Epidemiological models of Mycobacterium tuberculosis complex infections

Assessment of tuberculosis transmission probability in three Thai prisons based on five dynamic models

This study aimed to assess and compare the probability of tuberculosis (TB) transmission based on five dynamic models: the Wells-Riley equation, two Rudnick & Milton-proposed models based on air changes per hour (ACH) and liters per second per person (L/s/p), the model proposed by Issarow et al, and the Applied Susceptible-Exposed-Infected-Recovered (SEIR) TB transmission model. This study also aimed to determine the impact of model parameters on such probabilities in three Thai prisons. A cross-sectional study was conducted using data from 985 prison cells. The TB transmission probability for each cell was calculated using parameters relevant to the specific model formula, and the magnitude of the model agreement was examined by Spearman's rank correlation and Bland-Altman plot. Subsequently, a multiple linear regression analysis was conducted to investigate the influence of each model parameter on the estimated probability. Results revealed that the median (Quartiles 1 and 3) of TB transmission probability among these cells was 0.052 (0.017, 0.180). Compared with the pioneered Wells-Riley's model, the remaining models projected discrepant TB transmission probability from less to more commensurate to the degree of model modification from the pioneered model as follows: Rudnick & Milton (ACH), Issarow et al., and Rudnick & Milton (L/s/p), and the applied SEIR models. The ventilation rate and number of infectious TB patients in each cell or zone had the greatest impact on the estimated TB transmission probability in most models. Additionally, the number of inmates in each cell, the area per person in square meters, and the inmate turnover rate were identified as high-impact parameters in the applied SEIR model. All stakeholders must urgently address these influential parameters to reduce TB transmission in prisons. Moreover, further studies are required to determine their relative validity in accurately predicting TB incidence in prison settings.

Modelling the preventive treatment under media impact on tuberculosis: A comparison in four regions of China

Preventive treatment for people with latent Tuberculosis infection (LTBI) has aroused our great interest. In this paper, we propose and analyze a novel mathematical model of TB considering preventive treatment with media impact. The basic reproduction number R 0 is defined by the next generation matrix method. In the case without media impact, we prove that the disease-free equilibrium is globally asymptotically stable (unstable) if R 0 < 1 ( R 0 > 1 ) . Furthermore, we obtain that a unique endemic equilibrium exists when R 0 > 1 , which is globally asymptotically stable in the case of permanent immunity and no media impact. We fit the model to the newly reported TB cases data from 2009 to 2019 of four regions in China and estimate the parameters. And we estimated R 0 = 0.5013 < 1 in Hubei indicating that TB in Hubei will be eliminated in the future. However, the estimated R 0 = 1.015 > 1 in Henan, R 0 = 1.282 > 1 in Jiangxi and R 0 = 1.930 > 1 in Xinjiang imply that TB will continue to persist in these three regions without further prevention and control measures. Besides, sensitivity analysis is carried out to illustrate the role of model parameters for TB control. Our finding reveals that appropriately improving the rate of timely treatment for actively infected people and increasing the rate of individuals with LTBI seeking preventive treatment could achieve the goal of TB elimination. In addition, another interesting finding shows that media impact can only reduce the number of active infections to a limited extent, but cannot change the prevalence of TB.

Mathematical models of drug-resistant tuberculosis lack bacterial heterogeneity: A systematic review

Drug-resistant tuberculosis (DR-TB) threatens progress in the control of TB. Mathematical models are increasingly being used to guide public health decisions on managing both antimicrobial resistance (AMR) and TB. It is important to consider bacterial heterogeneity in models as it can have consequences for predictions of resistance prevalence, which may affect decision-making. We conducted a systematic review of published mathematical models to determine the modelling landscape and to explore methods for including bacterial heterogeneity. Our first objective was to identify and analyse the general characteristics of mathematical models of DR-mycobacteria, including M. tuberculosis. The second objective was to analyse methods of including bacterial heterogeneity in these models. We had different definitions of heterogeneity depending on the model level. For between-host models of mycobacterium, heterogeneity was defined as any model where bacteria of the same resistance level were further differentiated. For bacterial population models, heterogeneity was defined as having multiple distinct resistant populations. The search was conducted following PRISMA guidelines in five databases, with studies included if they were mechanistic or simulation models of DR-mycobacteria. We identified 195 studies modelling DR-mycobacteria, with most being dynamic transmission models of non-treatment intervention impact in M. tuberculosis (n = 58). Studies were set in a limited number of specific countries, and 44% of models (n = 85) included only a single level of "multidrug-resistance (MDR)". Only 23 models (8 between-host) included any bacterial heterogeneity. Most of these also captured multiple antibiotic-resistant classes (n = 17), but six models included heterogeneity in bacterial populations resistant to a single antibiotic. Heterogeneity was usually represented by different fitness values for bacteria resistant to the same antibiotic (61%, n = 14). A large and growing body of mathematical models of DR-mycobacterium is being used to explore intervention impact to support policy as well as theoretical explorations of resistance dynamics. However, the majority lack bacterial heterogeneity, suggesting that important evolutionary effects may be missed.

