Table 1 Summary of different mathematical models used to describe the dynamics of the COVID-19 pandemic

Acuña-Zegarra et al. [16]

\(SEI_{S} I_{A} RDV\)

This study used optimal control methods with mixed constraints to evaluate different vaccination strategies to minimize the burden of COVID-19 pandemic, which could help policy decision makers design vaccination plans for the homogeneous population

This study did not consider the age structure or heterogeneity of the population

Libotte et al. [17]

\(SIR\)

This study developed a method to solve the inverse problem to determine the parameters of the SIR model, and considered the single- and multi-objective optimization environment to determine the best vaccination strategy for the COVID-19 pandemic

This study did not consider the age structure or heterogeneity of the population

Choi et al. [18]

\(SVEPI_{S} I_{A} H^{M} H^{S} DR\)

This study established an age-structured mathematical model and combined actual epidemiological data in Korea to evaluate vaccination strategies on the infection incidence and mortality for each age group under different levels of social distance

This study did not consider the priority vaccination for essential workers which had been planned by the Korean government

Matrajt et al. [19]

\(SEPI_{S} I_{A} HH_{C}R\)

This study used a mathematical model of age structure and combined optimization algorithms to evaluate different combinations of vaccine effectiveness and vaccination coverage for four different indicators (minimize deaths, minimize symptomatic infections, maximum non-ICU and minimize ICU hospitalizations)

This study assumed that asymptomatic and symptomatic infections had the same immunity. However, asymptomatic individuals may have a weaker immune response

Iboi et al. [20]

\(S_{u} S_{v} E_{1} E_{2} I_{S} I_{A} HR\)

This study evaluated the impact of vaccines on the control of COVID-19 in the United States based on a deterministic mathematical model, and derived the expression for the vaccine-induced herd immunity threshold

This study did not consider the age structure or heterogeneity of the population

Shen et al. [21]

\(SVEI_{A} I_{1} I_{2} T_{1} T_{2} DR\)

This study established a deterministic mathematical model, and evaluated the required vaccine effectiveness and vaccination coverage rate to suppress the COVID-19 pandemic, when the social contact returned to pre-pandemic normal levels and the face mask use was reduced

This study did not consider the age structure or heterogeneity of the population

Bubar et al. [22]

\(SEIR\)

This study used an age structured model to evaluate the impact of five COVID-19 vaccine priority strategies on cumulative incidence, mortality, and years of life lost

Due to the lack of direct measurement data, this study extrapolated the contact matrix to people over 80

Foy et al.[23]

\(SVEI_{S} I_{A} QRD\)

This study used an age structured model to investigate the impact of four age-based vaccination strategies on the infections and cumulative deaths, they concluded that allocating COVID-19 vaccines to older age groups (> 60 years) was the optimal in all scenarios considered regardless of vaccine efficacy, dispensation speed, force of infection

This study assumed that some model parameters that may vary with age and time, such as the latent period, the force of infection and the recovery rate to be constant due to the lack of clear data

Buckner et al. [24]

\(SV_{P} V_{F} EPI_{S} I_{A} RD\)

This study used an age structured model to solve for optimal strategies to allocate the limit COVID-19 vaccines to essential workers that minimizes the number of total deaths, years of life lost, or infections, they concluded that prioritizing the limit COVID-19 vaccines to older essential workers can better reduce mortality, and prioritizing the limit COVID-19 vaccines to younger essential workers can better control spread

This study did not consider the seasonality of contact rates for children in the scenarios where schools are modeled as closed. This may have limited impact on the optimal solutions