American Institute of Mathematical Sciences

Advanced
2009, 6(2): 209-237. doi: 10.3934/mbe.2009.6.209

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, Puerto Rico
2. 

School of Human Evolution and Social Change, PO Box 872402 Tempe, AZ 85287-2402

Received  February 2008 Revised  November 2008 Published  March 2009

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: demography., stochastic models, tuberculosis, non-autonomous systems.
Mathematics Subject Classification: Primary: 92D25, 92D30; Secondary: 92C6.
Citation: Juan Pablo Aparicio, Carlos Castillo-Chávez. Mathematical modelling of tuberculosis epidemics. Mathematical Biosciences & Engineering, 2009, 6 (2) : 209-237. doi: 10.3934/mbe.2009.6.209
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