Integer time series models for tuberculosis in Africa

Tuberculosis, an airborne disease, is the deadliest human infectious disease caused by one single agent. The African region is among the most affected and most burdensome area in terms of tuberculosis cases. In this paper, we modeled the number of new cases of tuberculosis for 2000-2021 by integer time series. For each African country, we fitted twenty different models and selected the model that best fitted the data. The twenty models were mostly based on the number of new cases following either the Poisson or negative binomial distribution with the rate parameter allowed to vary linearly or quadratically with respect to year. The best fitted models were used to give predictions for 2022-2031.

A PHLID Model for Tomato Bacterial Canker Predicting on Epidemics of the Pathogen

A pathogen, healthy, latently infected, infectious, and diseased plant (PHLID) model for botanical epidemics was defined for tomato bacterial canker (TBC) caused by the pathogenic plant bacteria, Clavibacter michiganensis subsp. michiganensis (Cmm). First, the incubation period had to be defined to develop this type of model. To estimate the parameter of incubation period, inoculation experiments were conducted in which it was assumed that infection is transferred to healthy plants by cutting with contaminated scissors after cutting infected plants with early symptoms or symptomless. The concentration of Cmm was increased over 1 × 10⁶ cells/g plant tissue at 20 cm away from the inoculated point on the stem 10 days after inoculation, and then the approximate incubation period of TBC in symptomless infected plants was defined as 10 days. The developed PHLID model showed the dynamics of diseased plants incidence and fitted the curve of the proportion of diseased plants observed in fields well. This model also contains the factors of pathogen and disease control, and it was able to simulate the control effects and combined two different control methods, which were the soil and scissors disinfections to prevent primary and secondary transmissions, respectively. Thus, this PHLID model for TBC can be used to simulate not only the increasing number of diseased plants but also suppressing disease increase.

The WHO Global Tuberculosis 2021 Report - not so good news and turning the tide back to End TB

OBJECTIVE

To review the data presented in the 2021 WHO global TB report and discuss the current constraints in the global response.

INTRODUCTION AND METHODS

The WHO global TB reports, consolidate TB data from countries and provide up to date assessment of the global TB epidemic. We reviewed the data presented in the 2021 report.

RESULTS

We noted that the 2021 WHO global TB report presents a rather grim picture on the trajectory of the global epidemic of TB including a stagnation in the annual decline in TB incidence, a decline in TB notifications and an increase in estimated TB deaths. All the targets set at the 2018 United Nations High Level Meeting on TB were off track.

INTERPRETATION AND CONCLUSION

The sub-optimal global performance on achieving TB control targets in 2020 is attributed to the on-going COVID-19 pandemic, however, TB programs were already off track well before the onset of the pandemic, suggesting that the pandemic amplified an already fragile global TB response. We emphasize that ending the global TB epidemic will require bold leadership, optimization of existing interventions, widespread coverage, addressing social determinants of TB and importantly mobilization of adequate funding required for TB care and prevention.

Demographic Control Measure Implications of Tuberculosis Infection for Migrant Workers across Taiwan Regions

A sharp increase in migrant workers has raised concerns for TB epidemics, yet optimal TB control strategies remain unclear in Taiwan regions. This study assessed intervention efforts on reducing tuberculosis (TB) infection among migrant workers. We performed large-scale data analyses and used them to develop a control-based migrant worker-associated susceptible-latently infected-infectious-recovered (SLTR) model. We used the SLTR model to assess potential intervention strategies such as social distancing, early screening, and directly observed treatment, short-course (DOTS) for TB transmission among migrant workers and locals in three major hotspot cities from 2018 to 2023. We showed that social distancing was the best single strategy, while the best dual measure was social distancing coupled with early screening. However, the effectiveness of the triple strategy was marginally (1-3%) better than that of the dual measure. Our study provides a mechanistic framework to facilitate understanding of TB transmission dynamics between locals and migrant workers and to recommend better prevention strategies in anticipation of achieving WHO's milestones by the next decade. Our work has implications for migrant worker-associated TB infection prevention on a global scale and provides a knowledge base for exploring how outcomes can be best implemented by alternative control measure approaches.

Effect of different interventions for latent tuberculosis infections in China: a model-based study

BACKGROUND

Tuberculosis (TB) has a serious impact on people's health. China is one of 30 countries that has a high TB burden. As the currently decreasing speed of the incidence of TB, the WHO's goal of "End TB Strategy" is hard to achieve by 2035. As a result, a SEIR model that determines the impact of different tuberculosis preventive treatments (TPTs) in different age groups, and the effect of different interventions on latent TB infections (LTBIs) in China is developed.

METHODS

A Susceptible-Exposed-Infectious-Recovered (SEIR) model was established. Goodness-of-fit tests were used to assess model performance. Predictive analysis was used to assess the effect of different interventions on LTBIs and achieving the goals of the "End TB Strategy".

RESULTS

The Chi-square test indicated the model provided a good statistical fit to previous data on the incidence of TB (χ² = 0.3085, p > 0.999). The 1HP treatment regimen (daily rifapentine + isoniazid for 4 weeks) was most effective in reducing the number of TB cases by 2035. The model indicated that several strategies could achieve the 2035 target of the "End TB Strategy": completion of active case finding (ACF) for LTBI and TPT nation-wide within 5 years; completion of ACF for LTBIs and TPT within 2 years in high-incidence areas; completion of TPT in the elderly within 2 years; or introduction of a new vaccine in which the product of annual doses and vaccine efficiency in the three age groups above 14 years old reached 10.5 million.

