Article Contents

2022, Volume 17, Issue 3: 443-466. Doi: 10.3934/nhm.2022016

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

1.
Department of Industrial Engineering, Clemson University, Clemson, SC, USA
2.
Center for Computational and Integrative Biology, Rutgers Camden, Camden NJ, USA
3.
Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125, USA
4.
Sorbonne Université, CNRS, Université Paris Cité, Inria, Laboratoire Jacques-Louis Lions (LJLL), F-75005 Paris, France
5.
Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN, USA
6.
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, USA
7.
Joseph and Loretta Lopez chair professor of Mathematics, Center for Computational and Integrative Biology, Rutgers Camden, Camden NJ, USA

Received: September 2021

Revised: January 2022

Early access: March 2022

Published: June 2022

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

Abstract / Introduction Full Text(HTML) Figure(7) / Table(3) Related Papers Cited by

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.

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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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