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2008, 5(2): 389-402. doi: 10.3934/mbe.2008.5.389

SEIR epidemiological model with varying infectivity and infinite delay

Gergely Röst 1, and  Jianhong Wu 2,

1. 

Analysis and Stochastics Research Group, Hungarian Academy of Sciences, Bolyai Institute, University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1., Hungary
2. 

Center for Disease Modeling & Dept. of Mathematics and Statistics, York University, Toronto 4700 Keele str., M3J 1P3, ON, Canada

Received  August 2007 Revised  January 2008 Published  March 2008

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 $R_0$ < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if $R_0$ > 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 $R_0$ > 1.
Keywords: mathematical epidemiology, permanence., stability, SEIR model, infinite delay.
Mathematics Subject Classification: Primary 34K60, 92D3.
Citation: Gergely Röst, Jianhong Wu. SEIR epidemiological model with varying infectivity and infinite delay. Mathematical Biosciences & Engineering, 2008, 5 (2) : 389-402. doi: 10.3934/mbe.2008.5.389
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