Geodesic
Optimal Vaccination, Treatment, and Preventive Campaigns in Regard to the SIR Epidemic Model
E.V. Grigorieva1 ; E.N. Khailov2
1 Department of Mathematics and Computer Sciences, Texas Woman’s University, Denton, TX 76204, USA
2 Department of Computational Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russia
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 4, pp. 105-121.

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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.
DOI : 10.1051/mmnp/20149407

E.V. Grigorieva 1 ; E.N. Khailov 2

1 Department of Mathematics and Computer Sciences, Texas Woman’s University, Denton, TX 76204, USA
2 Department of Computational Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russia 
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E.V. Grigorieva; E.N. Khailov. Optimal Vaccination, Treatment, and Preventive Campaigns in Regard to the SIR Epidemic Model. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 4, pp. 105-121. doi : 10.1051/mmnp/20149407. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149407/

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