Sliding Mode Control of Outbreaks of Emerging Infectious Diseases
Identifieur interne : 001E23 ( Main/Exploration ); précédent : 001E22; suivant : 001E24Sliding Mode Control of Outbreaks of Emerging Infectious Diseases
Auteurs : Yanni Xiao [République populaire de Chine] ; Xiaxia Xu [République populaire de Chine] ; Sanyi Tang [République populaire de Chine]Source :
- Bulletin of Mathematical Biology [ 0092-8240 ] ; 2012-10-01.
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Abstract
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.
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DOI: 10.1007/s11538-012-9758-5
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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. 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