title: Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects.
abstract: Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.
authors.affiliation: Department of Applied Stochastics and Operations Research, Clausthal University of Technology, Clausthal-Zellerfeld, Germany.
authors.forename: Hendrik
authors.initials: H
authors.lastname: Baumann
authors.affiliation: Department of Computer Science, Saarland University, Saarbrücken, Germany.
authors.forename: Werner
authors.initials: W
authors.lastname: Sandmann
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology; D003198:Computer Simulation; D003710:Demography / Q000379:methods*; D004641:Emigration and Immigration; D058872:Epidemics; D006801:Humans; D008390:Markov Chains; D015233:Models, Statistical; D011157:Population Dynamics; D011336:Probability; D013269:Stochastic Processes