CONCLUSION

The incidence of TB in China declined gradually from 2005 to 2019. Implementation of ACF for LTBIs and TPT nation-wide or in areas with high incidence, in the elderly, or administration of a new and effective vaccine could greatly reduce the number of TB cases and achieve the 2035 target of the "End TB Strategy" in China.

A cross-sectional study to determine the psychological distress among pulmonary tuberculosis patients during COVID-19 pandemic

COVID-19 pandemic had adversely affected the services of the National Tuberculosis (TB) Elimination Programme, resulting in psychological distress among pulmonary tuberculosis patients (PTB). This cross-sectional, hospital-based study included 361 PTB patients. Three pre-defined questionnaires were used for the analysis, a questionnaire to evaluate anxiety related to COVID-19, a patient health questionnaire (PHQ-9) for depression, and a fear of COVID-19 scale (FCV-19S) questionnaire. Among 361 PTB patients, 13% (n=47) had COVID-19 infection. Out of the total patients, 69% (n=250) were DR-TB (drug resistance-tuberculosis) cases. Proportion of anxiety, fear and depression due to COVID-19 was found in 49% (n=177), 23% (n=83), 67% (n=247) respectively. Delay in the initiation of anti-tubercular treatment was found in 58% (n=210) of the cases, among which the majority, i.e., 69% (n=172, p=0.011), were DR-TB. This pandemic has led to a sudden step-down of PTB. Trend analysis of the psychological distress showed a peak following the COVID-19 pandemic. Most DR-TB patients had delayed initiation of the anti-tubercular treatment during the pandemic. The preponderance of the younger age group was seen in the pulmonary tuberculosis patients, and a majority of them had DR-TB. Depression was the predominant psychological distress among the study subjects during the pandemic.

Structural identifiability analysis of age-structured PDE epidemic models

Computational and mathematical models rely heavily on estimated parameter values for model development. Identifiability analysis determines how well the parameters of a model can be estimated from experimental data. Identifiability analysis is crucial for interpreting and determining confidence in model parameter values and to provide biologically relevant predictions. Structural identifiability analysis, in which one assumes data to be noiseless and arbitrarily fine-grained, has been extensively studied in the context of ordinary differential equation (ODE) models, but has not yet been widely explored for age-structured partial differential equation (PDE) models. These models present additional difficulties due to increased number of variables and partial derivatives as well as the presence of boundary conditions. In this work, we establish a pipeline for structural identifiability analysis of age-structured PDE models using a differential algebra framework and derive identifiability results for specific age-structured models. We use epidemic models to demonstrate this framework because of their wide-spread use in many different diseases and for the corresponding parallel work previously done for ODEs. In our application of the identifiability analysis pipeline, we focus on a Susceptible-Exposed-Infected model for which we compare identifiability results for a PDE and corresponding ODE system and explore effects of age-dependent parameters on identifiability. We also show how practical identifiability analysis can be applied in this example.

Analysis of an age-structured tuberculosis model with treatment and relapse

A new tuberculosis model consisting of ordinary differential equations and partial differential equations is established in this paper. The model includes latent age (i.e., the time elapsed since the individual became infected but not infectious) and relapse age (i.e., the time between cure and reappearance of symptoms of tuberculosis). We identify the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{0}$$\end{document}R0 for this model, and show that the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{0}$$\end{document}R0 determines the global dynamics of the model. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{0}<1$$\end{document}R0<1, the disease-free equilibrium is globally asymptotically stable, which means that tuberculosis will disappear, and if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{0}>1$$\end{document}R0>1, there exists a unique endemic equilibrium that attracts all solutions that can cause the spread of tuberculosis. Based on the tuberculosis data in China from 2007 to 2018, we use Grey Wolf Optimizer algorithm to find the optimal parameter values and initial values of the model. Furthermore, we perform uncertainty and sensitivity analysis to identify the parameters that have significant impact on the basic reproduction number. Finally, we give an effective measure to reach the goal of WHO of reducing the incidence of tuberculosis by 80% by 2030 compared to 2015.

"Diagnosis on the Dock" project: A proactive screening program for diagnosing pulmonary tuberculosis in disembarking refugees and new SEI model

OBJECTIVE

From 2011 to 2017, the total number of refugees arriving in Europe, particularly in Italy, climbed dramatically. Our aim was to diagnose pulmonary TB in migrants coming from the African coast using a clinical-based port of arrival (PoA) screening program.

METHODS

From 2016 to 2018, migrants coming via the Mediterranean Route were screened for body temperature and the presence of cough directly on the dock: if they were feverish with productive cough, their sputum was examined with NAAT; with a dry cough, they underwent Chest-X-ray (CXR). Those migrants with positive NAAT or CXR suggestive for TB were admitted to our ward. In addition, we plotted an SEI simulation of our project to evaluate the epidemiological impact of our screening.

