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 < 1, then the disease-free equilibrium is globally asymptotically stable
and this is the only equilibrium. On the contrary, if > 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 > 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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Abstract
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 < 1, then the disease-free equilibrium is globally asymptotically stable
and this is the only equilibrium. On the contrary, if > 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 > 1.
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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
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