Differential and Integral Equations

Global stability of an SIS epidemic model with a finite infectious period

Yukihiko Nakata and Gergely Röst

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Assuming a general distribution for the sojourn time in the infectious class, we consider an SIS type epidemic model formulated as a scalar integral equation. We prove that the endemic equilibrium of the model is globally asymptotically stable whenever it exists, solving the conjecture of Hethcote and van den Driessche (1995) for the case of nonfatal diseases.

Article information

Differential Integral Equations, Volume 31, Number 3/4 (2018), 161-172.

First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37N25: Dynamical systems in biology [See mainly 92-XX, but also 91-XX] 45D05: Volterra integral equations [See also 34A12]


Nakata, Yukihiko; Röst, Gergely. Global stability of an SIS epidemic model with a finite infectious period. Differential Integral Equations 31 (2018), no. 3/4, 161--172. https://projecteuclid.org/euclid.die/1513652421

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