Tuberculosis models with fast and slow dynamics: the role of close and casual contacts

Models that incorporate local and individual interactions are introduced in the context of the transmission dynamics of tuberculosis (TB). The multi-level contact structure implicitly assumes that individuals are at risk of infection from close contacts in generalized household (clusters) as well as from casual (random) contacts in the general population. Epidemiological time scales are used to reduce the dimensionality of the model and singular perturbation methods are used to corroborate the results of time-scale approximations. The concept and impact of optimal average cluster or generalized household size on TB dynamics is discussed. We also discuss the potential impact of our results on the spread of TB.     

Avian influenza H5N1 transmission in households, Indonesia

Background

Disease transmission patterns are needed to inform public health interventions, but remain largely unknown for avian influenza H5N1 virus infections. A recent study on the 139 outbreaks detected in Indonesia between 2005 and 2009 found that the type of exposure to sources of H5N1 virus for both the index case and their household members impacted the risk of additional cases in the household. This study describes the disease transmission patterns in those outbreak households.

Methodology/Principal Findings

We compared cases (n = 177) and contacts (n = 496) in the 113 sporadic and 26 cluster outbreaks detected between July 2005 and July 2009 to estimate attack rates and disease intervals. We used final size household models to fit transmission parameters to data on household size, cases and blood-related household contacts to assess the relative contribution of zoonotic and human-to-human transmission of the virus, as well as the reproduction number for human virus transmission. The overall household attack rate was 18.3% and secondary attack rate was 5.5%. Secondary attack rate remained stable as household size increased. The mean interval between onset of subsequent cases in outbreaks was 5.6 days. The transmission model found that human transmission was very rare, with a reproduction number between 0.1 and 0.25, and the upper confidence bounds below 0.4. Transmission model fit was best when the denominator population was restricted to blood-related household contacts of index cases.

Conclusions/Significance

The study only found strong support for human transmission of the virus when a single large cluster was included in the transmission model. The reproduction number was well below the threshold for sustained transmission. This study provides baseline information on the transmission dynamics for the current zoonotic virus and can be used to detect and define signatures of a virus with increasing capacity for human-to-human transmission.     

Towards eliminating bias in cluster analysis of TB genotyped data

The relative contributions of transmission and reactivation of latent infection to TB cases observed clinically has been reported in many situations, but always with some uncertainty. Genotyped data from TB organisms obtained from patients have been used as the basis for heuristic distinctions between circulating (clustered strains) and reactivated infections (unclustered strains). Naïve methods previously applied to the analysis of such data are known to provide biased estimates of the proportion of unclustered cases. The hypergeometric distribution, which generates probabilities of observing clusters of a given size as realized clusters of all possible sizes, is analyzed in this paper to yield a formal estimator for genotype cluster sizes. Subtle aspects of numerical stability, bias, and variance are explored. This formal estimator is seen to be stable with respect to the epidemiologically interesting properties of the cluster size distribution (the number of clusters and the number of singletons) though it does not yield satisfactory estimates of the number of clusters of larger sizes. The problem that even complete coverage of genotyping, in a practical sampling frame, will only provide a partial view of the actual transmission network remains to be explored.     

Projection of tuberculosis incidence with increasing immigration trends

Tuberculosis (TB) incidence rates vary substantially from regions to regions and from countries to countries. In countries such as Canada where TB incidence rate is low, increasing immigration trends may have significant impact on the TB transmission patterns in these countries. In this study we formulate a deterministic epidemiological model of TB transmission in two demographically distinct populations: Canadian born and foreign born populations, in order to investigate the effects of this demographic distinction on the short-term incidence and long-term transmission dynamics, and with special emphasis on the impact of immigration latent TB cases on the overall TB incidence rate in the whole population.     

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

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

Social contact patterns in Vietnam and implications for the control of infectious diseases

Background

The spread of infectious diseases from person to person is determined by the frequency and nature of contacts between infected and susceptible members of the population. Although there is a long history of using mathematical models to understand these transmission dynamics, there are still remarkably little empirical data on contact behaviors with which to parameterize these models. Even starker is the almost complete absence of data from developing countries. We sought to address this knowledge gap by conducting a household based social contact diary in rural Vietnam.

