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Sliding Mode Control of Outbreaks of Emerging Infectious Diseases

Sliding Mode Control of Outbreaks of Emerging Infectious Diseases This paper proposes and analyzes a mathematical model of an infectious disease system with a piecewise control function concerning threshold policy for disease management strategy. The proposed models extend the classic models by including a piecewise incidence rate to represent control or precautionary measures being triggered once the number of infected individuals exceeds a threshold level. The long-term behaviour of the proposed non-smooth system under this strategy consists of the so-called sliding motion—a very rapid switching between application and interruption of the control action. Model solutions ultimately approach either one of two endemic states for two structures or the sliding equilibrium on the switching surface, depending on the threshold level. Our findings suggest that proper combinations of threshold densities and control intensities based on threshold policy can either preclude outbreaks or lead the number of infecteds to a previously chosen level. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of Mathematical Biology Springer Journals

Sliding Mode Control of Outbreaks of Emerging Infectious Diseases

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References (52)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Society for Mathematical Biology
Subject
Mathematics; Cell Biology; Mathematical and Computational Biology; Life Sciences, general
ISSN
0092-8240
eISSN
1522-9602
DOI
10.1007/s11538-012-9758-5
pmid
22836868
Publisher site
See Article on Publisher Site

Abstract

This paper proposes and analyzes a mathematical model of an infectious disease system with a piecewise control function concerning threshold policy for disease management strategy. The proposed models extend the classic models by including a piecewise incidence rate to represent control or precautionary measures being triggered once the number of infected individuals exceeds a threshold level. The long-term behaviour of the proposed non-smooth system under this strategy consists of the so-called sliding motion—a very rapid switching between application and interruption of the control action. Model solutions ultimately approach either one of two endemic states for two structures or the sliding equilibrium on the switching surface, depending on the threshold level. Our findings suggest that proper combinations of threshold densities and control intensities based on threshold policy can either preclude outbreaks or lead the number of infecteds to a previously chosen level.

Journal

Bulletin of Mathematical BiologySpringer Journals

Published: Jul 27, 2012

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