Optimal Tuberculosis Prevention and Control Strategy from a Mathematical Model Based on Real Data

A mathematical control model for the transmission dynamics of tuberculosis (TB) in South Korea is developed on the basis of the reported active-TB and relapse-TB incidence data. In this work, optimal control theory is used to propose optimal TB prevention and control strategy and rearrange the government TB budget for the best TB elimination plan. The impact of distancing, case finding, and/or case holding controls are investigated when the number of infected and infectious individuals are minimized, while the intervention costs are kept low. The implementation of optimal control measures shows that the distancing control, such as isolation of infectious people, early TB patient detection, and educational program/campaign for healthy control, is the most effective control factor for the prevention of TB transmission in South Korea.     

Epidemiological models of Mycobacterium tuberculosis complex infections

The resurgence of tuberculosis in the 1990s and the emergence of drug-resistant tuberculosis in the first decade of the 21st century increased the importance of epidemiological models for the disease. Due to slow progression of tuberculosis, the transmission dynamics and its long-term effects can often be better observed and predicted using simulations of epidemiological models. This study provides a review of earlier study on modeling different aspects of tuberculosis dynamics. The models simulate tuberculosis transmission dynamics, treatment, drug resistance, control strategies for increasing compliance to treatment, HIV/TB co-infection, and patient groups. The models are based on various mathematical systems, such as systems of ordinary differential equations, simulation models, and Markov Chain Monte Carlo methods. The inferences from the models are justified by case studies and statistical analysis of TB patient datasets.     

How host heterogeneity governs tuberculosis reinfection?

Recurrent episodes of tuberculosis (TB) can be due to relapse of latent infection or exogenous reinfection, and discrimination is crucial for control planning. Molecular genotyping of Mycobacterium tuberculosis isolates offers concrete opportunities to measure the relative contribution of reinfection in recurrent disease. Here, a mathematical model of TB transmission is fitted to data from 14 molecular epidemiology studies, enabling the estimation of relevant epidemiological parameters. Meta-analysis reveals that rates of reinfection after successful treatment are higher than rates of new TB, raising an important question about the underlying mechanism. We formulate two alternative mechanisms within our model framework: (i) infection increases susceptibility to reinfection or (ii) infection affects individuals differentially, thereby recruiting high-risk individuals to the group at risk for reinfection. The second mechanism is better supported by the fittings to the data, suggesting that reinfection rates are inflated through a population phenomenon that occurs in the presence of heterogeneity in individual risk of infection. As a result, rates of reinfection are higher when measured at the population level even though they might be lower at the individual level. Finally, differential host recruitment is modulated by transmission intensity, being less pronounced when incidence is high.     

Population-Level Impact of Shorter-Course Regimens for Tuberculosis: A Model-Based Analysis

Despite current control efforts, global tuberculosis (TB) incidence is decreasing slowly. New regimens that can shorten treatment hold promise for improving treatment completion and success, but their impact on population-level transmission remains unclear. Earlier models projected that a four-month regimen could reduce TB incidence by 10% but assumed that an entire course of therapy must be completed to derive any benefit. We constructed a dynamic transmission model of TB disease calibrated to global estimates of incidence, prevalence, mortality, and treatment success. To account for the efficacy of partial treatment, we used data from clinical trials of early short-course regimens to estimate relapse rates among TB patients who completed one-third, one-half, two-thirds, and all of their first-line treatment regimens. We projected population-level incidence and mortality over 10 years, comparing standard six-month therapy to hypothetical shorter-course regimens with equivalent treatment success but fewer defaults. The impact of hypothetical four-month regimens on TB incidence after 10 years was smaller than estimated in previous modeling analyses (1.9% [95% uncertainty range 0.6–3.1%] vs. 10%). Impact on TB mortality was larger (3.5% at 10 years) but still modest. Transmission impact was most sensitive to the proportion of patients completing therapy: four-month therapy led to greater incidence reductions in settings where 25% of patients leave care (“default”) over six months. Our findings remained robust under one-way variation of model parameters. These findings suggest that novel regimens that shorten treatment duration may have only a modest effect on TB transmission except in settings of very low treatment completion.     

Estimates of tuberculosis progression rate of children in China

In this paper, a discrete mathematical model is formulated to describe tuberculosis (TB) progression from latent infection to active disease. The data of national TB epidemiology surveys in China are taken to estimate the TB progression rate for children aged 0-14 years. The progression rate obtained in this paper gives a detailed and better estimate of TB progression rate among children.     

