Mathematical Biosciences and Engineering (MBE)

Mathematical modelling of tuberculosis epidemics

Pages: 209 - 237, Volume 6, Issue 2, April 2009      doi:10.3934/mbe.2009.6.209

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Juan Pablo Aparicio - School of Science and Technology, Universidad Metropolitana, San Juan 00928-1150, Puerto Rico (email)
Carlos Castillo-Chávez - School of Human Evolution and Social Change, PO Box 872402 Tempe, AZ 85287-2402, United States (email)

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.

Keywords:  tuberculosis, non-autonomous systems, stochastic models, demography.
Mathematics Subject Classification:  Primary: 92D25, 92D30; Secondary: 92C60.

Received: February 2008;      Accepted: November 2008;      Available Online: March 2009.