Modeling the Spread of Tuberculosis in Semiclosed Communities

Mauricio Herrera,Ximena Aguilera,Paul Bosch,Manuel Nájera

doi:10.1155/2013/648291

Mauricio Herrera, Ximena Aguilera + Show 2 more

Open Access

https://doi.org/10.1155/2013/648291

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Abstract

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.

Highlights

Dynamics of tuberculosis (TB) spread has been the subject of a considerable body of theoretical and mathematical work
The choice of a particular model is strongly connected to the questions we want to answer, and in the present work we will address the problem of long-term dynamics of tuberculosis and latent tuberculosis (LTB) in semiclosed communities
In order to consider high incidence and prevalence of TB and LTB in semiclosed communities, we have used in this work a compartmental SEIR model with five possible pathways to TB disease

Summary

Introduction

Dynamics of tuberculosis (TB) spread has been the subject of a considerable body of theoretical and mathematical work. We will use an SEIR standard compartmental model; see for example the works by Blower et al [23] and more recently by Liao et al [24] with some modifications explained bellow that turn out to be quite useful in the study of the particularities of TB spread at this type of communities This model assumes that the population in the community is homogeneous that it does not consider the heterogeneities in the social structure between community members, and it is based on the so-called mass action or fully mixing approximation. It is estimated that only about 5 to 10 percent of LTB individuals develop clinical or active TB [16], but due to the above described extreme conditions at semiclosed communities such as prisons, persons lived in these communities may be at risk of rapid progression from LTB to active TB following recent infection or reactivation of latent infection, or reinfection, see [6]. The extent to which latent tuberculosis infection could reduce the risk of progressive disease following reinfection is not known [31]

A Compartmental Model for the TB Spread

Numerical Simulations

Findings

Discussion and Conclusions