RESULTS

Out of 33.676 disembarking migrants, 314 (0.9%) had fever and cough: 80 (25.47%) with productive cough underwent NAAT in sputum, and 16 were positive for TB; 234 (74.52%) with dry cough had a CXR examination, and 39 were suggestive of TB, later confirmed by mycobacterial culture. The SEI-new model analysis demonstrated that our screening program significantly reduced TB spreading all over the country.

CONCLUSIONS

For possible future high migrant flows, PoA screening for TB has to be considered feasible and effective in decreasing TB spreading.

Targeting TB or MRSA in Norwegian municipalities during 'the refugee crisis' of 2015: a framework for priority setting in screening

Introduction

In 2015, there was an increase in the number of asylum seekers arriving in Europe. Like in other countries, deciding screening priorities for tuberculosis (TB) and meticillin-resistant Staphylococcus aureus (MRSA) was a challenge. At least five of 428 municipalities chose to screen asylum seekers for MRSA before TB; the Norwegian Institute for Public Health advised against this.

Aim

To evaluate the MRSA/TB screening results from 2014 to 2016 and create a generalised framework for screening prioritisation in Norway through simulation modelling.

Methods

This is a register-based cohort study of asylum seekers using data from the Norwegian Surveillance System for Communicable Diseases from 2014 to 2016. We used survey data from municipalities that screened all asylum seekers for MRSA and denominator data from the Directorate of Immigration. A comparative risk assessment model was built to investigate the outcomes of prioritising between TB and MRSA in screening regimes.

Results

Of 46,090 asylum seekers, 137 (0.30%) were diagnosed with active TB (notification rate: 300/100,000 person-years). In the municipalities that screened all asylum seekers for MRSA, 13 of 1,768 (0.74%) were found to be infected with MRSA. The model estimated that screening for MRSA would prevent eight MRSA infections while prioritising TB screening would prevent 24 cases of active TB and one death.

Conclusion

Our findings support the decision to advise against screening for MRSA before TB among newly arrived asylum seekers. The model was an effective tool for comparing screening priorities and can be applied to other scenarios in other countries.

Origin of tuberculosis in the Paleolithic predicts unprecedented population growth and female resistance

Current data estimate the origin of Mycobacterium tuberculosis complex (MtbC) infection around 73,000 years before the common era (BCE), and its evolution to “modern” lineages around 46,000 BCE. Being MtbC a major killer of humanity, the question is how both species could persist. To answer this question, we have developed two new epidemiological models (SEIR type), adapted to sex dimorphism and comparing coinfection and superinfection for different MtbC lineages. We have attributed a higher resistance/tolerance to females to explain the lower incidence noted in this sex, a better health status in the Paleolithic compared to the Neolithic, and a higher dissemination of “modern” lineages compared to “ancient” ones. Our findings show the extraordinary impact caused by “modern” lineages, provoking the extinction of the groups infected. This could only be overcomed by an unprecedented population increase (x20 times in 100 years) and helped with the protection generated by previous infection with “ancient” lineages. Our findings also suggest a key role of female resistance against MtbC. This data obliges us to rethink the growth population parameters in the Paleolithic, which is crucial to understanding the survival of both MtbC and humans, and to decipher the nature of human female resistance against TB.

Localized spatial distributions of disease phases yield long-term persistence of infection

We explore the emergence of persistent infection in two patches where the phases of disease progression of the individuals is given by the well known SIRS cycle modelling non-fatal communicable diseases. We find that a population structured into two patches with significantly different initial states, yields persistent infection, though interestingly, the infection does not persist in a homogeneous population having the same average initial composition as the average of the initial states of the two patches. This holds true for inter-patch links ranging from a single connection to connections across the entire inter-patch boundary. So a population with spatially uniform distribution of disease phases leads to disease extinction, while a population spatially separated into distinct patches aids the long-term persistence of disease. After transience, even very dissimilar patches settle down to the same average infected sub-population size. However the patterns of disease spreading in the patches remain discernibly dissimilar, with the evolution of the total number of infecteds in the two patches displaying distinct periodic wave forms, having markedly different amplitudes, though identical frequencies. We quantify the persistent infection through the size of the asymptotic infected set. We find that the number of inter-patch links does not affect the persistence in any significant manner. The most important feature determining persistence of infection is the disparity in the initial states of the patches, and it is clearly evident that persistence increases with increasing difference in the constitution of the patches. So we conclude that populations with very non-uniform distributions, where the individuals in different phases of disease are strongly compartmentalized spatially, lead to sustained persistence of disease in the entire population.

