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Optimal Vaccination, Treatment, and Preventive Campaigns in Regard 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: egrigorieva@mail.twu.edu
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Abstract

The Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease in a 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 a reduction of the incidence rate (e. g. quarantine). The optimal control problem of minimizing the total number of the infected individuals on a given time interval is stated and solved. The optimal solutions are obtained with the use of the Pontryagin Maximum Principle and investigated analytically. Numerical results are presented to illustrate the optimal 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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