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Optimization of vaccination for COVID-19 in the midst of a pandemic

The authors acknowledge the support of the NSF CMMI project # 2033580 "Managing pandemic by managing mobility". R.W., S.T.M. and B.P. acknowledge the support of the Joseph and Loretta Lopez Chair endowment

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  • 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.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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

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

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

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

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

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

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

    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
     | Show Table
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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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
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