title: Dynamics of an SIR model with vaccination dependent on past prevalence with high-order distributed delay.
abstract: This paper investigates the dynamics of an SIR model of childhood vaccination under the assumption that the vaccination uptake rate depends on past values of disease prevalence. The delay kernel is a high order Erlang function, which allows no instantaneous feedback between prevalence at time t and vaccinations at time t. Multiple types of endemic equilibria are found, as are stable and unstable equilibria, periodic orbits, dependence on initial conditions, and apparent chaos.
authors.affiliation: California State University, Chico, CA 95929, United States. Electronic address: jeckalbar@csuchico.edu.
authors.forename: John C
authors.initials: JC
authors.lastname: Eckalbar
authors.affiliation: University of California, San Francisco, CA 94143, United States.
authors.forename: Walter L
authors.initials: WL
authors.lastname: Eckalbar
mesh_terms: D003140:Communicable Disease Control; D003141:Communicable Diseases / Q000453:epidemiology*; D006801:Humans; D008962:Models, Theoretical; D015995:Prevalence; D014611:Vaccination