Drug resistance in tuberculosis—a reinfection model

Dynamics of antibiotic resistance genes in the sediments of a water-diversion lake and its human exposure risk behaviour

The dynamics and exposure risk behaviours of antibiotic resistance genes (ARGs) in the sediments of water-diversion lakes remain poorly understood. In this study, spatiotemporal investigations of ARG profiles in sediments targeting non-water (NWDP) and water diversion periods (WDP) were conducted in Luoma Lake, a typical water-diversion lake, and an innovative dynamics-based risk assessment framework was constructed to evaluate ARG exposure risks to local residents. ARGs in sediments were significantly more abundant in the WDP than in the NWDP, but there was no significant variation in their spatial distribution in either period. Moreover, the pattern of ARG dissemination in sediments was unchanged between the WDP and NWDP, with horizontal gene transfer (HGT) and vertical gene transfer (VGT) contributing to ARG dissemination in both periods. However, water diversion altered the pattern in lake water, with HGT and VGT in the NWDP but only HGT in the WDP, which were critical pathways for the dissemination of ARGs. The significantly lower ARG sediment-water partition coefficient in the WDP indicated that water diversion could shift the fate of ARGs and facilitate their aqueous partitioning. Risk assessment showed that all age groups faced a higher human exposure risk of ARGs (HERA) in the WDP than in the NWDP, with the 45-59 age group having the highest risk. Furthermore, HERA increased overall with the bacterial carrying capacity in the local environment and peaked when the carrying capacity reached three (NWDP) or four (WDP) orders of magnitude higher than the observed bacterial population. HGT and VGT promoted, whereas ODF covering gene mutation and loss mainly reduced HERA in the lake. As the carrying capacity increased, the relative contribution of ODF to HERA remained relatively stable, whereas the dominant mechanism of HERA development shifted from HGT to VGT.

A diffusive tuberculosis model with early and late latent infections: New Lyapunov function approach to global stability

This paper formulates a diffusive tuberculosis (TB) model with early and late latent infections, vaccination and treatment that may more properly describe the slow and fast dynamics of TB transmission. We develop a new concise approach to determine the combination coefficients in the Lyapunov function candidate for the model and its time derivative in the case that both are the linear combinations of several Volterra-type functions, which highly simplifies the computations in global dynamical analysis for the nonlinear high-dimensional model. Based on the TB case data reported in China, the parameter values of the model are estimated. We further predict the TB prevalence trend in China. Sensitivity analysis for the control reproduction number and endemic equilibrium is conducted to seek some effective interventions that can significantly reduce initial TB transmission and lower TB prevalence levels in China. In the end, numerical simulations show that the bigger diffusive rates pick up the speeds of convergence to the equilibria of the model.

An efficient numerical simulation and mathematical modeling for the prevention of tuberculosis

The main purpose of this research is to use a fractional-mathematical model including Atangana–Baleanu derivatives to explore the clinical associations and dynamical behavior of the tuberculosis. Herein, we used a lately introduced fractional operator having Mittag-Leffler kernel. The existence and inimitability problems to the relevant model were examined through the fixed-point theory. To verify the significance of the arbitrary fractional-order derivative, numerical outcomes were explored from the biological and mathematical viewpoints using the values of model parameters. The graphical simulations show the comparison of the predictor–corrector method (PCM) and Caputo method (CM) for different fractional orders and the results indicated the significant preference of PCM over CM.

Modeling the effect of vaccination on selection for antibiotic resistance in Streptococcus pneumonia e