Methods and Findings

A diary based survey of social contact patterns was conducted in a household-structured community cohort in North Vietnam in 2007. We used generalized estimating equations to model the number of contacts while taking into account the household sampling design, and used weighting to balance the household size and age distribution towards the Vietnamese population. We recorded 6675 contacts from 865 participants in 264 different households and found that mixing patterns were assortative by age but were more homogenous than observed in a recent European study. We also observed that physical contacts were more concentrated in the home setting in Vietnam than in Europe but the overall level of physical contact was lower. A model of individual versus household vaccination strategies revealed no difference between strategies in the impact on R ₀.

Conclusions and Significance

This work is the first to estimate contact patterns relevant to the spread of infections transmitted from person to person by non-sexual routes in a developing country setting. The results show interesting similarities and differences from European data and demonstrate the importance of context specific data.     

Modeling the impact of early therapy for latent tuberculosis patients and its optimal control analysis

Effective tuberculosis (TB) control depends on case findings to discover infectious cases, investigation of contacts of those with TB, as well as appropriate treatment. Adherence and successful completion of the treatment are equally important. Unfortunately, due to a number of personal, psychosocial, economic, medical, and health service factors, a significant number of TB patients become irregular and default from treatment. In this paper, a mathematical model is developed to assess the impact of early therapy for latent TB and non-adherence on controlling TB transmission dynamics. Equilibrium states of the model are determined and their local stability is examined. With the aid of the center manifold theory, it is established that the model undergoes a backward bifurcation. Qualitative mathematical analysis of the model suggests that a high level of latent tuberculosis case findings, coupled with a decrease of defaulting rate, may be effective in controlling TB transmission dynamics in the community. Population-level effects of organized campaigns to improve early therapy and to guarantee successful completion of each treatment are evaluated through numerical simulations and presented in support of the analytical results.     

Regional,Household and Individual Factors that Influence Soil Transmitted Helminth Reinfection Dynamics in Preschool Children from Rural Indigenous Panamá

Background

Few studies have investigated the relative influence of individual susceptibility versus household exposure factors versus regional clustering of infection on soil transmitted helminth (STH) transmission. The present study examined reinfection dynamics and spatial clustering of Ascaris lumbricoides, Trichuris trichiura and hookworm in an extremely impoverished indigenous setting in rural Panamá over a 16 month period that included two treatment and reinfection cycles in preschool children.

Methodology/Principle Findings

Spatial cluster analyses were used to identify high prevalence clusters for each nematode. Multivariate models were then used (1) to identify factors that differentiated households within and outside the cluster, and (2) to examine the relative contribution of regional (presence in a high prevalence cluster), household (household density, asset-based household wealth, household crowding, maternal education) and individual (age, sex, pre-treatment eggs per gram (epg) feces, height-for-age, latrine use) factors on preschool child reinfection epgs for each STH. High prevalence spatial clusters were detected for Trichuris and hookworm but not for Ascaris. These clusters were characterized by low household density and low household wealth indices (HWI). Reinfection epg of both hookworm and Ascaris was positively associated with pre-treatment epg and was higher in stunted children. Additional individual (latrine use) as well as household variables (HWI, maternal education) entered the reinfection models for Ascaris but not for hookworm.

Conclusions/Significance

Even within the context of extreme poverty in this remote rural setting, the distinct transmission patterns for hookworm, Trichuris and Ascaris highlight the need for multi-pronged intervention strategies. In addition to poverty reduction, improved sanitation and attention to chronic malnutrition will be key to reducing Ascaris and hookworm transmission.     

