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Abstract

• Abstract

  During the Covid-19 pandemic a key role is played by vaccination to combat the virus. There are many possible policies for prioritizing vaccines, and different criteria for optimization: minimize death, time to herd immunity, functioning of the health system. Using an age-structured population compartmental finite-dimensional optimal control model, our results suggest that the eldest to youngest vaccination policy is optimal to minimize deaths. Our model includes the possible infection of vaccinated populations. We apply our model to real-life data from the US Census for New Jersey and Florida, which have a significantly different population structure. We also provide various estimates of the number of lives saved by optimizing the vaccine schedule and compared to no vaccination.

  Keywords:
  • COVID-19,
  • SARS-CoV-2,
  • SEIR compartmental models,
  • vaccine,
  • optimal control.
  Mathematics Subject Classification:Primary: 58F15, 58F17; Secondary: 53C35.

  Citation:

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  Figure 1. All possible paths through which populations may flow into other populations

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  Figure 2. Sample tests for New Jersey with a choice of $ R0 = 1.0 $ (mildest case) while varying percent of essential worker and beta

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  Figure 3. Results using New Jersey data-set plotted by initial replication rate

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  Figure 4. Results using Florida data-set plotted by initial replication rate

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  Figure 6. Population dynamics for the unvaccinated compartments: Susceptible, Exposed, Infected, and Recovered

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  Figure 5. Optimal vaccination strategy for Reproduction number 1.2, Percent of workers considered essential 44

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  Figure 7. Population dynamics of the vaccinated compartments: Susceptible, Vaccinated, Exposed vaccinated, Infected vaccinated, and Recovered vaccinated

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  Table 1. Groups by Age

  Name	Description
  Group 1	Age 0-4 population
  Group 2	Age 5-14 population
  Group 3	Age 15-19 population with no job or non-essential
  Group 4	Age 20-39 population with no job or non-essential
  Group 5	Age 40-59 population with no job or non-essential
  Group 6	Age 60-69 population with no job or non-essential
  Group 7	Age 70+ population
  Group 8	Age 15-19 population who are essential workers
  Group 9	Age 20-39 population who are essential workers
  Group 10	Age 40-59 population who are essential workers
  Group 11	Age 60-69 population who are essential workers

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  Table 2. Description of Variables

  Name	Description	Estimate	Units
  $ R_0 $	Rate of infection	1.0-1.2	–
  $ D_I $	Infectious period	5-14	days
  $ D_E $	Latent period	4-7	days

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  Table 3. Deaths Projected with Varying$ R0 $

  State	$ R0 $	Projected Deaths With No Vaccine	Projected Deaths With Vaccine
  New Jersey	$ 1.0 $	9316	6710
  New Jersey	$ 1.1 $	15609	6906
  New Jersey	$ 1.2 $	31681	7289
  Florida	$ 1.0 $	28467	21678
  Florida	$ 1.1 $	44657	22287
  Florida	$ 1.2 $	87349	23298

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