Global stability for infectious disease models that include immigration of infected individuals and delay in the incidence
Date
2018-03-07
Authors
Uggenti, Chelsea
McCluskey, C. Connell
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Global stability, Lyapunov function, Epidemiology, Immigration
Citation
Uggenti, C., & McCluskey, C. C. (2018). Global stability for infectious disease models that include immigration of infected individuals and delay in the incidence. <i>Electronic Journal of Differential Equations, 2018</i>(64), pp. 1-14.
Rights
Attribution 4.0 International