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Mathematical Biosciences and Engineering

2008, Volume 5, Issue 2: 389-402. doi: 10.3934/mbe.2008.5.389
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SEIR epidemiological model with varying infectivity and infinite delay

  • 1.
    Analysis and Stochastics Research Group, Hungarian Academy of Sciences, Bolyai Institute, University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1.
  • 2.
    Center for Disease Modeling & Dept. of Mathematics and Statistics, York University, Toronto 4700 Keele str., M3J 1P3, ON
  • Received: 01 August 2007 Accepted: 29 June 2018 Published: 01 March 2008

  • MSC : Primary 34K60, 92D30.

  • A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R0, which is a threshold quantity for the stability of equilibria, is calculated. If R0 < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if R0 > 1, then an endemic equilibrium appears which is locally asymptotically stable. Applying a perma- nence theorem for infinite dimensional systems, we obtain that the disease is always present when R0 > 1.

    Citation: Gergely Röst, Jianhong Wu. SEIR epidemiological model with varying infectivity and infinite delay[J]. Mathematical Biosciences and Engineering, 2008, 5(2): 389-402. doi: 10.3934/mbe.2008.5.389

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  • A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R0, which is a threshold quantity for the stability of equilibria, is calculated. If R0 < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if R0 > 1, then an endemic equilibrium appears which is locally asymptotically stable. Applying a perma- nence theorem for infinite dimensional systems, we obtain that the disease is always present when R0 > 1.


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