Vaccines against bacterial pathogens can protect recipients from becoming infected with potentially antibiotic-resistant pathogens. However, by altering the selective balance between antibiotic-sensitive and antibiotic-resistant bacterial strains, vaccines may also suppress-or spread-antibiotic resistance among unvaccinated individuals. Predicting the outcome of vaccination requires knowing what drives selection for drug-resistant bacterial pathogens and what maintains the circulation of both antibiotic-sensitive and antibiotic-resistant strains of bacteria. To address this question, we used mathematical modeling and data from 2007 on penicillin consumption and penicillin nonsusceptibility in Streptococcus pneumoniae (pneumococcus) invasive isolates from 27 European countries. We show that the frequency of penicillin resistance in S. pneumoniae can be explained by between-host diversity in antibiotic use, heritable diversity in pneumococcal carriage duration, or frequency-dependent selection brought about by within-host competition between antibiotic-resistant and antibiotic-sensitive S. pneumoniae strains. We used our calibrated models to predict the impact of non-serotype-specific pneumococcal vaccination upon the prevalence of S. pneumoniae carriage, incidence of disease, and frequency of S. pneumoniae antibiotic resistance. We found that the relative strength and directionality of competition between drug-resistant and drug-sensitive pneumococcal strains was the most important determinant of whether vaccination would promote, inhibit, or have little effect upon the evolution of antibiotic resistance. Last, we show that country-specific differences in pathogen transmission substantially altered the predicted impact of vaccination, highlighting that policies for managing antibiotic resistance with vaccines must be tailored to a specific pathogen and setting.

The prevention and control of tuberculosis: an analysis based on a tuberculosis dynamic model derived from the cases of Americans

Background

Tuberculosis (TB), a preventable and curable disease, is claimed as the second largest number of fatalities, and there are 9,025 cases reported in the United States in 2018. Many researchers have done a lot of research and achieved remarkable results, but TB is still a severe problem for human beings. The study is a further exploration of the prevention and control of tuberculosis.

Methods

In the paper, we propose a new dynamic model to study the transmission dynamics of TB, and then use global differential evolution and local sequential quadratic programming (DESQP) optimization algorithm to estimate parameters of the model. Finally, we use Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) to analyze the influence of parameters on 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) and the total infectious (including the diagnosed, undiagnosed and incomplete treatment infectious), respectively.

Results

According to the research, the basic reproduction number is computed as 2.3597 from 1984 to 2018, which means TB is also an epidemic in the US. The diagnosed rate is 0.6082, which means the undiagnosed will be diagnosed after 1.6442 years. The diagnosed will recover after an average of 1.9912 years. Moreover, some diagnosed will end the treatment after 1.7550 years for some reason. From the study, it’s shown that 2.40% of the recovered will be reactivated, and 13.88% of the newborn will be vaccinated. However, the immune system will be lost after about 19.6078 years.

Conclusion

Through the results of this study, we give some suggestions to help prevent and control the TB epidemic in the United States, such as prolonging the protection period of the vaccine by developing new and more effective vaccines to prevent TB; using the Chemoprophylaxis for incubation patients to prevent their conversion into active TB; raising people’s awareness of the prevention and control of TB and treatment after illness; isolating the infected to reduce the spread of TB. According to the latest report in the announcement that came at the first WHO Global Ministerial Conference on Ending tuberculosis in the Sustainable Development Era, we predict that it is challenging to control TB by 2030.

A survey of within-host and between-hosts modelling for antibiotic resistance

Antibiotic resistance is a global public health problem which has the attention of many stakeholders including clinicians, the pharmaceutical industry, researchers and policy makers. Despite the existence of many studies, control of resistance transmission has become a rather daunting task as the mechanisms underlying resistance evolution and development are not fully known. Here, we discuss the mechanisms underlying antibiotic resistance development, explore some treatment strategies used in the fight against antibiotic resistance and consider recent findings on collateral susceptibilities amongst antibiotic classes. Mathematical models have proved valuable for unravelling complex mechanisms in biology and such models have been used in the quest of understanding the development and spread of antibiotic resistance. While assessing the importance of such mathematical models, previous systematic reviews were interested in investigating whether these models follow good modelling practice. We focus on theoretical approaches used for resistance modelling considering both within and between host models as well as some pharmacodynamic and pharmakokinetic approaches and further examine the interaction between drugs and host immune response during treatment with antibiotics. Finally, we provide an outlook for future research aimed at modelling approaches for combating antibiotic resistance.