Mathematical analysis of a tuberculosis model with imperfect vaccine

Since 1921, the Bacille Calmette–Guerin (BCG) vaccine continues to be the most widely used vaccine for the prevention of Tuberculosis (TB). However, the immunity induced by BCG wanes out after some time making the vaccinated individual susceptible to TB infection. In this work, we formulate a mathematical model that incorporates the vaccination of newly born children and older susceptible individuals in the transmission dynamics of TB in a population, with a vaccine that can confer protection on older susceptible individuals. In the absence of disease-induced deaths, the model is shown to undergo the phenomenon of backward bifurcation where a stable disease-free equilibrium (DFE) co-exists with a stable positive (endemic) equilibrium when the associated reproduction number is less than unity. It is shown that this phenomenon does not exist in the absence of imperfect vaccine, exogenous reinfection, and reinfection of previously treated individuals. It is further shown that a special case of the model has a unique endemic equilibrium point (EEP), which is globally asymptotically stable when the associated reproduction number exceeds unity. Uncertainty and sensitivity analysis are carried out to identify key parameters that have the greatest influence on the transmission dynamics of TB in the population using the total population of latently infected individuals, total number of actively infected individuals, disease incidence, and the effective reproduction number as output responses. The analysis shows that the top five parameters of the model that have the greatest influence on the effective reproduction number of the model are the transmission rate, the fraction of fast disease progression, modification parameter which accounts for reduced likelihood to infection by vaccinated individuals due to imperfect vaccine, rate of progression from latent to active TB, and the treatment rate of actively infected individuals, with other key parameters influencing the outcomes of the other output responses. Numerical simulations suggest that with higher vaccination rate of older susceptible individuals, fewer new born children need to be vaccinated, in order to achieve disease eradication.

Observer-based adaptive PI sliding mode control of developed uncertain SEIAR influenza epidemic model considering dynamic population

This paper presents a new Susceptible, Exposed, Infected, Asymptomatic, and Recovered individuals (SEIAR) model for influenza considering a dynamic population. In the given model, the possibility of transmission of asymptomatic individuals (infectious with no visible symptoms) to infected individuals (infectious exhibiting symptoms) is considered. The basic reproduction number and the equilibrium points of the new model are given while the stability of the equilibrium points is analyzed by using the Jacobian matrix. Then a multi-controller scheme consisting of a parallel controller defined by two control inputs (vaccination and antiviral treatment) is given where both of them are based on Proportional-Integral (PI) and sliding mode controllers, which are parameterized adaptively to guarantee the convergence of trajectories to the sliding surface with minimum amount of chattering. The proposed control scheme is able to asymptotically stabilize the SEIAR model in the sense of eradication of the infected and susceptible individuals. Moreover, a (reduced-order) observer is designed to estimate the actual state variables that are used in the implementation of the control signals. By using MATLAB® software, a comprehensive simulation and evaluation of treatment and performance are carried out to support the presented theoretical results.

Modeling tuberculosis dynamics with the presence of hyper-susceptible individuals for Ho Chi Minh City from 1996 to 2015

BACKGROUND

The depletion of CD4 cell is the underlying reason for TB hyper-susceptibility among people with HIV. Consequently, the trend of TB dynamics is usually hidden by the HIV outbreak.

METHODS

Here, we aim to evaluate the trend of TB dynamics quantitatively by a simple mathematical model using the known prevalence of hyper-susceptible individuals in the population. In order to estimate the parameters governing transmission we fit this model in a maximum likelihood framework to both reported TB cases and data from samples tested with Interferon Gamma Assay from Ho Chi Minh City - a city with high TB transmission and strong synchronization between HIV/AIDS and TB dynamics.

RESULTS

Our results show that TB transmission in HCMC has been declining among people without HIV; we estimate a 18% (95% CI: 9-25%) decline in the transmission parameter between 1996 and 2015. Furthermore, we show that co-infected patients have limited contribution to the transmission process. For hyper-susceptible individuals, our model suggests that the risk of a new active TB infection occurring is significantly higher than the risk of relapsed active TB, while this is not the case for people without hyper-susceptibility.

CONCLUSIONS

The increase of TB notifications in Ho Chi Minh City from 1996 to 2008 is evitable when, as occurred, the number of hyper-susceptible individuals increased faster than the decrease of TB transmission rate. The sharp decrease in TB notifications observed in this city from 2008 to 2015 is the combined result of the decrease of TB transmission rate and the decrease of hyper-susceptible individuals in the population. For hyper-susceptible individuals, we propose that the reason for the reduced relapsed active TB risk is HIV treatment delay. According to HIV treatment guidelines issued by Vietnam's Ministry of Health, hyper-susceptible individuals usually have to wait until their CD4 cell count falls under 350 cells/μl to start ART. Once patients begin ART, they will remain on ART for the rest of their life and thus have greater protection against relapses of TB. We therefore hypothesize that the delay in using ART imposes considerable TB burden on HCMC despite the declining transmission process.

Data Analysis and Forecasting of Tuberculosis Prevalence Rates for Smart Healthcare Based on a Novel Combination Model

In recent years, healthcare has attracted much attention, which is looking for more and more data analytics in healthcare to relieve medical problems in medical staff shortage, ageing population, people living alone, and quality of life. Data mining, analysis, and forecasting play a vital role in modern social and medical fields. However, how to select a proper model to mine and analyze the relevant medical information in the data is not only an extremely challenging problem, but also a concerning problem. Tuberculosis remains a major global health problem despite recent and continued progress in prevention and treatment. There is no doubt that the effective analysis and accurate forecasting of global tuberculosis prevalence rates lay a solid foundation for the construction of an epidemic disease warning and monitoring system from a global perspective. In this paper, the tuberculosis prevalence rate time series for four World Bank income groups are targeted. Kruskal–Wallis analysis of variance and multiple comparison tests are conducted to determine whether the differences of tuberculosis prevalence rates for different income groups are statistically significant or not, and a novel combined forecasting model with its weights optimized by a recently developed artificial intelligence algorithm—cuckoo search—is proposed to forecast the hierarchical tuberculosis prevalence rates from 2013 to 2016. Numerical results show that the developed combination model is not only simple, but is also able to satisfactorily approximate the actual tuberculosis prevalence rate, and can be an effective tool in mining and analyzing big data in the medical field.