Integrating data mining and transmission theory in the ecology of infectious diseases

Our understanding of ecological processes is built on patterns inferred from data. Applying modern analytical tools such as machine learning to increasingly high dimensional data offers the potential to expand our perspectives on these processes, shedding new light on complex ecological phenomena such as pathogen transmission in wild populations. Here, we propose a novel approach that combines data mining with theoretical models of disease dynamics. Using rodents as an example, we incorporate statistical differences in the life history features of zoonotic reservoir hosts into pathogen transmission models, enabling us to bound the range of dynamical phenomena associated with hosts, based on their traits. We then test for associations between equilibrium prevalence, a key epidemiological metric and data on human outbreaks of rodent‐borne zoonoses, identifying matches between empirical evidence and theoretical predictions of transmission dynamics. We show how this framework can be generalized to other systems through a rubric of disease models and parameters that can be derived from empirical data. By linking life history components directly to their effects on disease dynamics, our mining‐modelling approach integrates machine learning and theoretical models to explore mechanisms in the macroecology of pathogen transmission and their consequences for spillover infection to humans.     

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.     

Pertussis in England and Wales: an investigation of transmission dynamics and control by mass vaccination

The epidemiology of pertussis and its prospects for control by mass vaccination in England and Wales are investigated by analyses of longitudinal records on incidence and vaccine uptake, and horizontal data on age-stratified case reports. Mathematical models of the transmission dynamics of the infection that incorporate loss of natural and vaccine-induced immunity plus variable vaccine efficacy are developed, and their predictions compared with observed trends. Analyses of case reports reveal that the individual force of infection is age dependent, with peak transmission in the 5- to 10-year-old age class. A model incorporating this age dependency, along with partial vaccine efficacy and loss of vaccine-induced immunity, generates predicted patterns that best mirror observed trends since mass vaccination was inaugurated in 1957 in England and Wales. Model projections accurately mirror the failure of mass vaccination to increase the inter-epidemic period of the infection (three years) over that pertaining before control. The analysis suggests that this is due to the impact of partial vaccine efficacy. Projected trends do not accurately reflect the low levels of pertussis incidence reported between epidemics in the periods of high vaccine uptake. This is thought to arise from a combination of factors, including loss of natural and vaccine induced immunity, biases in case reporting (where reporting efficiency is positively associated with the incidence of pertussis), and seasonal variations in transmission. Model predictions suggest that the vaccination of 88% of each birth cohort before the age of 1 year will eliminate bacterial transmission, provided the vaccine confers lifelong protection against infection. If vaccine-induced immunity is significantly less than lifelong (or if vaccination fails to protect all its recipients) repeated cohort immunization is predicted to be necessary to eliminate transmission. Future research needs are discussed, and emphasis is placed on the need for more refined data on vaccine efficacy, the duration of natural and vaccine-induced immunity and the incidence of clinical pertussis and subclinical infections (perhaps by the development of reliable serological tests). Future mathematical models will need especially to incorporate seasonality in transmission.     

Spatiotemporal Clustering of Mycobacterium tuberculosis Complex Genotypes in Florida: Genetic Diversity Segregated by Country of Birth

BackgroundTuberculosis (TB) is caused by members of the Mycobacterium tuberculosis complex (MTBC). Although the MTBC is highly clonal, between-strain genetic diversity has been observed. In low TB incidence settings, immigration may facilitate the importation of MTBC strains with a potential to complicate TB control efforts.MethodsWe investigated the genetic diversity and spatiotemporal clustering of 2,510 MTBC strains isolated in Florida, United States, between 2009 and 2013 and genotyped using spoligotyping and 24-locus MIRU-VNTR. We mapped the genetic diversity to the centroid of patient residential zip codes using a geographic information system (GIS). We assessed transmission dynamics and the influence of immigration on genotype clustering using space-time permutation models adjusted for foreign-born population density and county-level HIV risk and multinomial models stratified by country of birth and timing of immigration in SaTScan.Conclusions/SignificanceAlmost five percent of TB cases reported in Florida during 2009–2013 were potentially due to recent transmission. Improvements to TB screening practices among the prison population and recent immigrants are likely to impact TB control. Due to the monomorphic nature of available markers, whole genome sequencing is needed to conclusively delineate recent transmission events between U.S. and foreign-born persons.     