GLOBAL DYNAMICS OF A MATHEMATICAL MODEL OF TUBERCULOSIS WITH AGE-DEPENDENT LATENCY AND ACTIVE INFECTION

In this paper, mathematical analysis is carried out for a mathematical model of Tuberculosis (TB) with age-dependent latency and active infection. The model divides latent TB infection into two stages: an early stage of high risk of developing active TB and a late stage of lower risk for developing active TB. Infected persons initially progress through the early latent TB stage and then can either progress to active TB infection or progress to late latent TB infection. The model is formulated by incorporating the duration that an individual has spent in the stages of the early latent TB, the late latent TB and the active TB infection as variables. By constructing suitable Lyapunov functionals and using LaSalle’s invariance principle, it is shown that the global dynamics of the disease is completely determined by the basic reproduction number: if the basic reproduction number is less than unity, the TB always dies out; if the basic reproduction number is greater than unity, a unique endemic steady state exists and is globally asymptotically stable in the interior of the feasible region and therefore the TB becomes endemic. Numerical simulations are carried out to illustrate the theoretical results.

Global dynamics of a tuberculosis model with fast and slow progression and age-dependent latency and infection

In this paper, a mathematical model describing tuberculosis transmission with fast and slow progression and age-dependent latency and infection is investigated. It is assumed in the model that infected individuals can develop tuberculosis by either of two pathogenic mechanisms: direct progression or endogenous reactivation. It is shown that the transmission dynamics of the disease is fully determined by the basic reproduction number. By analyzing corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By using the persistence theory for infinite dimensional system, it is proved that the system is uniformly persistent when the basic reproduction number is greater than unity. By constructing suitable Lyapunov functionals and using LaSalle's invariance principle, it is verified that the global dynamics of the system is completely determined by the basic reproduction number.

Nonlinear adaptive control of tuberculosis with consideration of the risk of endogenous reactivation and exogenous reinfection

Tuberculosis is one of deadly diseases in many countries that attacks to the human body and causes damage to the lung, causing bloody coughing and if left untreated, it will kill half of the affected people. Tuberculosis bacteria can stay latent and reactivate after passing appropriate conditions. For this reason, control of this disease and treatment of infected people has a significant importance, and observing health issues can prevent the spread of it. In this paper, a nonlinear adaptive control method is proposed for the first time in order to control and treat tuberculosis outbreak subjected to the modeling uncertainty. To design a control system being robust against uncertainties, an adaptation law is defined to update values of estimated parameters and ensures the whole system stability. The treatment achievement and stability of the closed-loop system is proved by the Lyapunov theorem and confirmed by some simulations. The proposed strategy has the capability to control the tuberculosis outbreak by reducing the numbers of active infectious and persistent latent individuals based on their desired values in the society.

Effect of mixed infection on TB dynamics

Poor living conditions, overcrowding and strain diversity are some of the factors that influence mixed infection in Tuberculosis (TB) at the population level. We formulate a mathematical model for mixed infection in TB using nonlinear ordinary differential equations where such factors were represented as probabilities of acquiring mixed infection. A qualitative analysis of the model shows that it exhibits multiple endemic equilibria and backward bifurcation for certain parameter values. The reactivation rate and transmission rate of individuals with mixed infection were of importance as well as the probabilities for latent individuals to acquire mixed infection. We calculate the prevalence of mixed infection from the model and the effect of mixed infection on TB incidence, TB prevalence and Mycobacterium tuberculosis (MTB) infection rate. Numerical simulations show that mixed infection may explain high TB incidences in areas which have a high strain diversity, poor living conditions and are overcrowded even without HIV.

Population-level mathematical modeling of antimicrobial resistance: a systematic review

BACKGROUND

Mathematical transmission models are increasingly used to guide public health interventions for infectious diseases, particularly in the context of emerging pathogens; however, the contribution of modeling to the growing issue of antimicrobial resistance (AMR) remains unclear. Here, we systematically evaluate publications on population-level transmission models of AMR over a recent period (2006-2016) to gauge the state of research and identify gaps warranting further work.

