Integrating immunological and epidemiological models

F. A. Milner, L. M. Sega

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Disease affects populations in two major and complementary ways: at the individual level, the infected may die or suffer other non-lethal but still undesirable consequences from the disease; at the population level, there may be devastation caused be it by diseases that decimate large numbers of individuals, or by creating endemic situations that are very costly in terms of treatment, prevention or isolation, for example. For many decades mathematical models have been proposed and analyzed to describe the evolution of epidemics through populations. Aside from the simplest ODE-based models that contain only epidemiologically relevant variables, several structural variables have been introduced through the years, such as size, age of disease, chronological age, gender, etc. Separately, in last few decades, several models have been proposed and analyzed for the immunological response at the individual level that is the main determinant of recovery, chronic disease, or death. Even though these types of models naturally beckon modelers to combine them, only very recently has this idea taken strength. We propose a general framework for immuno-epidemiological models that use variables of immunological nature (e.g. viral load and some measure of immune response such as T-cell density) as structure variables of epidemiological models. This results in coupled systems of ordinary and partial differential equations, possibly with nonlocal terms and/or boundary conditions. Under this general framework, we describe a simple such combination in an SIR case, and present a partial analysis of the resulting model, as well as generalizations.

Original languageEnglish (US)
Title of host publication18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation
Subtitle of host publicationInterfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings
Pages685-690
Number of pages6
StatePublished - Dec 1 2009
Externally publishedYes
Event18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM09 - Cairns, QLD, Australia
Duration: Jul 13 2009Jul 17 2009

Publication series

Name18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings

Other

Other18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM09
CountryAustralia
CityCairns, QLD
Period7/13/097/17/09

Keywords

  • Epidemiology
  • Immunology
  • Mathematical models
  • Partial differential equations

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computational Mathematics
  • Modeling and Simulation

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  • Cite this

    Milner, F. A., & Sega, L. M. (2009). Integrating immunological and epidemiological models. In 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings (pp. 685-690). (18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings).