Journal
MATHEMATICS AND COMPUTERS IN SIMULATION
Volume 100, Issue -, Pages 88-102Publisher
ELSEVIER
DOI: 10.1016/j.matcom.2013.11.005
Keywords
Epidemic model; Backward bifurcation; Global stability; Optimal control; Vaccination
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We focus on an epidemic model which incorporates a non-linear force of infection and two controls: an imperfect preventive vaccine given to susceptible individuals and therapeutic treatment given to infectious. We study both the cases of constant and non constant controls. In the case of constant controls we perform a qualitative analysis based on Lyapunov stability which allows to integrate the bifurcation analysis performed in a previous paper. The occurrence of a backward bifurcation is discussed in the perspective of disease control. The case of time-dependent controls is studied by means of the optimal control theory. The strategy is to minimize both the disease burden and the intervention costs. We derive the optimality system and solve it numerically. The characterization of the optimal time profile of the controls, together with the qualitative analysis provides a rather complete picture of the possible outcomes of the model. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.
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