TY - GEN
T1 - Integrating immunological and epidemiological models
AU - Milner, F. A.
AU - Sega, L. M.
N1 - Publisher Copyright:
© MODSIM 2009.All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Epidemiology
KW - Immunology
KW - Mathematical models
KW - Partial differential equations
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M3 - Conference contribution
AN - SCOPUS:85086241902
T3 - 18th World IMACS Congress and MODSIM 2009 - International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings
SP - 685
EP - 690
BT - 18th World IMACS Congress and MODSIM 2009 - International Congress on Modelling and Simulation
A2 - Anderssen, R.S.
A2 - Braddock, R.D.
A2 - Newham, L.T.H.
PB - Modelling and Simulation Society of Australia and New Zealand Inc. (MSSANZ)
T2 - 18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM 2009
Y2 - 13 July 2009 through 17 July 2009
ER -