Estimates of tuberculosis progression rate of children in China

In this paper, a discrete mathematical model is formulated to describe tuberculosis (TB) progression from latent infection to active disease. The data of national TB epidemiology surveys in China are taken to estimate the TB progression rate for children aged 0–14 years. The progression rate obtained in this paper gives a detailed and better estimate of TB progression rate among children.     

Not to wake a sleeping giant: new insights into host-pathogen interactions identify new targets for vaccination against latent Mycobacterium tuberculosis infection

Mycobacterium tuberculosis is one of the worlds' most successful and sophisticated pathogens. It is estimated that over 2 billion people today harbour latent M. tuberculosis infection without any clinical symptoms. As most new cases of active tuberculosis (TB) arise from this (growing) number of latently infected individuals, urgent measures to control TB reactivation are required, including post-exposure/therapeutic vaccines. The current bacille Calmette-Guérin (BCG) vaccine and all new generation TB vaccines being developed and tested are essentially designed as prophylactic vaccines. Unfortunately, these vaccines are unlikely to be effective in individuals already latently infected with M. tuberculosis. Here, we argue that detailed analysis of M. tuberculosis genes that are switched on predominantly during latent stage infection may lead to the identification of new antigenic targets for anti-TB strategies. We will describe essential host-pathogen interactions in TB with particular emphasis on TB latency and persistent infection. Subsequently, we will focus on novel groups of late-stage specific genes, encoded amongst others by the M. tuberculosis dormancy (dosR) regulon, and summarise recent studies describing human T-cell recognition of these dormancy antigens in relation to (latent) M. tuberculosis infection. We will discuss the possible relevance of these new classes of antigens for vaccine development against TB.     

Analysis of a mathematical model for tuberculosis: What could be done to increase case detection

This paper presents qualitative and quantitative study of a TB mathematical model to test results from a survey carried out in Benin City, Nigeria. The purpose of the survey was to determine factors that could enhance the case detection rate of tuberculosis. Results from the survey identified four key factors that must be combined for an effective control of TB and increase the case detection rate: effective awareness programme, active cough identification, associated cost factor for treatment of identified cases and effective treatment. The overall effect of these factors on the basic reproduction number under treatment, R_T, of the TB model was considered. In all, a serious concentration on tuberculosis awareness programmes and active cough identification as a marker for someone having TB was shown to significantly reduce the value of the reproduction number, hereby reducing the severity of the disease in the presence of treatment.     

Latent M. tuberculosis infection--pathogenesis, diagnosis, treatment and prevention strategies

One third of the earths population is infected with Mycobacterium tuberculosis (Mtb), but only 5-10% of the infected individuals develop active tuberculosis (TB) over their lifetime. The remaining 90-95% stay healthy and are called latently infected individuals. They are the biggest reservoir of the tubercle bacilli and identifying the cases of latent TB is a part of the global plan of TB control. From the clinical point of view detection of latent TB infections (LTBI) in individuals with the highest active TB risk including cases of HIV infection, autoimmune inflammatory diseases or cancer, is a priority. This review summarizes the recent findings in the pathogenesis of latent TB, its diagnosis, treatment and prevention.     

Impact of Latent Infection Treatment in Indigenous Populations

The aims of the present study were to identify risk factors associated with latent tuberculosis (TB), examine the development of active disease among contacts, and assess the effectiveness of treating latent infection in indigenous Brazilians from January 2006 to December 2011. This was a retrospective study consisting of 1,371 tuberculosis contacts, 392 of whom underwent treatment for latent infection. Morbidity-from-TB data were obtained from the Information System for Disease Notification (SINAN) database, and the contacts’ data were collected from the clinical records using forms employed by Special Department of Indigenous Health (SESAI) multidisciplinary teams, according to SESAI’s instructions. The variables that were associated with latent infection among the contacts were age (odds ratio [OR]: 1.03; 95% confidence interval [CI]: 1.02–1.04) and close contact with a smear-positive index case (OR: 2.26, 95% CI: 1.59–3.22). The variables associated with the development of active TB among the contacts were a tuberculin skin test (TST) ≥10 mm (relative risk [RR]: 1.12, 95% CI: 1.07–1.17), age (RR: 1.01, 95% CI: 1.00–1.03), and treatment of latent infection (RR: 0.03, 95% CI: 0.01–0.27). The estimated number of latent infection treatments needed to prevent one case of active TB among the contacts was 51 treatments (95% CI: 33–182). In contacts with TST ≥10 mm, 10 (95% CI: 6–19) latent infection treatments were necessary to prevent one case of active TB. Age and close contact with a smear-positive index case were associated with latent TB. Screening with TST is a high priority among individuals contacting smear-positive index cases. Age and TST are associated with the development of active TB among contacts, and treatment of latent infection is an effective measure to control TB in indigenous communities.     

