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Optimal Vaccination, Treatment, and Preventive Campaigns inRegard to the SIR Epidemic Model

Published online by Cambridge University Press:  20 June 2014

E.V. Grigorieva  and
E.N. Khailov
E.V. Grigorieva*
Affiliation:
Department of Mathematics and Computer Sciences, Texas Woman’s University, Denton, TX 76204, USA
E.N. Khailov
Affiliation:
Department of Computational Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russia
*
⋆ Corresponding author. E-mail: [email protected]
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Abstract

The Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease ina population of constant size is considered. In order to control the spread of infection,we propose the model with four bounded controls which describe vaccination of newborns,vaccination of the susceptible, treatment of infected, and indirect strategies aimed at areduction of the incidence rate (e. g. quarantine). The optimal control problem ofminimizing the total number of the infected individuals on a given time interval is statedand solved. The optimal solutions are obtained with the use of the Pontryagin MaximumPrinciple and investigated analytically. Numerical results are presented to illustrate theoptimal solutions.

Keywords

SIR modelcontrol the spread of infectionnonlinear control systemPontryagin maximum principleRiccati equationgeneralized Rolle’s theorem
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 4: Optimal control , 2014 , pp. 105 - 121
Copyright
© EDP Sciences, 2014

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