Math. Model. Nat. Phenom.
Volume 9, Number 4, 2014Optimal control
|Page(s)||105 - 121|
|Published online||20 June 2014|
Optimal Vaccination, Treatment, and Preventive Campaigns in Regard to the SIR Epidemic Model
Department of Mathematics and Computer Sciences, Texas Woman’s
2 Department of Computational Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russia
⋆ Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 49J15 / 58E25 / 92D30
Key words: SIR model / control the spread of infection / nonlinear control system / Pontryagin maximum principle / Riccati equation / generalized Rolle’s theorem
© EDP Sciences, 2014
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