On treatment of tuberculosis in heterogeneous populations

Addressing mechanism bias in model-based impact forecasts of new tuberculosis vaccines

In tuberculosis (TB) vaccine development, multiple factors hinder the design and interpretation of the clinical trials used to estimate vaccine efficacy. The complex transmission chain of TB includes multiple routes to disease, making it hard to link the vaccine efficacy observed in a trial to specific protective mechanisms. Here, we present a Bayesian framework to evaluate the compatibility of different vaccine descriptions with clinical trial outcomes, unlocking impact forecasting from vaccines whose specific mechanisms of action are unknown. Applying our method to the analysis of the M72/AS01E vaccine trial -conducted on IGRA+ individuals- as a case study, we found that most plausible models for this vaccine needed to include protection against, at least, two over the three possible routes to active TB classically considered in the literature: namely, primary TB, latent TB reactivation and TB upon re-infection. Gathering new data regarding the impact of TB vaccines in various epidemiological settings would be instrumental to improve our model estimates of the underlying mechanisms.

Backward bifurcation and hysteresis in models of recurrent tuberculosis

An epidemiological model is presented that provides a comprehensive description of the transmission pathways involved for recurrent tuberculosis (TB), whereby cured individuals can become reinfected. Our main goal is to determine conditions that lead to the appearance of a backward bifurcation. This occurs when an asymptotically stable infection free equilibrium concurrently exists with a stable non-trivial equilibria even though the basic reproduction number R₀ is less than unity. Although, some 10-30% cases of TB are recurrent, the role of recurrent TB as far as the formation of backward bifurcation is concerned, is rarely if ever studied. The model used here incorporates progressive primary infection, exogenous reinfection, endogenous reactivation and recurrent TB as transmission mechanisms that contribute to TB progression. Unlike other studies of TB dynamics that make use of frequency dependent transmission rates, our analysis provides exact backward bifurcation threshold conditions without resorting to commonly applied approximations and simplifying assumptions. Exploration of the model through analytical and numerical analysis reveal that recurrent TB is sometimes capable of triggering hysteresis effects which allow TB to persist when R₀ < 1 even though there is no backward bifurcation. Furthermore, recurrent TB can independently induce backward bifurcation phenomena if it exceeds a certain threshold.

A patchy model for the transmission dynamics of tuberculosis in sub-Saharan Africa

Tuberculosis (TB) spreads through contact between a susceptible person and smear positive pulmonary TB case (TPM+). The spread of TB is highly dependent on people migration between cities or regions that may have different contact rates and different environmental parameters, leading to different disease spread speed in the population. In this work, a metapopulation model, i.e., networks of populations connected by migratory flows, which overcomes the assumption of homogeneous mixing between different regions was constructed. The TB model was combined to a simple demographic structure for the population living in a multi-patch environment (cities, towns, regions or countries). The model consist of a system of differential equations coupling TB epidemic at different strength and mobility between the patches. Constant recruitment rate, slow and fast progression to the disease, effective chemoprophylaxis, diagnostic and treatment are taken into account to make the model including the reality of people in the sub-Saharan African countries. The basic reproduction number ( R 0 ) was computed and it was demonstrated that the disease-free equilibrium is globally asymptotically stable ifR 0 < 1 . WhenR 0 > 1 , the disease-free equilibrium is unstable and there exists one endemic equilibrium. Moreover, the impact of increasing migration rate between patches on the TB spread was quantified using numerical implementation of the model. Using an example on 15 inter-connected patches on the same road, we demonstrated that most people was most likely to get infected if the disease starts in a patch in the middle than in border patches.

Parameter identification in a tuberculosis model for Cameroon

A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.

Interpreting measures of tuberculosis transmission: a case study on the Portuguese population

Background

Tuberculosis remains a high burden for Human society despite considerable investments in its control. Unique features in the history of infection and transmission dynamics of tuberculosis pose serious limitations on the direct interpretation of surveillance data and call for models that incorporate latent processes and simulate specific interventions.