Progression from latent infection to active disease in dynamic tuberculosis transmission models: a systematic review of the validity of modelling assumptions

Mathematical modelling is commonly used to evaluate infectious disease control policy and is influential in shaping policy and budgets. Mathematical models necessarily make assumptions about disease natural history and, if these assumptions are not valid, the results of these studies can be biased. We did a systematic review of published tuberculosis transmission models to assess the validity of assumptions about progression to active disease after initial infection (PROSPERO ID CRD42016030009). We searched PubMed, Web of Science, Embase, Biosis, and Cochrane Library, and included studies from the earliest available date (Jan 1, 1962) to Aug 31, 2017. We identified 312 studies that met inclusion criteria. Predicted tuberculosis incidence varied widely across studies for each risk factor investigated. For population groups with no individual risk factors, annual incidence varied by several orders of magnitude, and 20-year cumulative incidence ranged from close to 0% to 100%. A substantial proportion of modelled results were inconsistent with empirical evidence: for 10-year cumulative incidence, 40% of modelled results were more than double or less than half the empirical estimates. These results demonstrate substantial disagreement between modelling studies on a central feature of tuberculosis natural history. Greater attention to reproducing known features of epidemiology would strengthen future tuberculosis modelling studies, and readers of modelling studies are recommended to assess how well those studies demonstrate their validity.

Big Data's Role in Precision Public Health

Precision public health is an emerging practice to more granularly predict and understand public health risks and customize treatments for more specific and homogeneous subpopulations, often using new data, technologies, and methods. Big data is one element that has consistently helped to achieve these goals, through its ability to deliver to practitioners a volume and variety of structured or unstructured data not previously possible. Big data has enabled more widespread and specific research and trials of stratifying and segmenting populations at risk for a variety of health problems. Examples of success using big data are surveyed in surveillance and signal detection, predicting future risk, targeted interventions, and understanding disease. Using novel big data or big data approaches has risks that remain to be resolved. The continued growth in volume and variety of available data, decreased costs of data capture, and emerging computational methods mean big data success will likely be a required pillar of precision public health into the future. This review article aims to identify the precision public health use cases where big data has added value, identify classes of value that big data may bring, and outline the risks inherent in using big data in precision public health efforts.

Mathematical model and intervention strategies for mitigating tuberculosis in the Philippines

Tuberculosis (TB) is the sixth leading cause of morbidity and mortality in the Philippines. Although significant progress has been made in the detection and cure of TB under the Directly Observed Treatment Short Course, battling against the disease is still a burdensome task. It demands a concerted effort for specific and effective interventions. In this work, a mathematical TB model fitted to the Philippine data is developed to understand its transmission dynamics. Different control strategies such as distancing, latent case finding, case holding, active case finding controls, and combinations thereof are investigated within the framework of optimal control theory. This study proposes optimal control strategies for reducing the number of high-risk latent and infectious TB patients with minimum intervention implementation costs. Results suggest that distancing control is the most efficient control strategy when a single intervention is utilized. However, full scale employment of the distancing control measure is a daunting task. This burden can be circumvented by the combination of other control interventions. Our noble finding in this study is that enhancing active case finding control instead of case holding control together with distancing and latent case finding control is shown to have significant potential for curtailing the spread of TB in the Philippines.

Emergence of Persistent Infection due to Heterogeneity

We explore the emergence of persistent infection in a closed region where the disease progression of the individuals is given by the SIRS model, with an individual becoming infected on contact with another infected individual. We investigate the persistence of contagion qualitatively and quantitatively, under increasing heterogeneity in the partitioning of the population into different disease compartments, as well as increasing heterogeneity in the phases of the disease among individuals within a compartment. We observe that when the initial population is uniform, consisting of individuals at the same stage of disease progression, infection arising from a contagious seed does not persist. However when the initial population consists of randomly distributed refractory and susceptible individuals, a single source of infection can lead to sustained infection in the population, as heterogeneity facilitates the de-synchronization of the phases in the disease cycle of the individuals. We also show how the average size of the window of persistence of infection depends on the degree of heterogeneity in the initial composition of the population. In particular, we show that the infection eventually dies out when the entire initial population is susceptible, while even a few susceptibles among an heterogeneous refractory population gives rise to a large persistent infected set.

The role of mobility and health disparities on the transmission dynamics of Tuberculosis

Background

The transmission dynamics of Tuberculosis (TB) involve complex epidemiological and socio-economical interactions between individuals living in highly distinct regional conditions. The level of exogenous reinfection and first time infection rates within high-incidence settings may influence the impact of control programs on TB prevalence. The impact that effective population size and the distribution of individuals’ residence times in different patches have on TB transmission and control are studied using selected scenarios where risk is defined by the estimated or perceive first time infection and/or exogenous re-infection rates.

