title: An immuno-epidemiological model with threshold delay: a study of the effects of multiple exposures to a pathogen.
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.
authors.affiliation: École Supérieure de Technologie, Université Sidi Mohamed Ben Abdellah, 30000 , Fés, Morocco, qesmir@gmail.com.
authors.forename: Redouane
authors.initials: R
authors.lastname: Qesmi
authors.forename: Jane M
authors.initials: JM
authors.lastname: Heffernan
authors.forename: Jianhong
authors.initials: J
authors.lastname: Wu
mesh_terms: D000818:Animals; D050936:Basic Reproduction Number / Q000706:statistics & numerical data; D003141:Communicable Diseases / Q000453:epidemiology / Q000276:immunology; D018562:Disease Transmission, Infectious; D054884:Host-Pathogen Interactions / Q000276:immunology; D006801:Humans; D017053:Infection Control; D055641:Mathematical Concepts; D018448:Models, Immunological; D013997:Time Factors