Methods

A transmission model was adjusted to the dataset of active tuberculosis cases reported in Portugal between 2002 and 2009. We estimated key transmission parameters from the data (i.e. time to diagnosis, treatment length, default proportion, proportion of pulmonary TB cases). Using the adjusted model to the Portuguese case, we estimated the total burden of tuberculosis in Portugal. We further performed sensitivity analysis to heterogeneities in susceptibility to infection and exposure intensity.

Results

We calculated a mean time to diagnose of 2.81 months and treatment length of 8.80 months in Portugal. The proportion defaulting treatment was calculated as 0.04 and the proportion of pulmonary cases as 0.75. Using these values, we estimated a TB burden of 1.6 million infected persons, corresponding to more than 15% of the Portuguese population. We further described the sensitivity of these estimates to heterogeneity.

Conclusions

We showed that the model reproduces well the observed dynamics of the Portuguese data, thus demonstrating its adequacy for devising control strategies for TB and predicting the effects of interventions.

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.

Modelling the Dynamics of Host-Parasite Interactions: Basic Principles

Mathematical modelling is a valuable tool for the analysis of the infectious diseases spread. Dynamical models may help to represent and summarize available knowledge on transmission and disease evolution, to test assumptions and analyse scenarios, and to predict outcomes of the host-pathogen interactions. This chapter aims at introducing basic concepts and methods of epidemiological modelling, in order to provide a starting point for further developments. After positioning modelling in the process of disease investigation, we first present the main principles of model building and analysis, using simple biological and also mathematical systems. We then provide an overview of the methods that can be employed to describe more complex systems. Last, we illustrate how the modelling approach may help for different practical purposes, including evaluation of control strategies. A brief conclusion discusses the challenge of including genetic and molecular variability in epidemiological modelling.

EXOGENOUS REINFECTION AND RESURGENCE OF TUBERCULOSIS: A THEORETICAL FRAMEWORK

The importance of exogenous reinfection versus endogenous reactivation for the resurgence of tuberculosis (TB) has been a matter of ongoing debate. Previous mathematical models of TB give conflicting results on the possibility of multiple stable equilibria in the presence of reinfection, and hence the failure to control the disease even when the basic reproductive number is less than unity. The present study reconsiders the effect of exogenous reinfection, by extending previous studies to incorporate a generalized rate of reinfection as a function of the number of actively infected individuals. A mathematical model is developed to include all possible routes to the development of active TB (progressive primary infection, endogenous reactivation, and exogenous reinfection). The model is qualitatively analyzed to show the existence of multiple equilibria under realistic assumptions and plausible range of parameter values. Two examples, of unbounded and saturated incidence rates of reinfection, are given, and simulation results using estimated parameter values are presented. The results reflect exogenous reinfection as a major cause of TB emergence, especially in high prevalence areas, with important public health implications for controlling its spread.

Modeling socio-demography to capture tuberculosis transmission dynamics in a low burden setting

Evidence of preferential mixing through selected social routes has been suggested for the transmission of tuberculosis (TB) infection in low burden settings. A realistic modelization of these contact routes is needed to appropriately assess the impact of individually targeted control strategies, such as contact network investigation of index cases and treatment of latent TB infection (LTBI). We propose an age-structured, socio-demographic individual based model (IBM) with a realistic, time-evolving structure of preferential contacts in a population. In particular, transmission within households, schools and workplaces, together with a component of casual, distance-dependent contacts are considered. We also compared the model against two other formulations having no social structure of contacts (homogeneous mixing transmission): a baseline deterministic model without age structure and an age-structured IBM. The socio-demographic IBM better fitted recent longitudinal data on TB epidemiology in Arkansas, USA, which serves as an example of a low burden setting. Inclusion of age structure in the model proved fundamental to capturing actual proportions of reactivated TB cases (as opposed to recently transmitted) as well as profiling age-group specific incidence. The socio-demographic structure additionally provides a prediction of TB transmission rates (the rate of infection in household contacts and the rate of secondary cases in household and workplace contacts). These results suggest that the socio-demographic IBM is an optimal choice for evaluating current control strategies, including contact network investigation of index cases, and the simulation of alternative scenarios, particularly for TB eradication targets.

