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Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5534-5544. doi: 10.3934/mbe.2020297
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Research article

Poisson integral type quarantine in a stochastic SIR system

  • Department of Mathematics and Statistics, Queen’s University, 48 University Ave, Jeffery Hall Kingston, ON, Canada, K7L 3N6
  • Received: 13 June 2020 Accepted: 03 August 2020 Published: 14 August 2020

  • We propose a SIR system that includes a Poisson measure term to model the quarantine of infected individuals. An inequality concerning the term representing the transmission rate is given to establish the stochastic stability of the disease free equilibrium. It is further shown that if R0 > 1 then the long-run behavior the system will reside within a neighborhood of the equilibrium in the underlying deterministic version of this system.

    Citation: Andrew Vlasic, Troy Day. Poisson integral type quarantine in a stochastic SIR system[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5534-5544. doi: 10.3934/mbe.2020297

    Related Papers:

  • We propose a SIR system that includes a Poisson measure term to model the quarantine of infected individuals. An inequality concerning the term representing the transmission rate is given to establish the stochastic stability of the disease free equilibrium. It is further shown that if R0 > 1 then the long-run behavior the system will reside within a neighborhood of the equilibrium in the underlying deterministic version of this system.


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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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