METHODS

We performed a systematic literature search of relevant databases to identify transmission studies of AMR in viral, bacterial, and parasitic disease systems. We analyzed the temporal, geographic, and subject matter trends, described the predominant medical and behavioral interventions studied, and identified central findings relating to key pathogens.

RESULTS

We identified 273 modeling studies; the majority of which (> 70%) focused on 5 infectious diseases (human immunodeficiency virus (HIV), influenza virus, Plasmodium falciparum (malaria), Mycobacterium tuberculosis (TB), and methicillin-resistant Staphylococcus aureus (MRSA)). AMR studies of influenza and nosocomial pathogens were mainly set in industrialized nations, while HIV, TB, and malaria studies were heavily skewed towards developing countries. The majority of articles focused on AMR exclusively in humans (89%), either in community (58%) or healthcare (27%) settings. Model systems were largely compartmental (76%) and deterministic (66%). Only 43% of models were calibrated against epidemiological data, and few were validated against out-of-sample datasets (14%). The interventions considered were primarily the impact of different drug regimens, hygiene and infection control measures, screening, and diagnostics, while few studies addressed de novo resistance, vaccination strategies, economic, or behavioral changes to reduce antibiotic use in humans and animals.

CONCLUSIONS

The AMR modeling literature concentrates on disease systems where resistance has been long-established, while few studies pro-actively address recent rise in resistance in new pathogens or explore upstream strategies to reduce overall antibiotic consumption. Notable gaps include research on emerging resistance in Enterobacteriaceae and Neisseria gonorrhoeae; AMR transmission at the animal-human interface, particularly in agricultural and veterinary settings; transmission between hospitals and the community; the role of environmental factors in AMR transmission; and the potential of vaccines to combat AMR.

Modelling heterogeneity in host susceptibility to tuberculosis and its effect on public health interventions

A tuberculosis (TB) model that accounts for heterogeneity in host susceptibility to tuberculosis is proposed, with the aim of investigating the implications this may have for the effectiveness of public health interventions. The model examines the possibility that recovered individuals treated from active TB and individuals treated with preventive therapy acquire different levels of immunity. This contrasts with recent studies that assume the two cohorts acquire the same level of immunity, and therefore both groups are reinfected at the same rate. The analysis presented here examines the impact of this assumption when designing intervention strategies. Comparison of reinfection rates between cohorts treated with preventive therapy and recovered individuals who were previously treated for active TB provides important epidemiological insights. It is found that the reinfection rate of the cohort treated with preventive therapy is the one that plays the key role in qualitative changes in TB dynamics. By contrast, the reinfection rate of recovered individuals (previously treated from active TB) plays a minor role. Moreover, the study shows that preventive treatment of individuals during early latency is always beneficial regardless of the level of susceptibility to reinfection. Further, if patients have greater immunity following treatment for late latent infection, then treatment is again beneficial. However, if susceptibility increases following treatment for late latent infection, the effect of treatment depends on the epidemiological setting. That is: (i) in (very) low burden settings, the effect on reactivation predominates and the burden declines with treatment; (ii) in moderate to high burden settings the effect of reinfection predominates and burden increases with treatment. The effect is most dominant between the two reinfection thresholds, RT2 and RT1, respectively associated with individuals being treated with preventive therapy and individuals with untreated late latent TB infection.

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.

Send more data: a systematic review of mathematical models of antimicrobial resistance

Background

Antimicrobial resistance is a global health problem that demands all possible means to control it. Mathematical modelling is a valuable tool for understanding the mechanisms of AMR development and spread, and can help us to investigate and propose novel control strategies. However, it is of vital importance that mathematical models have a broad utility, which can be assured if good modelling practice is followed.

Objective

The objective of this study was to provide a comprehensive systematic review of published models of AMR development and spread. Furthermore, the study aimed to identify gaps in the knowledge required to develop useful models.

Methods

The review comprised a comprehensive literature search with 38 selected studies. Information was extracted from the selected papers using an adaptation of previously published frameworks, and was evaluated using the TRACE good modelling practice guidelines.

