Assessing the best time interval between doses in a two-dose vaccination regimen to reduce the number of deaths in an ongoing epidemic of SARS-CoV-2

Abstract

The SARS-CoV-2 pandemic is a major concern all over the world and, as vaccines became available at the end of 2020, optimal vaccination strategies were subjected to intense investigation. Considering their critical role in reducing disease burden, the increasing demand outpacing production, and that most currently approved vaccines follow a two-dose regimen, the cost-effectiveness of delaying the second dose to increment the coverage of the population receiving the first dose is often debated. Finding the best solution is complex due to the trade-off between vaccinating more people with lower level of protection and guaranteeing higher protection to a fewer number of individuals. Here we present a novel extended age-structured SEIR mathematical model that includes a two-dose vaccination schedule with a between-doses delay modelled through delay differential equations and linear optimization of vaccination rates. By maintaining the minimum stock of vaccines under a given production rate, we evaluate the dose interval that minimizes the number of deaths. We found that the best strategy depends on an interplay between the vaccine production rate and the relative efficacy of the first dose. In the scenario of low first-dose efficacy, it is always better to vaccinate the second dose as soon as possible, while for high first-dose efficacy, the best strategy of time window depends on the production rate and also on second-dose efficacy provided by each type of vaccine. We also found that the rate of spread of the infection does not affect significantly the thresholds of the best window, but is an important factor in the absolute number of total deaths. These conclusions point to the need to carefully take into account both vaccine characteristics and roll-out speed to optimize the outcome of vaccination strategies.

Fig 1. Diagram representing the full model structure.

Subscripts v and w indicate the first- and second-dose vaccinated classes, respectively. Black arrows indicate transitions between epidemiological stages, green arrows indicate vaccination. All classes pictured inside the gray box are infectious. Because epidemiological progressions happen at time-scales shorter than those related to vaccine effects, infectious classes are not vaccinated in the model.

Fig 2. Vaccination rate as a function of time for first (solid, black) and second doses (dashed, grey)—Scale is given by the left y-axis.

Number of stored vaccine doses as function of time (dot-dashed, blue), scale in the right y-axis. Taking into account 3 or 12 weeks (panels) as separation between doses. V₀ = 2.83% of population in doses, ρ(t) = 0.23% of population in doses/day, v_max = 0.45% of population in doses/day.

Fig 3. Reduction in total number of deaths as function of the first dose relative efficacy, considering three time windows between doses: 3,7 and 12 weeks (colors); varying vaccine type (columns); and effective reproduction number at the start of simulation (rows).

V₀ = 2.83% of population in doses, ρ(t) = 0.23% of population in doses/day, v_max = 0.45% of population in doses/day.

Fig 4. Best window (color) for reduction of deaths as function of production rate (x axis) and relative efficacy of first dose (y axis).

Each panel represents a different vaccine with the respective second dose parameters. The initial R_t is 1.1, V₀ is set to zero, vaccination rate limited to approximately 0.45% of population in doses per day.