Trade-off between BCG vaccination and the ability to detect and treat latent tuberculosis

Policies regarding the use of the Bacille Calmette-Guérin (BCG) vaccine for tuberculosis vary greatly throughout the international community. In several countries, consideration of discontinuing universal vaccination programs is currently under way. The arguments against mass vaccination are that the effectiveness of BCG in preventing tuberculosis is uncertain and that BCG vaccination can interfere with the detection and treatment of latent tuberculosis.In this work, we pose a dynamical systems model for the population-level dynamics of tuberculosis in order to study the trade-off which occurs between vaccination and detection/treatment of latent tuberculosis. We assume that latent infection in vaccinated individuals is completely undetectable. For the case of a country with very low levels of tuberculosis, we establish analytic thresholds, via stability analysis and the basic reproductive number, which determine the optimal vaccination policy, given the effectiveness of the vaccine and the detection/treatment rate of latent tuberculosis.The results of this work suggest that it is unlikely that a country detects and treats latent tuberculosis at a high enough rate to justify the discontinuation of mass vaccination from this perspective.     

The role of screening and treatment in the transmission dynamics of HIV/AIDS and tuberculosis co-infection: a mathematical study

In this paper, we present a deterministic non-linear mathematical model for the transmission dynamics of HIV and TB co-infection and analyze it in the presence of screening and treatment. The equilibria of the model are computed and stability of these equilibria is discussed. The basic reproduction numbers corresponding to both HIV and TB are found and we show that the disease-free equilibrium is stable only when the basic reproduction numbers for both the diseases are less than one. When both the reproduction numbers are greater than one, the co-infection equilibrium point may exist. The co-infection equilibrium is found to be locally stable whenever it exists. The TB-only and HIV-only equilibria are locally asymptotically stable under some restriction on parameters. We present numerical simulation results to support the analytical findings. We observe that screening with proper counseling of HIV infectives results in a significant reduction of the number of individuals progressing to HIV. Additionally, the screening of TB reduces the infection prevalence of TB disease. The results reported in this paper clearly indicate that proper screening and counseling can check the spread of HIV and TB diseases and effective control strategies can be formulated around ‘screening with proper counseling’.     

On treatment of tuberculosis in heterogeneous populations

Global eradication of tuberculosis (TB) is an international agenda. Thus understanding effects of treatment of TB in different settings is crucial. In previous work, we introduced the framework for a mathematical model of epidemic TB in demographically distinct, heterogeneous populations. Simulations showed the importance of genetic susceptibility in determining endemic prevalence levels. In the work presented here, we include treatment and investigate different strategies for treatment of latent and active TB disease in heterogeneous populations. We illustrate how the presence of a genetically susceptible subpopulation dramatically alters effects of treatment in the same way a core population does in the setting of sexually transmitted diseases. In addition, we evaluate treatment strategies that focus specifically on this subpopulation, and our results indicate that genetically susceptible subpopulations should be accounted for when designing treatment strategies to achieve the greatest reduction in disease prevalence.     

一个具有干预策略的肺结核模型的阈值动力学行为（英文）

文献[4]研究了肺结核传播的动力学行为.该文献仅从数值模拟上分析了疾病的传播和不同策略对疾病传播的影响.本文从理论上对疾病传播和不同策略对疾病传播的影响进行了分析.主要结论如下：得到了模型的基本再生数R_0.R_0决定了疾病传播的动力学行为：如果R_0〈1,则模型仅有一个无病平衡点且是局部渐近稳定的,若R_0〉1则模型存在一个地方病平衡点并且疾病是一致持续的.本文还得到了无病平衡点全局渐近稳定的充分条件.     