Results

None of the selected papers fulfilled the TRACE guidelines. We recommend that future mathematical models should: a) model the biological processes mechanistically, b) incorporate uncertainty and variability in the system using stochastic modelling, c) include a sensitivity analysis and model external and internal validation.

Conclusion

Many mathematical models of AMR development and spread exist. There is still a lack of knowledge about antimicrobial resistance, which restricts the development of useful mathematical models.

Mathematical analysis of multi-antibiotic resistance

BACKGROUND

Multi-antibiotic resistance in bacterial infections is a growing threat to public health. Some experiments were carried out to study the multi-antibiotic resistance.

METHODS

The changes of the multi-antibiotic resistance with time were achieved by numerical simulations and the mathematical models, with the calculated temperature field, velocity field, and the antibiotic concentration field.

RESULTS

The computed results and experimental results are compared.

CONCLUSIONS

Both numerical simulations and the analytic models suggest that minor low concentrations of antibiotics could induce antibiotic resistance in bacteria.

Mathematical modelling of bacterial resistance to multiple antibiotics and immune system response

Resistance of developed bacteria to antibiotic treatment is a very important issue, because introduction of any new antibiotic is after a little while followed by the formation of resistant bacterial isolates in the clinic. The significant increase in clinical resistance to antibiotics is a troubling situation especially in nosocomial infections, where already defenseless patients can be unsuccessful to respond to treatment, causing even greater health issue. Nosocomial infections can be identified as those happening within 2 days of hospital acceptance, 3 days of discharge or 1 month of an operation. They influence 1 out of 10 patients admitted to hospital. Annually, this outcomes in 5000 deaths only in UK with a cost to the National Health Service of a billion pounds. Despite these problems, antibiotic therapy is still the most common method used to treat bacterial infections. On the other hand, it is often mentioned that immune system plays a major role in the progress of infections. In this context, we proposed a mathematical model defining population dynamics of both the specific immune cells produced according to the properties of bacteria by host and the bacteria exposed to multiple antibiotics synchronically, presuming that resistance is gained through mutations due to exposure to antibiotic. Qualitative analysis found out infection-free equilibrium point and other equilibrium points where resistant bacteria and immune system cells exist, only resistant bacteria exists and sensitive bacteria, resistant bacteria and immune system cells exist. As a result of this analysis, our model highlights the fact that when an individual’s immune system weakens, he/she suffers more from the bacterial infections which are believed to have been confined or terminated. Also, these results was supported by numerical simulations.

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.

Magnitude and sources of bias in the detection of mixed strain M. tuberculosis infection

High resolution tests for genetic variation reveal that individuals may simultaneously host more than one distinct strain of Mycobacterium tuberculosis. Previous studies find that this phenomenon, which we will refer to as “mixed infection”, may affect the outcomes of treatment for infected individuals and may influence the impact of population-level interventions against tuberculosis. In areas where the incidence of TB is high, mixed infections have been found in nearly 20% of patients; these studies may underestimate the actual prevalence of mixed infection given that tests may not be sufficiently sensitive for detecting minority strains. Specific reasons for failing to detect mixed infections would include low initial numbers of minority strain cells in sputum, stochastic growth in culture and the physical division of initial samples into parts (typically only one of which is genotyped). In this paper, we develop a mathematical framework that models the study designs aimed to detect mixed infections. Using both a deterministic and a stochastic approach, we obtain posterior estimates of the prevalence of mixed infection. We find that the posterior estimate of the prevalence of mixed infection may be substantially higher than the fraction of cases in which it is detected. We characterize this bias in terms of the sensitivity of the genotyping method and the relative growth rates and initial population sizes of the different strains collected in sputum.

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.

