Optimizing vaccination strategies in an age structured SIR model

Rinaldo M. Colombo; Mauro Garavello; Rinaldo M. Colombo; Mauro Garavello

doi:10.3934/mbe.2020057

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 2: 1074-1089. doi: 10.3934/mbe.2020057

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Optimizing vaccination strategies in an age structured SIR model

Rinaldo M. Colombo ¹,
Mauro Garavello ^{2
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1.
INdAM Unit, University of Brescia, via Branze, 38, 25123 Brescia, Italy
2.
Department of Mathematics and its Applications, University of Milano - Bicocca, via R. Cozzi, 55, 20126 Milano, Italy

Received: 29 July 2019 Accepted: 07 November 2019 Published: 14 November 2019

We present a modeling framework based on a structured SIR model where different vaccination strategies can be tested and compared. Vaccinations can be dosed at prescribed ages or at prescribed times to prescribed portions of the susceptible population. Different choices of these prescriptions lead to entirely different evolutions of the disease. Once suitable "costs" are introduced, it is natural to seek, correspondingly, the "best" vaccination strategies. Rigorous results ensure the Lipschitz continuous dependence of various reasonable costs on the control parameters, thus ensuring the existence of optimal controls and suggesting their search, for instance, by means of the steepest descent method.
- optimal control,
- deterministic epidemics,
- Conservation Laws,
- renewal equations,
- hyperbolic SIR model
Citation: Rinaldo M. Colombo, Mauro Garavello. Optimizing vaccination strategies in an age structured SIR model[J]. Mathematical Biosciences and Engineering, 2020, 17(2): 1074-1089. doi: 10.3934/mbe.2020057

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Abstract

We present a modeling framework based on a structured SIR model where different vaccination strategies can be tested and compared. Vaccinations can be dosed at prescribed ages or at prescribed times to prescribed portions of the susceptible population. Different choices of these prescriptions lead to entirely different evolutions of the disease. Once suitable "costs" are introduced, it is natural to seek, correspondingly, the "best" vaccination strategies. Rigorous results ensure the Lipschitz continuous dependence of various reasonable costs on the control parameters, thus ensuring the existence of optimal controls and suggesting their search, for instance, by means of the steepest descent method.

References

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