Epidemiological Models With Parametric Heterogeneity : Deterministic Theory for Closed Populations

A.S. Novozhilov

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 3, page 147-167
  • ISSN: 0973-5348

Abstract

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We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed approach. In particular, we formulate and analyze an SIR model with distributed susceptibility and infectivity, showing that the epidemiological models for closed populations are well suited to the suggested framework. A number of known results from the literature is derived, including the final epidemic size equation for an SIR model with distributed susceptibility. It is proved that the bottom up approach of the theory of heterogeneous populations with parametric heterogeneity allows to infer the population level description, which was previously used without a firm mechanistic basis; in particular, the power law transmission function is shown to be a consequence of the initial gamma distributed susceptibility and infectivity. We discuss how the general theory can be applied to the modeling goals to include the heterogeneous contact population structure and provide analysis of an SI model with heterogeneous contacts. We conclude with a number of open questions and promising directions, where the theory of heterogeneous populations can lead to important simplifications and generalizations.

How to cite

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Novozhilov, A.S.. "Epidemiological Models With Parametric Heterogeneity : Deterministic Theory for Closed Populations." Mathematical Modelling of Natural Phenomena 7.3 (2012): 147-167. <http://eudml.org/doc/222445>.

@article{Novozhilov2012,
abstract = {We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed approach. In particular, we formulate and analyze an SIR model with distributed susceptibility and infectivity, showing that the epidemiological models for closed populations are well suited to the suggested framework. A number of known results from the literature is derived, including the final epidemic size equation for an SIR model with distributed susceptibility. It is proved that the bottom up approach of the theory of heterogeneous populations with parametric heterogeneity allows to infer the population level description, which was previously used without a firm mechanistic basis; in particular, the power law transmission function is shown to be a consequence of the initial gamma distributed susceptibility and infectivity. We discuss how the general theory can be applied to the modeling goals to include the heterogeneous contact population structure and provide analysis of an SI model with heterogeneous contacts. We conclude with a number of open questions and promising directions, where the theory of heterogeneous populations can lead to important simplifications and generalizations.},
author = {Novozhilov, A.S.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {SIR model; heterogeneous populations; distributed susceptibility; final epidemic size; heterogeneous contact structure; power law transmission function},
language = {eng},
month = {6},
number = {3},
pages = {147-167},
publisher = {EDP Sciences},
title = {Epidemiological Models With Parametric Heterogeneity : Deterministic Theory for Closed Populations},
url = {http://eudml.org/doc/222445},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Novozhilov, A.S.
TI - Epidemiological Models With Parametric Heterogeneity : Deterministic Theory for Closed Populations
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/6//
PB - EDP Sciences
VL - 7
IS - 3
SP - 147
EP - 167
AB - We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed approach. In particular, we formulate and analyze an SIR model with distributed susceptibility and infectivity, showing that the epidemiological models for closed populations are well suited to the suggested framework. A number of known results from the literature is derived, including the final epidemic size equation for an SIR model with distributed susceptibility. It is proved that the bottom up approach of the theory of heterogeneous populations with parametric heterogeneity allows to infer the population level description, which was previously used without a firm mechanistic basis; in particular, the power law transmission function is shown to be a consequence of the initial gamma distributed susceptibility and infectivity. We discuss how the general theory can be applied to the modeling goals to include the heterogeneous contact population structure and provide analysis of an SI model with heterogeneous contacts. We conclude with a number of open questions and promising directions, where the theory of heterogeneous populations can lead to important simplifications and generalizations.
LA - eng
KW - SIR model; heterogeneous populations; distributed susceptibility; final epidemic size; heterogeneous contact structure; power law transmission function
UR - http://eudml.org/doc/222445
ER -

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