A Bayesian nonparametric model for spatially distributed multivariate binary data with application to a multidrug-resistant tuberculosis (MDR-TB) study

There has been an increasing interest in the analysis of spatially distributed multivariate binary data motivated by a wide range of research problems. Two types of correlations are usually involved: the correlation between the multiple outcomes at one location and the spatial correlation between the locations for one particular outcome. The commonly used regression models only consider one type of correlations while ignoring or modeling inappropriately the other one. To address this limitation, we adopt a Bayesian nonparametric approach to jointly modeling multivariate spatial binary data by integrating both types of correlations. A multivariate probit model is employed to link the binary outcomes to Gaussian latent variables; and Gaussian processes are applied to specify the spatially correlated random effects. We develop an efficient Markov chain Monte Carlo algorithm for the posterior computation. We illustrate the proposed model on simulation studies and a multidrug-resistant tuberculosis case study.

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.

On the interactions of sensitive and resistant Mycobacterium tuberculosis to antibiotics

In this work we propose a system of non linear ordinary differential equations for the dynamics of Mycobacterium tuberculosis (Mtb) within the host, in order to study the role of macrophages, T cells and antibiotics in the control of sensitive and resistant Mtb. Conditions for the persistence of sensitive and resistant bacteria are given in terms of the secondary infections produced by bacteria and macrophages, the immune response, and the antibiotic treatment. Model analysis predicts backward bifurcations for certain values of the parameters. In this case, the dynamics is characterized by the coexistence of two infection states with low and high bacteria load, respectively.

A modeling framework for the evolution and spread of antibiotic resistance: literature review and model categorization

Antibiotic-resistant infections complicate treatment and increase morbidity and mortality. Mathematical modeling has played an integral role in improving our understanding of antibiotic resistance. In these models, parameter sensitivity is often assessed, while model structure sensitivity is not. To examine the implications of this, we first reviewed the literature on antibiotic-resistance modeling published between 1993 and 2011. We then classified each article's model structure into one or more of 6 categories based on the assumptions made in those articles regarding within-host and population-level competition between antibiotic-sensitive and antibiotic-resistant strains. Each model category has different dynamic implications with respect to how antibiotic use affects resistance prevalence, and therefore each may produce different conclusions about optimal treatment protocols that minimize resistance. Thus, even if all parameter values are correctly estimated, inferences may be incorrect because of the incorrect selection of model structure. Our framework provides insight into model selection.

Seasonal dynamics of tuberculosis epidemics and implications for multidrug-resistant infection risk assessment

Understanding how seasonality shapes the dynamics of tuberculosis (TB) is essential in determining risks of transmission and drug resistance in (sub)tropical regions. We developed a relative fitness-based multidrug-resistant (MDR) TB model incorporated with seasonality and a probabilistic assessment model to assess infection risk in Taiwan regions. The model accurately captures the seasonal transmission and population dynamics of TB incidence during 2006-2008 and MDR TB in high TB burden areas during 2006-2010 in Taiwan. There is ~3% probability of having exceeded 50% of the population infected attributed to MDR TB. Our model not only provides insight into the understanding of the interactions between seasonal dynamics of TB and environmental factors but is also capable of predicting the seasonal patterns of TB incidence associated with MDR TB infection risk. A better understanding of the mechanisms of TB seasonality will be critical in predicting the impact of public control programmes.

Mathematical models of the epidemiology and control of drug-resistant TB

Recent reports of extensively drug-resistant TB in South Africa have renewed concerns that antibiotic resistance may undermine progress in TB control. We review three major questions for which mathematical models elucidate the epidemiology and control of drug-resistant TB. How is multiple drug-resistant Mycobacterium tuberculosis selected for in individuals exposed to combination chemotherapy? What factors determine the prevalence of drug-resistant TB? Which interventions to prevent the spread of drug-resistant TB are effective and feasible? Models offer insight into the acquisition and amplification of drug resistance, reveal the importance of distinguishing the intrinsic and extrinsic determinants of the reproductive capacity of drug-resistant M. tuberculosis, and demonstrate the cost effectiveness of interventions for drug-resistant TB. These models also highlight knowledge gaps for which new research will improve our ability to project trends of drug resistance and develop more effective policies for its control.

Assessing the transmission risk of multidrug-resistant Mycobacterium tuberculosis epidemics in regions of Taiwan

OBJECTIVE

The objective of this study was to link transmission dynamics with a probabilistic risk model to provide a mechanistically explicit assessment for estimating the multidrug-resistant tuberculosis (MDR TB) infection risk in regions of Taiwan.

