COVID-19 optimal vaccination policies: A modeling study on efficacy, natural and vaccine-induced immunity responses

Abstract

About a year into the pandemic, COVID-19 accumulates more than two million deaths worldwide. Despite non-pharmaceutical interventions as social distance, mask-wearing, and restrictive lockdown, the daily confirmed cases remain growing. Vaccine developments from Pfizer, Moderna, and Gamaleya Institute reach more than 90% efficacy and sustain the vaccination campaigns in multiple countries. However, natural and vaccine-induced immunity responses remain poorly understood. There are great expectations, but the new SARS-CoV-2 variants demand to inquire if the vaccines will be highly protective or induce permanent immunity. Further, in the first quarter of 2021, vaccine supply is scarce. Consequently, some countries that are applying the Pfizer vaccine will delay its second required dose. Likewise, logistic supply, economic and political implications impose a set of grand challenges to develop vaccination policies. Therefore, health decision-makers require tools to evaluate hypothetical scenarios and evaluate admissible responses. Following some of the WHO-SAGE recommendations, we formulate an optimal control problem with mixed constraints to describe vaccination schedules. Our solution identifies vaccination policies that minimize the burden of COVID-19 quantified by the number of disability-adjusted years of life lost. These optimal policies ensure the vaccination coverage of a prescribed population fraction in a given time horizon and preserve hospitalization occupancy below a risk level. We explore via simulation plausible scenarios regarding efficacy, coverage, vaccine-induced, and natural immunity. Our simulations suggest that response regarding vaccine-induced immunity and reinfection periods would play a dominant role in mitigating COVID-19.

Mathematical Modeling for COVID-19 with Focus on Intervention Strategies and Cost-Effectiveness Analysis

“…Proof According to Pontryagins Maximum Principle, we can give the proof above. By differentiating the Hamiltonian function (22) partially with respect to the state variables S 1 , S 2 , E, I, A, H, R, we can obtain the adjoint state equations (23) as…”

“…Eikenberry et al [22] proposed a model to assess the inhibitory effect of the mask used by the asymptomatic public on COVID-19. Acuña-Zegarra et al proposed an optimal control problem to explore the optimal vaccination policies [23]. Inspired by the works above, we construct a novel COVID-19 epidemic model, which combines some non-pharmaceutical interventions being implemented in practice (i.e.…”

The trade-off between mobility and vaccination for COVID-19 control: a metapopulation modelling approach

“…where C i is the target immunization coverage and T i the target time to achieve that coverage. The vaccination rate u i is obtained from the approximation 1 − exp (− u i T i ) = C i [29]. To formulate our scenarios, we take into consideration the currently available information of the COVID-19 vaccine candidates [2].…”

The impact of vaccination on the spread of COVID-19: Studying by a mathematical model

“…The authors point out that due to the slow COVID-19 vaccination rate, non-drug prevention and control measures still need to be enforced until a sufficient proportion of the population is vaccinated. There are also some studies discussing vaccination prioritization strategies, such as [25] , [26] , [27] , [28] . In this paper, we present a SVAIRS (susceptible-vaccinated-asymptomatic-symptomatic-removed-susceptible) model to analyze whether the COVID-19 epidemic can be completely eliminated by vaccination alone.…”