Electron. J. Differential Equations, Vol. 2018 (2018), No. 64, pp. 1-14.

Global stability for infectious disease models that include immigration of infected individuals and delay in the incidence

Chelsea Uggenti, C. Connell McCluskey

Abstract:
We begin with a detailed study of a delayed SI model of disease transmission with immigration into both classes. The incidence function allows for a nonlinear dependence on the infected population, including mass action and saturating incidence as special cases. Due to the immigration of infectives, there is no disease-free equilibrium and hence no basic reproduction number. We show there is a unique endemic equilibrium and that this equilibrium is globally asymptotically stable for all parameter values. The results include vector-style delay and latency-style delay. Next, we show that previous global stability results for an SEI model and an SVI model that include immigration of infectives and non-linear incidence but not delay can be extended to systems with vector-style delay and latency-style delay.

Submitted September 11, 2017. Published March 7, 2018.
Math Subject Classifications: 34K20, 92D30, 93D30.
Key Words: Global stability; Lyapunov function; epidemiology; immigration.

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Chelsea Uggenti
Department of Mathematics
Wilfrid Laurier University
Waterloo, Ontario, Canada
email: cuggenti@uwo.ca
C. Connell McCluskey
Department of Mathematics
Wilfrid Laurier University
Waterloo, Ontario, Canada
email: ccmcc8@gmail.com

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