METHODS

A relative fitness (RF)-based MDR TB model was used to describe transmission, validated with disease data for the period 2006-2010. A dose-response model quantifying by basic reproduction number (R(0)) and total proportion of infected population was constructed to estimate the site-specific MDR TB infection risk.

RESULTS

We found that the incidence rate of MDR TB was highest in Hwalien County (4.91 per 100,000 population) in eastern Taiwan, with drug-sensitive and multidrug-resistant R(0) estimates of 0.89 (95% CI 0.23-2.17) and 0.38 (95% CI 0.05-1.30), respectively. The predictions were in apparent agreement with observed data in the 95% credible intervals. Our simulation showed that the incidence of MDR TB will be falling by 2013-2016. Our results indicated that the selected regions of Taiwan had only ∼1% probability of exceeding 50% of the population with infection attributed to MDR TB.

CONCLUSIONS

Our study found that the ongoing control programs implemented in Taiwan may succeed in curing most patients with MDR TB and will reduce the TB incidence countrywide.

QUALITATIVE STUDY FOR A MULTI-DRUG RESISTANT TB MODEL WITH EXOGENOUS REINFECTION AND RELAPSE

One tuberculosis transmission model is formulated by incorporating exogenous reinfection, relapse, and two treatment stages of infectious TB cases. The global stability of the unique disease-free equilibrium is obtained by applying the comparison principle if the effective reproduction number for the full model is less than unity. The existence and stability of the boundary equilibria are given by introducing the invasion reproduction numbers. Furthermore, the existence and local stability of the endemic equilibrium are addressed under some conditions.

A metapopulation model of tuberculosis transmission with a case study from high to low burden areas

Tuberculosis (TB) is a growing problem worldwide, especially with the emergence and high prevalence of multidrug-resistant strains. We develop a metapopulation model for TB spread, which is particularly suited to investigating transmission between areas of high and low prevalence. A case study of cross-border transmission in the Torres Strait region of Australia and Papua New Guinea (PNG) is considered and a sensitivity analysis is conducted. We find that only 6 of the 50 parameters analysed are important to the cumulative number of clinically active TB patients in the entire region. Of these, only the detection rate in PNG is found to be an important intervention parameter. We therefore give insight into the extent the area with the high burden of TB (PNG in the case study) is dominating the TB dynamics of the entire region. Furthermore, the sensitivity analysis results give insight into the data that most important to collect and refine, which is found to be data relating to the PNG parameters.

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.

A TUBERCULOSIS (TB) MODEL WITH UNDETECTED COMPARTMENT: AN APPLICATION TO CHINA

This article introduces a novel model that studies the major factors jeopardizing tuberculosis (TB) control programme in China. A previously developed two-strain TB model is augmented with a class of individuals not registered under the TB control programme. The paper investigates the basic reproduction number and proves the global stability of the disease-free equilibrium. The presence of three endemic equilibria is established in the model. With the help of numerical simulations, a comparative study has been performed to test the validity of the model presented here to the real data available from the Ministry of Health of the People's Republic of China. Sensitivity and elasticity analysis give the key parameters that would govern successful TB control in China.

A tuberculosis model with seasonality

The statistical data of tuberculosis (TB) cases show seasonal fluctuations in many countries. A TB model incorporating seasonality is developed and the basic reproduction ratio R(0) is defined. It is shown that the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears if R(0)<1, and there exists at least one positive periodic solution and the disease is uniformly persistent if R(0)>1. Numerical simulations indicate that there may be a unique positive periodic solution which is globally asymptotically stable if R(0)>1. Parameter values of the model are estimated according to demographic and epidemiological data in China. The simulation results are in good accordance with the seasonal variation of the reported cases of active TB in China.

