Computational and Mathematical Methods in Medicine
Volume 2013 (2013), Article ID 648291, 19 pages
Research Article

Modeling the Spread of Tuberculosis in Semiclosed Communities

1Facultad de Ingeniería, Universidad del Desarrollo, Santiago 7620001, Chile
2Facultad de Ingeniería, Universidad Diego Portales, Ejército 441, Santiago 8370179, Chile
3CEPS, Facultad de Medicina, Clínica Alemana, Universidad del Desarrollo, Santiago 7710162, Chile

Received 23 December 2012; Revised 11 March 2013; Accepted 11 March 2013

Academic Editor: Nestor V. Torres

Copyright © 2013 Mauricio Herrera et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We address the problem of long-term dynamics of tuberculosis (TB) and latent tuberculosis (LTB) in semiclosed communities. These communities are congregate settings with the potential for sustained daily contact for weeks, months, and even years between their members. Basic examples of these communities are prisons, but certain urban/rural communities, some schools, among others could possibly fit well into this definition. These communities present a sort of ideal conditions for TB spread. In order to describe key relevant dynamics of the disease in these communities, we consider a five compartments SEIR model with five possible routes toward TB infection: primary infection after a contact with infected and infectious individuals (fast TB), endogenous reactivation after a period of latency (slow TB), relapse by natural causes after a cure, exogenous reinfection of latently infected, and exogenous reinfection of recovered individuals. We discuss the possible existence of multiple endemic equilibrium states and the role that the two types of exogenous reinfections in the long-term dynamics of the disease could play.