Review
Epidemiological models of Mycobacterium tuberculosis complex infections

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Abstract

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.

Highlights

► This study provides a literature review of epidemiological models of tuberculosis. ► We present transmission dynamics of tuberculosis via epidemiological models. ► We explain the long-term outcomes of treatment based on model simulations. ► We use epidemiological models to simulate different levels of drug resistance. ► Simulations of co-infection of tuberculosis with other diseases are presented.

Introduction

Tuberculosis (TB) is a bacterial disease acquired through airborne infection. Mycobacterium tuberculosis complex (MTBC) is the causative agent of tuberculosis. According to the World Health Organization, one-third of the world’s population is infected, either latently or actively, with tuberculosis [1].

Epidemiology is the science of public health. It studies the distribution and determinants of disease status or events in populations, with the aim of controlling public health problems. The study of epidemiology ranges from cluster investigation at the individual level to building mathematical models to simulate disease dynamics at the population level.

Tuberculosis case counts and case rates have changed in the US and worldwide over the years. Fig. 1 shows the number of TB cases and case rates in the US from 1980 to 2009. The number of cases and case rates both follow a decreasing trend, with the exception of increasing TB cases and case rates in the early 1990s. The increase of TB in this period was attributed to several factors: the increasing HIV epidemic in the early 1990s leading to HIV/TB co-infection, the emergence of drug resistant TB, immigration to the US from developing countries, and increased mass transportation [2], [3], [4]. In order to understand these trends, we need to focus on the long-term consequences of tuberculosis epidemics, which can be observed with the analysis of epidemiological models.

Tuberculosis has slow intrinsic dynamics. The incubation period, latent period, and infectious period span long time intervals, in the order of years on average. The slow progression of tuberculosis at the individual level leads to slow temporal dynamics and long-term outcomes of tuberculosis at the population level. Therefore, mathematical models are needed to estimate prolonged results and future trends of tuberculosis [6], [7], [8]. In this study, we present a literature review of mathematical models that characterize various components of tuberculosis epidemics: transmission, treatment, drug resistance, co-infection, and patient population characteristics.

The organization of this survey is as follows: In Section 2, we give a brief background on the epidemiology of tuberculosis and the framework for describing epidemiological models. In Section 3, we explain the transmission dynamics of tuberculosis at the population and individual levels, in different demographics, and in heterogeneous populations using a variety of models. In Section 4, we describe models for treatment and give a brief summary of treatment strategies for different types of tuberculosis infections and the effects of combinations of control strategies for compliance to treatment. Section 5 covers drug-resistant strains of TB: we explain the dynamics of drug resistance and give an overview of models built for different levels of drug resistance as well as models for control strategies for compliance to drug resistant tuberculosis treatment. In Section 6, we explain the co-epidemics of tuberculosis with HIV and AIDS using epidemiological models. In Section 7, we present an overview of models based on patient groups to identify risk factors of tuberculosis.

Section snippets

Background

In this section, we give a brief introduction to the epidemiology of tuberculosis, as well as some of the commonly used terms. We also provide an introduction to epidemiological models of tuberculosis, their typical units, and central parameters for predicting the future of an epidemic.

Transmission dynamics

Tuberculosis case rates declined in the last decades due to reduction in transmission and progression of the disease as a consequence of improvements in living and working conditions and drug treatment or quarantine of more patients due to increased and early detection of tuberculosis [8], [23]. However, the brief increase in incidence rate around 1990 suggests a change in the epidemiology of tuberculosis. This increase is attributed to increased pathogen resistance to antituberculosis drugs

Treatment

Control strategies for TB treatment have to be modeled mathematically to observe their long-term effects. Although treatment is expected to decrease the number of cases intuitively, an incorrect choice of treatment strategy can lead to severe epidemics through various levels of drug resistance or to an insufficient decrease in the number of cases to eradicate the disease [53]. Therefore, proper care has to be given to the choice of combinations of treatment strategies.

Drug resistance

If the treatment is not accurate or if it is incomplete due to non-compliance, MTBC can become immune to first-line drugs. This new type of TB, called drug-resistant TB (DR-TB), is harder to treat, and second-line drugs are needed for treatment. After acquisition of drug-resistant TB, resistant strains can also be transmitted, leading to new drug-resistant cases.

The emergence of resistance to anti-TB drugs was noted very soon after anti-TB drugs were introduced, in the 1950s. However, there

Co-infection of TB and Other Diseases

Tuberculosis infection correlates with the infection of several other diseases. Most common of all is HIV (Human Immunodeficiency Virus), which causes the immune system to fail and leads to an infection-prone body. Given the deficient immune system of the host, MTBC can easily infect the individual with tuberculosis. It is estimated that one third of the HIV + population is also infected with tuberculosis. Other diseases, including AIDS (HIV infection with symptoms), leprosy (Hansen’s Disease),

Modeling various patient groups

Mathematical models have been built to find patterns in the epidemiology of TB within specific groups of patients. Patients can be classified based on their age, homeless status, race, ethnicity, disease status, or other attributes. It is important to understand how TB morbidity differs among specific population groups by examining it in the context of various socio-demographic factors.

Conclusion

Tuberculosis has slow intrinsic dynamics, therefore the long-term effects of tuberculosis can not be observed by investigation of infected individuals. It can only be explained by population-level studies. Epidemiological models of tuberculosis help us understand the dynamics of tuberculosis transmission at the population level. In this study, we presented a number of models from the literature which are modified to capture different types of tuberculosis infection, different treatment

Acknowledgements

We would like to thank Dr. Peter Kramer (Rensselaer Polytechnic Institute) and Dr. Ted Cohen (Harvard School of Public Health) for their assistance. We also thank two anonymous reviewers for their comments and suggestions. This study was supported by NIH R01LM009731.

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