Methods

This study aims at enhancing the understanding of TB dynamics, within simplified, two patch, risk-defined environments, in the presence of short term mobility and variations in reinfection and infection rates via a mathematical model. The modeling framework captures the role of individuals’ ‘daily’ dynamics within and between places of residency, work or business via the average proportion of time spent in residence and as visitors to TB-risk environments (patches). As a result, the effective population size of Patch i (home of i-residents) at time t must account for visitors and residents of Patch i, at time t.

Results

The study identifies critical social behaviors mechanisms that can facilitate or eliminate TB infection in vulnerable populations. The results suggest that short-term mobility between heterogeneous patches contributes to significant overall increases in TB prevalence when risk is considered only in terms of direct new infection transmission, compared to the effect of exogenous reinfection. Although, the role of exogenous reinfection increases the risk that come from large movement of individuals, due to catastrophes or conflict, to TB-free areas.

Conclusions

The study highlights that allowing infected individuals to move from high to low TB prevalence areas (for example via the sharing of treatment and isolation facilities) may lead to a reduction in the total TB prevalence in the overall population. The higher the population size heterogeneity between distinct risk patches, the larger the benefit (low overall prevalence) under the same “traveling” patterns. Policies need to account for population specific factors (such as risks that are inherent with high levels of migration, local and regional mobility patterns, and first time infection rates) in order to be long lasting, effective and results in low number of drug resistant cases.

MATHEMATICAL MODELING OF BACTERIAL RESISTANCE TO ANTIBIOTICS BY MUTATIONS AND PLASMIDS

Diversity of drugs against bacterial infections, and development of resistance to such drugs are increasing. We formulate and analyze a deterministic model for the population dynamics of sensitive and resistant bacteria to multiple bactericidal and bacteriostatic antibiotics, assuming that drug resistance is acquired through mutations and plasmid transmission. Model equilibria are determined from qualitative analysis, and numerical simulations are used to assess temporal dynamics of sensitive and drug-resistant bacteria. The model presents three possibilities: elimination of bacteria, persistence of only resistant bacteria, or coexistence of sensitive and resistant bacteria. Evolution to one of these scenarios depends on thresholds numbers involving sensitive and resistant bacteria.

Artificial infectious disease optimization: A SEIQR epidemic dynamic model-based function optimization algorithm

To solve some complicated function optimization problems, an artificial infectious disease optimization algorithm based on the SEIQR epidemic model is constructed, it is called as the SEIQR algorithm, or SEIQRA in short. The algorithm supposes that some human individuals exist in an ecosystem; each individual is characterized by a number of features; an infectious disease (SARS) exists in the ecosystem and spreads among individuals, the disease attacks only a part of features of an individual. Each infected individual may pass through such states as susceptibility (S), exposure (E), infection (I), quarantine (Q) and recovery (R). State S, E, I, Q and R can automatically and dynamically divide all people in the ecosystem into five classes, it provides the diversity for SEIQRA; that people can be attacked by the infectious disease and then transfer it to other people can cause information exchange among people, information exchange can make a person to transit from one state to another; state transitions can be transformed into operators of SEIQRA; the algorithm has 13 legal state transitions, which corresponds to 13 operators; the transmission rules of the infectious disease among people is just the logic to control state transitions of individuals among S, E, I, Q and R, it is just the synergy of SEIQRA, the synergy can be transformed into the logic structure of the algorithm. The 13 operators in the algorithm provide a native opportunity to integrate many operations with different purposes; these operations include average, differential, expansion, chevy, reflection and crossover. The 13 operators are executed equi-probably; a stable heart rhythm of the algorithm is realized. Because the infectious disease can only attack a small part of organs of a person when it spreads among people, the part variables iteration strategy (PVI) can be ingeniously applied, thus enabling the algorithm to possess of high performance of computation, high suitability for solving some kinds of complicated optimization problems, especially high dimensional optimization problems. Results show that SEIQRA has characteristics of strong search capability and global convergence, and has a high convergence speed for some complicated functions optimization problems.

Tuberculosis in Cape Town: An age-structured transmission model

BACKGROUND

Tuberculosis (TB) is the leading cause of death in South Africa. The burden of disease varies by age, with peaks in TB notification rates in the HIV-negative population at ages 0-5, 20-24, and 45-49 years. There is little variation between age groups in the rates in the HIV-positive population. The drivers of this age pattern remain unknown.

METHODS

We developed an age-structured simulation model of Mycobacterium tuberculosis (Mtb) transmission in Cape Town, South Africa. We considered five states of TB progression: susceptible, infected (latent TB), active TB, treated TB, and treatment default. Latently infected individuals could be re-infected; a previous Mtb infection slowed progression to active disease. We further considered three states of HIV progression: HIV negative, HIV positive, on antiretroviral therapy. To parameterize the model, we analysed treatment outcomes from the Cape Town electronic TB register, social mixing patterns from a Cape Town community and used literature estimates for other parameters. To investigate the main drivers behind the age patterns, we conducted sensitivity analyses on all parameters related to the age structure.

