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. 2023 Mar 24;11(4):722.
doi: 10.3390/vaccines11040722.

Mathematical Modeling Evaluates How Vaccinations Affected the Course of COVID-19 Disease Progression

Eleftheria Tzamali  1 , Vangelis Sakkalis  1 , Georgios Tzedakis  1 , Emmanouil G Spanakis  1 , Nikos Tzanakis  2
Affiliations

Mathematical Modeling Evaluates How Vaccinations Affected the Course of COVID-19 Disease Progression

Eleftheria Tzamali et al. Vaccines (Basel). .

Abstract

The regulation policies implemented, the characteristics of vaccines, and the evolution of the virus continue to play a significant role in the progression of the SARS-CoV-2 pandemic. Numerous research articles have proposed using mathematical models to predict the outcomes of different scenarios, with the aim of improving awareness and informing policy-making. In this work, we propose an expansion to the classical SEIR epidemiological model that is designed to fit the complex epidemiological data of COVID-19. The model includes compartments for vaccinated, asymptomatic, hospitalized, and deceased individuals, splitting the population into two branches based on the severity of progression. In order to investigate the impact of the vaccination program on the spread of COVID-19 in Greece, this study takes into account the realistic vaccination program implemented in Greece, which includes various vaccination rates, different dosages, and the administration of booster shots. It also examines for the first time policy scenarios at crucial time-intervention points for Greece. In particular, we explore how alterations in the vaccination rate, immunity loss, and relaxation of measures regarding the vaccinated individuals affect the dynamics of COVID-19 spread. The modeling parameters revealed an alarming increase in the death rate during the dominance of the delta variant and before the initiation of the booster shot program in Greece. The existing probability of vaccinated people becoming infected and transmitting the virus sets them as catalytic players in COVID-19 progression. Overall, the modeling observations showcase how the criticism of different intervention measures, the vaccination program, and the virus evolution has been present throughout the various stages of the pandemic. As long as immunity declines, new variants emerge, and vaccine protection in reducing transmission remains incompetent; monitoring the complex vaccine and virus evolution is critical to respond proactively in the future.

Keywords: COVID-19; SARS-CoV-2; SEIR model; epidemics; mathematical modeling; scenario analyses; vaccination.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Proportion of SARS-CoV-2 variants in Greece for the time period 1 February 2021–15 June 2022. Data are provided by https://www.ecdc.europa.eu/ (accessed on 14 February 2023).
Figure 2
Figure 2
Schematic overview of the proposed model (SEAIR-severe/mild). Individuals in the model are classified into susceptible (S), unvaccinated exposed (E), unvaccinated asymptomatic (A), unvaccinated detected incidents (I), recovered (R), hospitalized (H), perished (P), vaccinated before immunity has been reached (V), fully vaccinated (F), vaccinated exposed (Ev), vaccinated asymptomatic (Av) and vaccinated detected incidents (Iv).
Figure 3
Figure 3
Impact of altering the vaccination rate after 23 April 2021 (decline of the second wave in Greece) on disease dynamics. The daily (a) incidents, (b) hospital admissions, and (c) deaths are highly reduced when the vaccination rate is increased. A three-month prediction is depicted. An indicative data point from the future (1 June 2021) is shown with a yellow asterisk for comparison.
Figure 4
Figure 4
Impact of altering the vaccination rate after 10 August 2021 (rise of the third wave in Greece) on disease dynamics. The daily (a) incidents, (b) hospital admissions, and (c) deaths are affected indicating the importance of keeping up the high vaccination pace. An indicative data point from the future (1 October 2021) is shown with a yellow asterisk for comparison.
Figure 5
Figure 5
Impact of vaccine effectiveness against infection and transmission on driving the disease dynamics after 10 August 2021. The daily (a) incidents, (b) hospital admissions, and (c) deaths are considerably affected indicating the importance of self-awareness in vaccinated individuals. An indicative data point from the future (1 October 2021) is shown with a yellow asterisk for comparison.
Figure 6
Figure 6
Impact of immunity loss on the disease dynamics after 10 August 2021. The daily (a) incidents, (b) hospital admissions, and (c) deaths are shown. An indicative data point from the future (1 October 2021) is shown with a yellow asterisk for comparison.
Figure 7
Figure 7
Real and fitted data for Greece from daily incidents, vaccinations, deaths, admission to and discharges from the hospitals for the fitting time period 1 February 2021–15 June 2022. The real data are shown with blue dots. The model fitting is shown with a continuous line and the future two-week predictions are shown with a dashed line.
Figure 8
Figure 8
Fitted parameters over time for the fitting time period 1 February 2021–15 June 2022. (a) Transmission rate of asymptomatic individuals (aa), (b) transmission rate of confirmed cases (ai), (c) mortality rate (μ), (d) admission rate to hospitals (hin), (e) discharge rate from hospital (hout), and (f) vaccination rate over time (vin).
Figure 9
Figure 9
Relative hospitalization rate (calculated by dividing the hospitalization rate after vaccinations by the hospitalization rate before vaccinations) depicted with the blue line against the percentage of vaccinated individuals in the population (depicted with the orange line) for the time period 1 February 2021–15 June 2022. The percentage of individuals who have received a booster shot is also shown (dashed orange line).
Figure 10
Figure 10
The impact of an effective booster shot is shown under the dominance of omicron sub-variants. The fitting time period is 1 February 2021–15 June 2022. The daily (a) incidents, (b) hospital admissions, and (c) deaths are shown.
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