# Epidemiological Models With Parametric Heterogeneity : Deterministic Theory for Closed Populations

Mathematical Modelling of Natural Phenomena (2012)

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

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topNovozhilov, 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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