title: Two SIS epidemiologic models with delays.
abstract: The SIS epidemiologic models have a delay corresponding to the infectious period, and disease-related deaths, so that the population size is variable. The population dynamics structures are either logistic or recruitment with natural deaths. Here the thresholds and equilibria are determined, and stabilities are examined. In a similar SIS model with exponential population dynamics, the delay destabilized the endemic equilibrium and led to periodic solutions. In the model with logistic dynamics, periodic solutions in the infectious fraction can occur as the population approaches extinction for a small set of parameter values.
authors.affiliation: Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA. hethcote@math.uiowa.edu
authors.forename: H W
authors.initials: HW
authors.lastname: Hethcote
authors.forename: P
authors.initials: P
authors.lastname: van den Driessche
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology; D004813:Epidemiology / Q000706:statistics & numerical data*; D006801:Humans; D016015:Logistic Models; D008433:Mathematics; D008954:Models, Biological; D010507:Periodicity; D011157:Population Dynamics