title: Stochastic epidemics in growing populations.
abstract: Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that three different scenarios may occur: (i) an epidemic never takes off, (ii) an epidemic gets going and grows but at a slower rate than the community thus still being negligible in terms of population fractions, or (iii) an epidemic takes off and grows quicker than the community eventually leading to an endemic equilibrium. Depending on the parameter values, either scenario (i) is the only possibility, both scenarios (i) and (ii) are possible, or scenarios (i) and (iii) are possible.
authors.affiliation: Department of Mathematics, Stockholm University, 106 91, Stockholm, Sweden, tom.britton@math.su.se.
authors.forename: Tom
authors.initials: T
authors.lastname: Britton
authors.forename: Pieter
authors.initials: P
authors.lastname: Trapman
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology / Q000276:immunology*; D003198:Computer Simulation; D058872:Epidemics; D006801:Humans; D008390:Markov Chains; D018448:Models, Immunological; D011158:Population Growth; D013269:Stochastic Processes