The investigation of variant vaccination models in Iran

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran

2 Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, 1841, Rasht, Guilan, Iran

10.22075/ijnaa.2023.31446.4631

Abstract

Kermack-McKendrick-type epidemic models are commonly used for modeling epidemic diseases. In this study, we have proposed a Kermack-McKendrick-based model to elucidate the impact of COVID-19 vaccination on the spread of the virus in Iran. This model serves as an endemic assessment tool, tailored to fit reported data in Iran, for gauging the potential population-level effects of the COVID-19 vaccine. It's important to note that COVID-19 vaccines do not guarantee complete protection against the disease. A vaccinated person may still become infected, highlighting the necessity of continuous vaccination while an individual is in the system. To address this, we considered two models—one with only one strain and the other containing two strains. We hypothesize that the vaccine results in complete immunization against one strain while conferring partial immunization against the other. To explore this, we consider two scenarios. In the first scenario, we assume that the vaccine does not provide complete immunity, and individuals may become infected again after vaccination. In the second scenario, a dual-strain model is considered, positing that individuals, when vaccinated, remain immune to the strain present in the vaccine, but are susceptible to another strain for which the vaccine provides partial protection. However, this other strain may still lead to infection in individuals. The analysis of the proposed models revealed that where the prevalence rate, or the basic reproduction number (R0) - an index measuring the spreading potential of a pathogenic agent and the average number of individuals each infected person can potentially transmit the infectious agent to susceptible individuals - has a direct correlation with vaccination. Therefore, to assess the extent of vaccine efficacy, this indicator is employed, with a lower prevalence rate being the targeted outcome.

