<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Chelsea Uggenti</style></author><author><style face="normal" font="default" size="100%">Connell C. McCluskey</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Global stability for infectious disease models that include immigration of infected individuals and delay in the incidence</style></title><secondary-title><style face="normal" font="default" size="100%">Electronic Journal of Differential Equations</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><volume><style face="normal" font="default" size="100%">2018</style></volume><pages><style face="normal" font="default" size="100%">1-14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">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.</style></abstract><issue><style face="normal" font="default" size="100%">64</style></issue></record></records></xml>