A model to predict cell-mediated immune regulatory mechanisms during human infection with Mycobacterium tuberculosis

A key issue for the study of tuberculosis infection (TB) is to understand why individuals infected with Mycobacterium tuberculosis experience different clinical outcomes. Elaborating the immune mechanisms that determine whether an infected individual will suffer active TB or latent infection can aid in developing treatment and prevention strategies. To better understand the dynamics of M. tuberculosis infection and immunity, we have developed a virtual human model that qualitatively and quantitatively characterizes the cellular and cytokine control network operational during TB infection. Using this model, we identify key regulatory elements in the host response. In particular, factors affecting cell functions, such as macrophage activation and bactericidal capabilities, and effector T cell functions such as cytotoxicity and cytokine production can each be determinative. The model indicates, however, that even if latency is achieved, it may come at the expense of tissue damage if the response is not properly regulated. A balance in Th1 and Th2 immune responses governed by IFN-gamma, IL-10, and IL-4 facilitate this down-regulation. These results are further explored through virtual deletion and depletion experiments.     

A Theoretical Assessment of the Effects of Smoking on the Transmission Dynamics of Tuberculosis

Smoking has long being associated with tuberculosis. We present a tuberculosis dynamics model taking into account the fact that some people in the population are smoking in order to assess the effects of smoking on tuberculosis transmission. The epidemic thresholds known as the reproduction numbers and equilibria for the model are determined and stabilities analyzed. Qualitative analysis of the model including positivity and persistence of solutions are presented. The model is numerically analyzed to assess the effects of smoking on the transmission dynamics of tuberculosis. Numerical simulations of the model show that smoking enhances tuberculosis transmission, progression to active disease and in a population of smokers, tuberculosis cannot be controlled even when treatment success is assumed to be as high as 88%. Further, analysis of the reproduction numbers indicates that the number of active tuberculosis cases increases as the number of smokers increase.     

Cost-Effectiveness Analysis of Optimal Control Measures for Tuberculosis

We propose and analyze an optimal control problem where the control system is a mathematical model for tuberculosis that considers reinfection. The control functions represent the fraction of early latent and persistent latent individuals that are treated. Our aim was to study how these control measures should be implemented, for a certain time period, in order to reduce the number of active infected individuals, while minimizing the interventions implementation costs. The optimal intervention is compared along different epidemiological scenarios, by varying the transmission coefficient. The impact of variation of the risk of reinfection, as a result of acquired immunity to a previous infection for treated individuals on the optimal controls and associated solutions, is analyzed. A cost-effectiveness analysis is done, to compare the application of each one of the control measures, separately or in combination.     

TAIMA (Stop) TB: The Impact of a Multifaceted TB Awareness and Door-to-Door Campaign in Residential Areas of High Risk for TB in Iqaluit,Nunavut

Background

The incidence rate of active tuberculosis (TB) disease in the Canadian Territory of Nunavut has shown a rising trend over the past 10 years. In 2010 it was 60 times greater than the national incidence rate. The objective of the Taima (translates to “stop” in Inuktitut) TB study was to implement and evaluate a public health campaign to enhance existing TB prevention efforts in Nunavut.

Methods

A TB awareness campaign followed by a door-to-door screening campaign was carried out in Iqaluit, Nunavut. The aim of the campaign was to raise awareness about TB, and to provide in-home screening and treatment for people living in residential areas at high risk for TB. Screening was based on geographic location rather than on individual risk factors.

Results

During the general awareness campaign an increase in the number of people who requested TB testing at the local public health clinic was observed. However, this increase was not sustained following cessation of the awareness campaign. Targeted TB screening in high risk residential areas in Iqaluit resulted in 224 individuals having TSTs read, and detection of 42 previously unidentified cases of latent TB, (overall yield of 18.8% or number needed to screen = 5.3). These cases of latent TB infection (LTBI) were extra cases that had not been picked up by traditional screening practices (34% relative increase within the community). This resulted in a 33% relative increase in the completion of LTBI treatment within the community. The program directly and indirectly identified 5/17 new cases of active TB disease in Iqaluit during the study period (29.5% of all incident cases).

Conclusions

While contact tracing investigations remain a cornerstone of TB prevention, additional awareness, screening, and treatment programs like Taima TB may contribute to the successful control of TB in Aboriginal communities.