Mathematical modelling of tuberculosis epidemics

Juan Pablo Aparicio; Carlos Castillo-Chávez

doi:10.3934/mbe.2009.6.209

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2009, Volume 6, Issue 2: 209-237. Doi: 10.3934/mbe.2009.6.209 open access

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Mathematical modelling of tuberculosis epidemics

Juan Pablo Aparicio^1, and
Carlos Castillo-Chávez^2,

1.
School of Science and Technology, Universidad Metropolitana, San Juan 00928-1150
2.
School of Human Evolution and Social Change, PO Box 872402 Tempe, AZ 85287-2402

Received: February 2008

Revised: November 2008

Published: March 2009

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Abstract

The strengths and limitations of using homogeneous mixing and heterogeneous mixing epidemic models are explored in the context of the transmission dynamics of tuberculosis. The focus is on three types of models: a standard incidence homogeneous mixing model, a non-homogeneous mixing model that incorporates 'household' contacts, and an age-structured model. The models are parameterized using demographic and epidemiological data and the patterns generated from these models are compared. Furthermore, the effects of population growth, stochasticity, clustering of contacts, and age structure on disease dynamics are explored. This framework is used to asses the possible causes for the observed historical decline of tuberculosis notifications.

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Mathematics Subject Classification: Primary: 92D25, 92D30; Secondary: 92C60.

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