Tuberculosis models with fast and slow dynamics: The role of close and casual contacts

Baojun Song; Carlos Castillo-Chavez; Juan Pablo Aparicio

doi:10.1016/S0025-5564(02)00112-8

Tuberculosis models with fast and slow dynamics: The role of close and casual contacts

Baojun Song, Carlos Castillo-Chavez, Juan Pablo Aparicio

Research output: Contribution to journal › Article › peer-review

108 Scopus citations

Abstract

Models that incorporate local and individual interactions are introduced in the context of the transmission dynamics of tuberculosis (TB). The multi-level contact structure implicitly assumes that individuals are at risk of infection from close contacts in generalized household (clusters) as well as from casual (random) contacts in the general population. Epidemiological time scales are used to reduce the dimensionality of the model and singular perturbation methods are used to corroborate the results of time-scale approximations. The concept and impact of optimal average cluster or generalized household size on TB dynamics is discussed. We also discuss the potential impact of our results on the spread of TB.

Original language	English (US)
Pages (from-to)	187-205
Number of pages	19
Journal	Mathematical Biosciences
Volume	180
Issue number	1-2
DOIs	https://doi.org/10.1016/S0025-5564(02)00112-8
State	Published - 2002
Externally published	Yes

Keywords

Epidemic models
Generalized households
Singular perturbation theory
Social networks
Time scales
Tuberculosis

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
General Biochemistry, Genetics and Molecular Biology
General Immunology and Microbiology
General Agricultural and Biological Sciences
Applied Mathematics

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10.1016/S0025-5564(02)00112-8

Cite this

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title = "Tuberculosis models with fast and slow dynamics: The role of close and casual contacts",

abstract = "Models that incorporate local and individual interactions are introduced in the context of the transmission dynamics of tuberculosis (TB). The multi-level contact structure implicitly assumes that individuals are at risk of infection from close contacts in generalized household (clusters) as well as from casual (random) contacts in the general population. Epidemiological time scales are used to reduce the dimensionality of the model and singular perturbation methods are used to corroborate the results of time-scale approximations. The concept and impact of optimal average cluster or generalized household size on TB dynamics is discussed. We also discuss the potential impact of our results on the spread of TB.",

keywords = "Epidemic models, Generalized households, Singular perturbation theory, Social networks, Time scales, Tuberculosis",

author = "Baojun Song and Carlos Castillo-Chavez and Aparicio, {Juan Pablo}",

note = "Funding Information: This work was partially supported by NSF, NSA, and Sloan grants to the Mathematical and Theoretical Biology Institute at Cornell University. Song also thanks J. Guckenheimer for valuable discussions. ",

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doi = "10.1016/S0025-5564(02)00112-8",

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TY - JOUR

T1 - Tuberculosis models with fast and slow dynamics

T2 - The role of close and casual contacts

AU - Song, Baojun

AU - Castillo-Chavez, Carlos

AU - Aparicio, Juan Pablo

N1 - Funding Information: This work was partially supported by NSF, NSA, and Sloan grants to the Mathematical and Theoretical Biology Institute at Cornell University. Song also thanks J. Guckenheimer for valuable discussions.

PY - 2002

Y1 - 2002

N2 - Models that incorporate local and individual interactions are introduced in the context of the transmission dynamics of tuberculosis (TB). The multi-level contact structure implicitly assumes that individuals are at risk of infection from close contacts in generalized household (clusters) as well as from casual (random) contacts in the general population. Epidemiological time scales are used to reduce the dimensionality of the model and singular perturbation methods are used to corroborate the results of time-scale approximations. The concept and impact of optimal average cluster or generalized household size on TB dynamics is discussed. We also discuss the potential impact of our results on the spread of TB.

AB - Models that incorporate local and individual interactions are introduced in the context of the transmission dynamics of tuberculosis (TB). The multi-level contact structure implicitly assumes that individuals are at risk of infection from close contacts in generalized household (clusters) as well as from casual (random) contacts in the general population. Epidemiological time scales are used to reduce the dimensionality of the model and singular perturbation methods are used to corroborate the results of time-scale approximations. The concept and impact of optimal average cluster or generalized household size on TB dynamics is discussed. We also discuss the potential impact of our results on the spread of TB.

KW - Epidemic models

KW - Generalized households

KW - Singular perturbation theory

KW - Social networks

KW - Time scales

KW - Tuberculosis

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ER -

Tuberculosis models with fast and slow dynamics: The role of close and casual contacts

Abstract

Keywords

ASJC Scopus subject areas

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