RESULTS

The model replicated the age patterns in HIV-negative TB notification rates of Cape Town in 2009. Simulated TB notification rate in HIV-negative patients was 1000/100,000 person-years (pyrs) in children aged <5 years and decreased to 51/100,000 in children 5-15 years. The peak in early adulthood occurred at 25-29 years (463/100,000 pyrs). After a subsequent decline, simulated TB notification rates gradually increased from the age of 30 years. Sensitivity analyses showed that the dip after the early adult peak was due to the protective effect of latent TB and that retreatment TB was mainly responsible for the rise in TB notification rates from the age of 30 years.

CONCLUSION

The protective effect of a first latent infection on subsequent infections and the faster progression in previously treated patients are the key determinants of the age-structure of TB notification rates in Cape Town.

Individual-Based Modeling of Tuberculosis in a User-Friendly Interface: Understanding the Epidemiological Role of Population Heterogeneity in a City

For millennia tuberculosis (TB) has shown a successful strategy to survive, making it one of the world’s deadliest infectious diseases. This resilient behavior is based not only on remaining hidden in most of the infected population, but also by showing slow evolution in most sick people. The course of the disease within a population is highly related to its heterogeneity. Thus, classic epidemiological approaches with a top-down perspective have not succeeded in understanding its dynamics. In the past decade a few individual-based models were built, but most of them preserved a top-down view that makes it difficult to study a heterogeneous population. We propose an individual-based model developed with a bottom-up approach to studying the dynamics of pulmonary TB in a certain population, considered constant. Individuals may belong to the following classes: healthy, infected, sick, under treatment, and treated with a probability of relapse. Several variables and parameters account for their age, origin (native or immigrant), immunodeficiency, diabetes, and other risk factors (smoking and alcoholism). The time within each infection state is controlled, and sick individuals may show a cavitated disease or not that conditions infectiousness. It was implemented in NetLogo because it allows non-modelers to perform virtual experiments with a user-friendly interface. The simulation was conducted with data from Ciutat Vella, a district of Barcelona with an incidence of 67 TB cases per 100,000 inhabitants in 2013. Several virtual experiments were performed to relate the disease dynamics with the structure of the infected subpopulation (e.g., the distribution of infected times). Moreover, the short-term effect of health control policies on modifying that structure was studied. Results show that the characteristics of the population are crucial for the local epidemiology of TB. The developed user-friendly tool is ready to test control strategies of disease in any city in the short-term.

Computational Studies of the Intestinal Host-Microbiota Interactome

A large and growing body of research implicates aberrant immune response and compositional shifts of the intestinal microbiota in the pathogenesis of many intestinal disorders. The molecular and physical interaction between the host and the microbiota, known as the host-microbiota interactome, is one of the key drivers in the pathophysiology of many of these disorders. This host-microbiota interactome is a set of dynamic and complex processes, and needs to be treated as a distinct entity and subject for study. Disentangling this complex web of interactions will require novel approaches, using a combination of data-driven bioinformatics with knowledge-driven computational modeling. This review describes the computational approaches for investigating the host-microbiota interactome, with emphasis on the human intestinal tract and innate immunity, and highlights open challenges and existing gaps in the computation methodology for advancing our knowledge about this important facet of human health.

Revisiting Styblo's law: could mathematical models aid in estimating incidence from prevalence data?

Estimation of the true incidence of tuberculosis (TB) is challenging. The approach proposed by Styblo in 1985 is known to be inaccurate in the modern era where there is widespread availability of treatment for TB. This study re-examines the relationship of incidence to prevalence and other disease indicators that can be derived from surveys. We adapt a simple, previously published model that describes the epidemiology of TB in the presence of treatment to investigate a revised ratio-based approach to estimating incidence. We show that, following changes to treatment programmes for TB, the ratio of incidence to prevalence reaches an equilibrium value rapidly; long before other model indicators have stabilized. We also show that this ratio relies on few parameters but is strongly dependent on, and requires knowledge of, the efficacy and timeliness of treatment.

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.

Can high-risk fungicides be used in mixtures without selecting for fungicide resistance?

Fungicide mixtures produced by the agrochemical industry often contain low-risk fungicides, to which fungal pathogens are fully sensitive, together with high-risk fungicides known to be prone to fungicide resistance. Can these mixtures provide adequate disease control while minimizing the risk for the development of resistance? We present a population dynamics model to address this question. We found that the fitness cost of resistance is a crucial parameter to determine the outcome of competition between the sensitive and resistant pathogen strains and to assess the usefulness of a mixture. If fitness costs are absent, then the use of the high-risk fungicide in a mixture selects for resistance and the fungicide eventually becomes nonfunctional. If there is a cost of resistance, then an optimal ratio of fungicides in the mixture can be found, at which selection for resistance is expected to vanish and the level of disease control can be optimized.

Mathematical modeling on bacterial resistance to multiple antibiotics caused by spontaneous mutations

We formulate a mathematical model that describes the population dynamics of bacteria exposed to multiple antibiotics simultaneously, assuming that acquisition of resistance is through mutations due to antibiotic exposure. Qualitative analysis reveals the existence of a free-bacteria equilibrium, resistant-bacteria equilibrium and an endemic equilibrium where both bacteria coexist.

Modeling the spread of tuberculosis in semiclosed communities

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.