Modeling the Spread of Tuberculosis in Semiclosed Communities

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.

Backward bifurcation and hysteresis in models of recurrent tuberculosis

“…Indeed, Feng et al [ 23 ] incorporated a particular recurrent TB pathway in their model; however, their simplifying assumptions hindered further exploration with regard to its role in causing a backward bifurcation. The models developed by Gomes et al [ 25 ] and Herrera et al [ 26 ] attempted to incorporate exogenous re-infection, partial immunity to reinfection and primary progression. However, neither group examined how recurrent TB reinfection pathways could lead to a backward bifurcation.…”

“…σ measures the probability of fast progression to the infectious class after reinfection. Following the studies of [ 22 , 23 , 25 , 26 , 29 ], p = 1 implies that the body does not render protection against exogenous reinfection while 0 < p < 1 implies the body is partially immune against exogenous reinfection (i.e latent infection provides immunity against new infections) [ 27 , 30 ]. Note that p > 1 would imply that an individual with latent TB infection has increased susceptibility to become newly infected, as compared to the susceptibility of the general population [ 27 ].…”

Disease Control of Delay SEIR Model with Nonlinear Incidence Rate and Vertical Transmission

“…Our model is more approach to the realistic problem which is different from [17, 19]. Moreover, the methods in our model are different from the existing results because more factors are considered.…”

“…The offspring of infected parents may already be infected with the disease at birth, so many infections in nature transmit through both horizontal and vertical modes, such as tuberculosis (TB), rubella, hepatitis B, and AIDS [17–21]. …”

A population-based tuberculosis contact investigation in the country of Georgia

“…1 The early diagnosis of pulmonary TB (PTB) is critically important to prevent TB transmission. As each untreated sputum smear-positive patient with TB is estimated to infect 10-15 contacts annually, 2 early identification, diagnosis, and treatment of contacts of TB patients can be an effective method to reduce transmission of Mycobacterium tuberculosis. 3 Contacts of patients with active PTB are at increased risk of tuberculous infection and disease.…”