Isaac Scientific Publishing

Advances in Analysis

Feedback Linearization and Optimal Control of the Kermack-McKendrick Model for the Spread of Epidemics

Download PDF (523 KB) PP. 157 - 166 Pub. Date: May 3, 2017

DOI: 10.22606/aan.2017.23003

Author(s)

  • Adela Ionescu
    Department of Applied Mathematics, University of Craiova Al.I. Cuza 13, Craiova 200585, Romania
  • Mario Lefebvre*

    Department of Mathematics and Industrial Engineering, Polytechnique Montréal C.P. 6079, Succursale Centre-ville, Montréal, Québec H3C 3A7, Canada
  • Florian Munteanu

    Department of Applied Mathematics, University of Craiova Al.I. Cuza 13, Craiova 200585, Romania

Abstract

Using the feedback linearization method, a state feedback control for the two-dimensional Kermack-McKendrick model for the spread of epidemics is obtained. This form of the dynamical system is suitable to carry out a qualitative analysis of the model. An optimal control problem for a stochastic version of the model is also set up and solved explicitly in a particular instance.

Keywords

SIR model; Bailey model; dynamical systems; LQG homing; Brownian motion.

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