An immuno-epidemiological model with threshold delay: a study of the effects of multiple exposures to a pathogen.

TitleAn immuno-epidemiological model with threshold delay: a study of the effects of multiple exposures to a pathogen.
Publication TypeJournal Article
Year of Publication2014
AuthorsQesmi R, Heffernan JM, Wu J
JournalJournal of mathematical biology
Date Published2014 Feb 28
ISSN1432-1416
Abstract

An immuno-epidemiological model of pathogen transmission is developed. This model incorporates two main features: (i) the epidemiological model includes within-host pathogen dynamics for an infectious disease, (ii) the susceptible individuals to the infection experience a series of exposures via the pathogen before becoming infectious. It is shown that this model leads naturally to a system of differential delay equations of the threshold type and that these equations can be transformed, in a biologically natural way, to differential equations with state-dependent delay. An interesting dynamical behavior of the model is the bistability phenomena, when the basic reproductive ratio [Formula: see text] is less than unity, which raises many new challenges to effective infection control.

DOI10.1007/s00285-014-0764-0
Alternate JournalJ Math Biol