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 Publication2015
AuthorsQesmi R, Heffernan JM, Wu J
JournalJournal of mathematical biology
Volume70
Issue1-2
Pagination343-66
Date Published2015 Jan
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 R0 is less than unity, which raises many new challenges to effective infection control.

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