The reinfection threshold promotes variability in tuberculosis epidemiology and vaccine efficacy

Population patterns of infection are determined largely by susceptibility to infection. Infection and vaccination induce an immune response that, typically, reduces susceptibility to subsequent infections. With a general epidemic model, we detect a 'reinfection threshold', above which reinfection is the principal type of transmission and, consequently, infection levels are much higher and vaccination fails. The model is further developed to address human tuberculosis (TB) and the impact of vaccination. The bacille Calmette-Guérin (BCG) is the only vaccine in current use against TB, and there is no consensus about its usefulness. Estimates of protection range from 0 to 80%, and this variability is aggravated by an association between low vaccine efficacy and high prevalence of the disease. We propose an explanation based on three postulates: (i) the potential for transmission varies between populations, owing to differences in socio-economic and environmental factors; (ii) exposure to mycobacteria induces an immune response that is partially protective against reinfection; and (iii) this protection is not significantly improved by BCG vaccination. These postulates combine to reproduce the observed trends, and this is attributed to a reinfection threshold intrinsic to the transmission dynamics. Finally, we demonstrate how reinfection thresholds can be manipulated by vaccination programmes, suggesting that they have a potentially powerful role in global control.     

Effect of Active Case Finding on Prevalence and Transmission of Pulmonary Tuberculosis in Dhaka Central Jail,Bangladesh

BackgroundUnderstanding tuberculosis (TB) transmission dynamics is essential for establishing effective TB control strategies in settings where the burden and risk of transmission are high. The objectives of this study were to evaluate the effect of active screening on controlling TB transmission and also to characterize Mycobacterium tuberculosis strains for investigating transmission dynamics in a correctional setting.MethodsThe study was carried out in Dhaka Central Jail (DCJ), from October 2005 to February 2010. An active case finding strategy for pulmonary TB was established both at the entry point to the prison and inside the prison. Three sputum specimens were collected from all pulmonary TB suspects and subjected to smear microscopy, culture, and drug susceptibility testing as well as genotyping which included deletion analysis, spoligotyping and analysis of mycobacterial interspersed repetitive units (MIRU).ResultsA total of 60,585 inmates were screened during the study period. We found 466 inmates with pulmonary TB of whom 357 (77%) had positive smear microscopy results and 109 (23%) had negative smear microscopy results but had positive results on culture. The number of pulmonary TB cases declined significantly, from 49 cases during the first quarter to 8 cases in the final quarter of the study period (p=0.001). Deletion analysis identified all isolates as M. tuberculosis and further identified 229 (70%) strains as ‘modern’ and 100 (30%) strains as ‘ancestral’. Analysis of MIRU showed that 347 strains (85%) exhibited unique patterns, whereas 61 strains (15%) clustered into 22 groups. The largest cluster comprised eight strains of the Beijing M. tuberculosis type. The rate of recent transmission was estimated to be 9.6%.ConclusionsImplementation of active screening for TB was associated with a decline in TB cases in DCJ. Implementation of active screening in prison settings might substantially reduce the national burden of TB in Bangladesh.     

An investigation into the statistical properties of TB episodes in a South African community with high HIV prevalence

Continuous differential equations are often applied to small populations with little time spent on understanding uncertainty brought about by small-population effects. Despite large numbers of individuals being latently infected with Mycobacterium tuberculosis (TB), progression from latent infection to observable disease is a relatively rare event. For small communities, this means case counts are subject to stochasticity, and deterministic models may not be appropriate tools for interpreting transmission trends. Furthermore, the nonlinear nature of the underlying dynamics means that fluctuations are autocorrelated, which can invalidate standard statistical analyses which assume independent fluctuations.Here we extend recent work using a system of differential equations to study the HIV-TB epidemic in Masiphumelele, a community near Cape Town in South Africa [Bacaër, et al., J. Mol. Biol. 57(4), 557-593] by studying the statistical properties of active TB events. We apply van Kampen's system-size (or population-size) expansion technique to obtain an approximation to a master equation describing the dynamics. We use the resulting Fokker-Planck equation and point-process theory to derive two-time correlation functions for active TB events. This method can be used to gain insight into the temporal aspect of cluster identification, which currently relies on DNA classification only.     