Tuberculosis reinfection rate as a proportion of total infection rate correlates with the logarithm of the incidence rate: a mathematical model

In a significant number of instances, an episode of tuberculosis can be attributed to a reinfection event. Because reinfection is more likely in high incidence regions than in regions of low incidence, more tuberculosis (TB) cases due to reinfection could be expected in high-incidence regions than in low-incidence regions. Empirical data from regions with various incidence rates appear to confirm the conjecture that, in fact, the incidence rate due to reinfection only, as a proportion of all cases, correlates with the logarithm of the incidence rate, rather than with the incidence rate itself. A theoretical model that supports this conjecture is presented. A Markov model was used to obtain a relationship between incidence and reinfection rates. It was assumed in this model that the rate of reinfection is a multiple, rho (the reinfection factor), of the rate of first-time infection, lambda. The results obtained show a relationship between the proportion of cases due to reinfection and the rate of incidence that is approximately logarithmic for a range of values of the incidence rate typical of those observed in communities across the globe. A value of rho is determined such that the relationship between the proportion of cases due to reinfection and the logarithm of the incidence rate closely correlates with empirical data. From a purely theoretical investigation, it is shown that a simple relationship can be expected between the logarithm of the incidence rates and the proportions of cases due to reinfection after a prior episode of TB. This relationship is sustained by a rate of reinfection that is higher than the rate of first-time infection and this latter consideration underscores the great importance of monitoring recovered TB cases for repeat disease episodes, especially in regions where TB incidence is high. Awareness of this may assist in attempts to control the epidemic.

Latent coinfection and the maintenance of strain diversity

Technologies for strain differentiation and typing have made it possible to detect genetic diversity of pathogens, both within individual hosts and within communities. Coinfection of a host by more than one pathogen strain may affect the relative frequency of these strains at the population level through complex within- and between-host interactions; in infectious diseases that have a long latent period, interstrain competition during latency is likely to play an important role in disease dynamics. We show that SEIR models that include a class of latently coinfected individuals can have markedly different long-term dynamics than models without coinfection, and that coinfection can greatly facilitate the stable coexistence of strains. We demonstrate these dynamics using a model relevant to tuberculosis in which people may experience latent coinfection with both drug sensitive and drug resistant strains. Using this model, we show that the existence of a latent coinfected state allows the possibility that disease control interventions that target latency may facilitate the emergence of drug resistance.

Prevention of nosocomial transmission of extensively drug-resistant tuberculosis in rural South African district hospitals: an epidemiological modelling study

BACKGROUND

Extensively drug-resistant (XDR) tuberculosis has spread among hospitalised patients in South Africa, but the epidemic-level effect of hospital-based infection control strategies remains unknown. We modelled the plausible effect of rapidly available infection control strategies on the overall course of the XDR tuberculosis epidemic in a rural area of South Africa.

METHODS

We investigated the effect of administrative, environmental, and personal infection control measures on the epidemic trajectory of XDR tuberculosis in the rural community of Tugela Ferry. Assessments were done with a mathematical model incorporating over 2 years of longitudinal inpatient and community-based data. The model simulated inpatient airborne tuberculosis transmission, community tuberculosis transmission, and the effect of HIV and antiretroviral therapy.

FINDINGS

If no new interventions are introduced, about 1300 cases of XDR tuberculosis are predicted to occur in the area of Tugela Ferry by the end of 2012, more than half of which are likely to be nosocomially transmitted. Mask use alone would avert fewer than 10% of cases in the overall epidemic, but could prevent a large proportion of cases of XDR tuberculosis in hospital staff. The combination of mask use with reduced hospitalisation time and a shift to outpatient therapy could prevent nearly a third of XDR tuberculosis cases. Supplementing this approach with improved ventilation, rapid drug resistance testing, HIV treatment, and tuberculosis isolation facilities could avert 48% of XDR tuberculosis cases (range 34-50%) by the end of 2012. However, involuntary detention could result in an unexpected rise in incidence due to restricted isolation capacity.

INTERPRETATION

A synergistic combination of available nosocomial infection control strategies could prevent nearly half of XDR tuberculosis cases, even in a resource-limited setting. XDR tuberculosis transmission will probably continue in the community, indicating the need to develop and implement parallel community-based programmes.