Keywords

[1] A. Azar, Control Applications for Biomedical Engineering Systems, Elsevier Science, 2020.
[2] T. Britton, F. Ball, and P. Trapman, A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2, Science 369 (2020), 846–849.
[3] F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, 2012.
[4] K.J. Bruxvoort, L.S. Sy, L. Qian, B.K. Ackerson, Y. Luo, G.S. Lee, Y. Tian, A. Florea, H.S. Takhar, J.E. Tubert, and C.A. Talarico, Real-world effectiveness of the mRNA-1273 vaccine against COVID-19: interim results from a prospective observational cohort study, Lancet Regional Health–Americas 6 (2022).
[5] P. Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), 29–48.
[6] M. Frieman, A.D. Harris, R.S. Herati, F. Krammer, A. Mantovani, M. Rescigno, M.M. Sajadi, and V. Simon, SARS-CoV-2 vaccines for all but a single dose for COVID-19 survivors, eBioMedicine 68 (2021), 103401.
[7] N.M. Ferguson, D. Laydon, G. Nedjati-Gilani, N. Imai, K. Ainslie, M. Baguelin, S. Bhatia, A. Boonyasiri, Z. Cucunuba, G. Cuomo-Dannenburg, and A. Dighe, Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand, London: Imperial College COVID-19 Response Team. March 16 (2020).
[8] A.B. Gumel, E.A. Iboi, C.N. Ngonghala, and E.H. Elbasha, A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations, Infect. Disease Modell. 6 (2021), 148–168.
[9] F. Havers, H. Phm and C. Taylor et al., COVID-19-associated hospitalizations among vaccinated and unvaccinated adults ≥ 18 years – COVID-NET, JAMA Internal Med. 182 (2022), no. 10, 1071–1081.
[10] J. Haefner, Modeling Biological Systems: Principles and Applications, Springer, 2005.
[11] H.W. Hethcote, The mathematics of infectious diseases, SIAM Rev. 42 (2020), no. 4, 599-–653.
[12] Islamic Republic of Iran Ministry of Health and Medical Education, https://ird.behdasht.gov.ir/
[13] B. Ivorra and A.M. Ramos, Application of the Be-CoDis mathematical model to forecast the international spread of the 2019 Wuhan coronavirus outbreak, Technical Report. (2020) 1-–13 DOI:  10.13140/RG.2.2.31460.94081.
[14] B. Ivorra and A.M. Ramos, Validation of the forecasts for the international spread of the coronavirus disease 2019 (COVID-19) done with the Be-CoDis mathematical model, Technical Report (2020) 1-–7 DOI:10.13140/RG.2.2.34877.00485.
[15] B. Ivorra, A.M. Ramos, and D. Ngom, Be-CoDiS: A mathematical model to predict the risk of human diseases spread between countries-validation and application to the 2014-2015 Ebola Virus Disease epidemic, Bull. Math. Bio. 77 (2015), no. 9, 1668-–1704.
[16] Sh. Jiang, Q. Li, C. Li, Sh. Liu, X. He, T. Wang, H. Li, C. Corpe, X. Zhang, J. Xu, and J. Wang, Mathematical models for devising the optimal SARS-CoV-2 strategy for eradication in China, South Korea, and Italy, J. Translat. Med. 18 (2020), 345.
[17] Y.N. Kyrychko, K.B. Blyuss, and I. Brovchenko, Mathematical modelling of the dynamics and containment of COVID-19 in Ukraine, Sci. Rep. 10 (2020), no. 1, 19662.
[18] P. Lancaster, Theory of Matrices, Academic Press, New York USA, 1969.
[19] M. Makhoul, H.H. Ayoub, H. Chemaitelly, Sh. Seedat, G.R. Mumtaz, S. Al-Omari, and L.J. Abu-Raddad, Epidemiological impact of SARS-CoV-2 vaccination: Mathematical modeling analyses, Vaccines 8 (2020), no. 4, 668.
[20] Mc. McDonnell, R.V. Exan, S. Loyd, L. Subramanian, K. Chalkidou, A.L. Porta, J. Li, E. Maiza, D. Reader, J. Rosenberg, J. Scannell, V. Thomas, R. Weintraub, and P. Yadav, COVID-19 Vaccine Predictions: Using Mathematical Modelling and Expert Opinions to Estimate Timelines and Probabilities of Success of COVID-19 Vaccines, Center for Global Development, 2020.
[21] S.M. Moghadas, Gaining insights into human viral diseases through mathematics, Eur. J. Epidem. 21 (2006), no. 5, 337-–342.
[22] H. Taheri, N. Eghbali, M. Pourabd, and H. Zhu, Assessment of the mathematical model for investigating Covid-19 peak as a global epidemic in Iran, Math. Anal. Convex Optim. 3 (2022), no. 2, 129-–142.
[23] M. Thompson, E. Stenehjem and S. Grannis, S.W. Ball, A.L. Naleway, T.C. Ong, M.B. DeSilva, K. Natarajan, C.H. Bozio, N. Lewis, and K. Dascomb, Effectiveness of COVID-19 vaccines in ambulatory and inpatient care settings, New Engl. J. Med. 385 (2021), no. 15, 1355–1371.
[24] G. Vries, T. Hillen, M. Lewis, B. Sch˜onfisch, and J. Muller, A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Methods, ser. Monographs on Mathematical Modeling and Computation, Society for Industrial and Applied Mathematics, 2006.
[25] L. Wang and R. Xu, Global stability of an SEIR epidemic model with vaccination, Int. J. Biomath. 9 (2016), no. 6, Article ID 1650082.
[26] W. Yang, A. Karspeck, and J. Shaman, Comparison of filtering methods for the modeling and retrospective forecasting of influenza epidemics, PLOS Comput. Bio. 10 (2014), no. 4.
[27] Z. Yu, J. Liu, X. Wang, X. Zhu, D. Wang, and G. Han, Efficient vaccine distribution based on a hybrid compartmental model, PLoS ONE. 11 (2016), no. 5, Article ID e0155416.
[29] L. Zou, F. Ruan, M. Huang, L. Liang, H. Huang, Z. Hong, J. Yu, M. Kang, Y. Song, J. Xia, and Q. Guo, SARSCoV- 2 viral load in upper respiratory specimens of infected patients, New England J. Med. 382 (2020), 1177-–1179.

Articles in Press, Corrected Proof
Available Online from 18 February 2024
  • Receive Date: 07 August 2023
  • Revise Date: 14 December 2023
  • Accept Date: 27 December 2023