two-strain disease model with double dose vaccination control policies. Results in Physics, 53:106930.
40. Van den Driessche, P. and Watmough, J. (2002). Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1-2):29–48.
41. Van den Driessche, P. and Watmough, J. (2008). Further notes on the basic reproduction number. Mathematical Epidemiology, pages 159–178.
42. Wang, Y., Ullah, S., Khan, I. U., AlQahtani, S. A., Hassan, A. M., et al. (2023). Numerical assessment of multiple vaccinations to mitigate the transmission of COVID-19 via a new epidemiological modeling approach. Results in Physics, 52:106889.
43. Zhou, T., Liu, Q., Yang, Z., Liao, J., Yang, K., Bai, W., Lu, X., and Zhang, W. (2020). Preliminary prediction of the basic reproduction number of the Wuhan novel coronavirus 2019-nCoV. Journal of Evidence-Based Medicine, 13(1):3–7.

Download all article in PDF

WSN 195 (2024) 42-65

ADVERTISEMENT