Vaccine Effects on Susceptibility and Symptomatology Can Change the Optimal Allocation of COVID-19 Vaccines: South Korea as an Example

Abstract

The approved coronavirus disease (COVID-19) vaccines reduce the risk of disease by 70-95%; however, their efficacy in preventing COVID-19 is unclear. Moreover, the limited vaccine supply raises questions on how they can be used effectively. To examine the optimal allocation of COVID-19 vaccines in South Korea, we constructed an age-structured mathematical model, calibrated using country-specific demographic and epidemiological data. The optimal control problem was formulated with the aim of finding time-dependent age-specific optimal vaccination strategies to minimize costs related to COVID-19 infections and vaccination, considering a limited vaccine supply and various vaccine effects on susceptibility and symptomatology. Our results suggest that "susceptibility-reducing" vaccines should be relatively evenly distributed among all age groups, resulting in more than 40% of eligible age groups being vaccinated. In contrast, "symptom-reducing" vaccines should be administered mainly to individuals aged 20-29 and ≥60 years. Thus, our study suggests that the vaccine profile should determine the optimal vaccination strategy. Our findings highlight the importance of understanding vaccine's effects on susceptibility and symptomatology for effective public health interventions.

Keywords: COVID-19; mathematical model; optimal control theory; vaccination; vaccine efficacy.

Figure 1

COVID-19 transmission model with vaccination. All individuals are stratified by age, although age indices have been omitted for clarity.

Figure 2

Optimal vaccination strategies in various vaccine scenarios. The first row represents age-specific levels of optimal vaccination coverage in the vaccine 1 (A), vaccine 2 (B), and vaccine 3 (C) scenarios. The second row represents time-dependent cumulative vaccination coverage levels under optimal vaccination schemes in the vaccine 1 (D), vaccine 2 (E), and vaccine 3 (F) scenarios.

Figure 3

Optimal vaccination strategies in various vaccine scenarios when vaccines provide 95% of reduction in the risk of disease per exposure. The first row represents age-specific levels of optimal vaccination coverage in the vaccine 4 (A), vaccine 5 (B), and vaccine 6 (C) scenarios. The second row represents time-dependent cumulative vaccination coverage levels under optimal vaccination schemes in the vaccine 4 (D), vaccine 5 (E), and vaccine 6 (F) scenarios.

Figure 4

Optimal vaccination strategies in various vaccine scenarios with higher vaccine supply level (B = 70%). The first row represents age-specific levels of optimal vaccination coverage in the vaccine 1 (A), vaccine 2 (B), and vaccine 3 (C) scenarios. The second row represents time-dependent cumulative vaccination coverage levels under optimal vaccination schemes in the vaccine 1 (D), vaccine 2 (E), and vaccine 3 (F) scenarios.

Figure 5

Effect of the relative infectiousness of asymptomatic infections on optimal vaccination strategies. (A–C) Age-specific optimal vaccination coverage levels with vaccines 1, 2, and 3, when b = 0.25 (A), 0.75 (B), and 1 (C). (D) Corresponding proportion of reduction in number of patients with symptomatic infections relative to non-vaccinated cases. (E) Corresponding proportion of reduction in hospitalizations relative to non-vaccination cases.

Figure 6

Effect of vaccine rollouts on optimal vaccination strategies. (A–C) Age-specific optimal vaccination coverage levels in various vaccine efficacy profiles (1, 2, and 3) with ${\psi }_{max}=$ 0.005 (A), 0.01 (B), and 0.015 (C). (D) Corresponding proportion of reduction in symptomatic infections relative to cases without vaccination. (E) Corresponding proportion of reduction in hospitalization relative to cases without vaccination.