%0 Journal Article
%J Electronic Journal of Differential Equations
%D 2018
%T Global stability for infectious disease models that include immigration of infected individuals and delay in the incidence
%A Chelsea Uggenti
%A Connell C. McCluskey
%X 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.
%B Electronic Journal of Differential Equations
%V 2018
%P 1-14
%G eng
%N 64