A SEIR model for control of infectious diseases with constraints

M. H. A. Biswas; L. T. Paiva; MdR de Pinho

doi:10.3934/mbe.2014.11.761

Article Contents

2014, Volume 11, Issue 4: 761-784. Doi: 10.3934/mbe.2014.11.761

This issue Previous Article On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients Next Article Stability and bifurcation analysis of epidemic models with saturated incidence rates: An application to a nonmonotone incidence rate

A SEIR model for control of infectious diseases with constraints

1.
Faculdade de Engenharia da Universidade do Porto, DEEC and ISR-Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto

Received: April 2013

Revised: December 2013

Published: March 2014

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Abstract

Optimal control can be of help to test and compare different vaccination strategies of a certain disease. In this paper we propose the introduction of constraints involving state variables on an optimal control problem applied to a compartmental SEIR (Susceptible. Exposed, Infectious and Recovered) model. We study the solution of such problems when mixed state control constraints are used to impose upper bounds on the available vaccines at each instant of time. We also explore the possibility of imposing upper bounds on the number of susceptible individuals with and without limitations on the number of vaccines available. In the case of mere mixed constraints a numerical and analytical study is conducted while in the other two situations only numerical results are presented.

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Mathematics Subject Classification: Primary: 92D30, 49K15; Secondary: 34A34.

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