Mathematical Modeling to Study Optimal Allocation of Vaccines against COVID-19 Using an Age-Structured Population

Abstract

Vaccination against the coronavirus disease 2019 (COVID-19) started in early December of 2020 in the USA. The efficacy of the vaccines vary depending on the SARS-CoV-2 variant. Some countries have been able to deploy strong vaccination programs, and large proportions of their populations have been fully vaccinated. In other countries, low proportions of their populations have been vaccinated, due to different factors. For instance, countries such as Afghanistan, Cameroon, Ghana, Haiti and Syria have less than 10% of their populations fully vaccinated at this time. Implementing an optimal vaccination program is a very complex process due to a variety of variables that affect the programs. Besides, science, policy and ethics are all involved in the determination of the main objectives of the vaccination program. We present two nonlinear mathematical models that allow us to gain insight into the optimal vaccination strategy under different situations, taking into account the case fatality rate and age-structure of the population. We study scenarios with different availabilities and efficacies of the vaccines. The results of this study show that for most scenarios, the optimal allocation of vaccines is to first give the doses to people in the 55+ age group. However, in some situations the optimal strategy is to first allocate vaccines to the 15–54 age group. This situation occurs whenever the SARS-CoV-2 transmission rate is relatively high and the people in the 55+ age group have a transmission rate 50% or less that of those in the 15–54 age group. This study and similar ones can provide scientific recommendations for countries where the proportion of vaccinated individuals is relatively small or for future pandemics.

Mathematical Model of COVID-19 Pandemic with Double Dose Vaccination

“… 2022 ; González-Parra et al. 2022 ). Specifically, Aguilar-Canto et al ( 2022 ) proposed and analysed a mathematical model with multiple types of vaccines and trained the model with COVID-19 data from six different countries including Germany and Italy.…”

“…From late 2020, USA, United Kingdom (UK) and European countries among many other countries have deployed different vaccination campaigns (González-Parra et al. 2022 ; Biswas et al. 2021 ).…”

“…In the work of Demongeot et al ( 2022 ), a deterministic compartmental model taking into consideration a variable vaccination in terms of effectiveness for COVID-19 transmission dynamics based on the reported cases and vaccination data of New York City was studied. Furthermore, González-Parra et al ( 2022 ) constructed and parametrized an age-structured non-linear mathematical vaccination model for COVID-19 to assess the optimal vaccination strategy under different scenarios based on data related to USA. In view of the new development in the control of community spread of COVID-19 pandemic in different countries, and Malaysia in particular, this paper aims to construct and analyse a non-linear mathematical model that explicitly includes different compartmental classes for the populations of vaccinated individual with first and second doses for the global epidemic and to investigate the impact of transmission rate, the rate of first vaccine dose, the second dose vaccination rate and the recovery rate due to the second dose of vaccination on the dynamics of the disease outbreak.…”

“…The non-pharmaceutical interventions (precautionary measures) enforced by various countries to halt the chain of COVID-19 transmission include social distancing, wearing masks, regular hand washing, a ban on air traffic, bans on social gatherings in different areas, lockdowns, isolation, social distance, quarantine, awareness programs, and personal hygiene, such as wearing a mask and washing hands regularly (Chatterjee et al 2022;Ali et al 2022) and PCR testing for case detection (Baker et al 2021). From late 2020, USA, United Kingdom (UK) and European countries among many other countries have deployed different vaccination campaigns (González-Parra et al 2022;Biswas et al 2021). This approval of vaccines for public use marked the commencement of a slow recovery (The Lancet Regional Health 2022).…”

Exploring Impacts to COVID-19 Herd Immunity Thresholds Under Demographic Heterogeneity that Lowers Vaccine Effectiveness

“…With the availability of vaccines in the public, in the absence of eradication, an open question has been how to define a quantitative threshold for worldwide vaccine success [14]. Several studies have addressed the question of vaccine effectiveness using age-structured models, with the goal of prioritizing vaccine allocation [2, 11, 29, 37, 38]. However, age-structured modeling studies that evaluate the impacts of differing vaccine efficacies on infection levels have not been as numerous [20].…”