Epidemiological benefits of more-effective tuberculosis vaccines, drugs, and diagnostics

The Bill and Melinda Gates Foundation supports an ambitious portfolio of novel vaccines, drug regimens, and diagnostic tools for tuberculosis (TB). We elicited the expected efficacies and improvements of the novel interventions in discussions with the foundations managing their development. Using an age-structured mathematical model of TB, we explored the potential benefits of novel interventions under development and those not yet in the portfolio, focusing on the WHO Southeast Asia region. Neonatal vaccination with the portfolio vaccine decreases TB incidence by 39% to 52% by 2050. Drug regimens that shorten treatment duration and are efficacious against drug-resistant strains reduce incidence by 10-27%. New diagnostics reduce incidence by 13-42%. A triple combination of a portfolio vaccine, drug regimen, and diagnostics reduces incidence by 71%. A short mass vaccination catch-up campaign, not yet in the portfolio, to augment the triple combination, accelerates the decrease, preventing >30% more cases by 2050 than just the triple combination. New vaccines and drug regimens targeted at the vast reservoir of latently infected people, not in the portfolio, would reduce incidence by 37% and 82%, respectively. The combination of preventive latent therapy and a 2-month drug treatment regimen reduces incidence by 94%. Novel technologies in the pipeline would achieve substantial reductions in TB incidence, but not the Stop TB Partnership target for elimination. Elimination will require new delivery strategies, such as mass vaccination campaigns, and new products targeted at latently infected people.

Modeling the joint epidemics of TB and HIV in a South African township

We present a simple mathematical model with six compartments for the interaction between HIV and TB epidemics. Using data from a township near Cape Town, South Africa, where the prevalence of HIV is above 20% and where the TB notification rate is close to 2,000 per 100,000 per year, we estimate some of the model parameters and study how various control measures might change the course of these epidemics. Condom promotion, increased TB detection and TB preventive therapy have a clear positive effect. The impact of antiretroviral therapy on the incidence of HIV is unclear and depends on the extent to which it reduces sexual transmission. However, our analysis suggests that it will greatly reduce the TB notification rate.

Implications of partial immunity on the prospects for tuberculosis control by post-exposure interventions

One-third of the world population (approximately 2 billion individuals) is currently infected with Mycobacterium tuberculosis, the vast majority harboring a latent infection. As the risk of reactivation is around 10% in a lifetime, it follows that 200 million of these will eventually develop active pulmonary disease. Only therapeutic or post-exposure interventions can tame this vast reservoir of infection. Treatment of latent infections can reduce the risk of reactivation, and there is accumulating evidence that combination with post-exposure vaccines can reduce the risk of reinfection. Here we develop mathematical models to explore the potential of these post-exposure interventions to control tuberculosis on a global scale. Intensive programs targeting recent infections appear generally effective, but the benefit is potentially greater in intermediate prevalence scenarios. Extending these strategies to longer-term persistent infections appears more beneficial where prevalence is low. Finally, we consider that susceptibility to reinfection is altered by therapy, and explore its epidemiological consequences. When we assume that therapy reduces susceptibility to subsequent reinfection, catastrophic dynamics are observed. Thus, a bipolar outcome is obtained, where either small or large reductions in prevalence levels result, depending on the rate of detection and treatment of latent infections. By contrast, increased susceptibility after therapy may induce an increase in disease prevalence and does not lead to catastrophic dynamics. These potential outcomes are silent unless a widespread intervention is implemented.

How do pathogen evolution and host heterogeneity interact in disease emergence?

Heterogeneity in the parameters governing the spread of infectious diseases is a common feature of real-world epidemics. It has been suggested that for pathogens with basic reproductive number R(0)>1, increasing heterogeneity makes extinction of disease more likely during the early rounds of transmission. The basic reproductive number R(0) of the introduced pathogen may, however, be less than 1 after the introduction, and evolutionary changes are then required for R(0) to increase to above 1 and the pathogen to emerge. In this paper, we consider how host heterogeneity influences the emergence of both non-evolving pathogens and those that must undergo adaptive changes to spread in the host population. In contrast to previous results, we find that heterogeneity does not always make extinction more likely and that if adaptation is required for emergence, the effect of host heterogeneity is relatively small. We discuss the application of these ideas to vaccination strategies.