Population dynamics of botanical epidemics involving primary and secondary infection

In this paper we study the dynamical properties of models for botanical epidemics, especially for soil-borne fungal infection. The models develop several new concepts, involving dual sources of infection, host and inoculum dynamics. Epidemics are modelled with respect to the infection status of whole plants and plant organs (the G model) or to lesion density and size (the SW model). The infection can originate in two sources, either from the initial inoculum (primary infection) or by a direct transmission between plant tissue (secondary infection). The first term corresponds to the transmission through the free-living stages of macroparasites or an external source of infection in certain medical models, whereas the second term is equivalent to direct transmission between the hosts in microparasitic infections. The models allow for dynamics of host growth and inoculum decay. We show that the two models for root and lesion dynamics can be derived as special cases of a single generic model. Analytical and numerical methods are used to analyse the behaviour of the models for static, unlimited (exponential) and asymptotically limited host growth with and without secondary infection, and with and without decay of initial inoculum. The models are shown to exhibit a range of epidemic behaviour within single seasons that extends from simple monotonic increase with saturation of the host population, through temporary plateaux as the system switches from primary to secondary infection, to effective elimination of the pathogen by the host outgrowing the fungal infection. For certain conditions, the equilibrium values are shown to depend on initial conditions. These results have important consequences for the control of plant disease. They can be applied beyond soil-borne plant pathogens to mycorrhizal fungi and aerial pathogens while the principles of primary and secondary infection with host and inoculum dynamics may be used to link classical models for both microparasitic and macroparasitic infections.     

Social organization and movement influence the incidence of bovine tuberculosis in an undisturbed high-density badger Meles meles population

1. The culling of European badgers Meles meles has been a central part of attempts to control bovine tuberculosis (TB) in British cattle for many years. Recent results, however, indicate that this approach could in practice enhance disease spread. 2. This paper looks at the relationship between TB incidence and badger ecology in a high-density population in south-west England, which has been the subject of a long-term intensive study. The principal aims were to relate the probability of TB incidence, as detected by culture of clinical samples (i.e. excretion of bacilli), at the level of the individual and of the social group to demographic processes, movement, social organization and disease dynamics. 3. The probability of an individual being an incident case was greater in groups where TB was already present, although this was less influential in groups that were subject to some instability in numbers. Both individuals and groups were more likely to be incident cases where the social group was diminishing in size, although no relationship was observed with group size itself. This suggests that the process of group size reduction rather than group size per se has most influence on disease dynamics. The likelihood that either an individual or a group was an incident case was positively correlated with both individual and group-level movement. When the proportion of females in a social group was high, the positive association between movement and incidence was found to be more pronounced and there was a significantly higher probability of incident cases among males. 4. These relationships highlight the importance of social structure in driving TB transmission dynamics in this stable, high-density badger population. The results support the idea that a stable social structure mitigates against new incident cases of disease, and are consistent with the contention that badger culling may create the social circumstances for enhanced transmission of TB.     

A versatile ODE approximation to a network model for the spread of sexually transmitted diseases

 We develop a moment closure approximation (MCA) to a network model of sexually transmitted disease (STD) spread through a steady/casual partnership network. MCA has been used previously to approximate static, regular lattices, whereas application to dynamic, irregular networks is a new endeavour, and application to sociologically-motivated network models has not been attempted. Our goals are 1) to investigate issues relating to the application of moment closure approximations to dynamic and irregular networks, and 2) to understand the impact of concurrent casual partnerships on STD transmission through a population of predominantly steady monogamous partnerships. We are able to derive a moment closure approximation for a dynamic irregular network representing sexual partnership dynamics, however, we are forced to use a triple approximation due to the large error of the standard pair approximation. This example underscores the importance of doing error analysis for moment closure approximations. We also find that a small number of casual partnerships drastically increases the prevalence and rate of spread of the epidemic. Finally, although the approximation is derived for a specific network model, we can recover approximations to a broad range of network models simply by varying model parameters which control the structure of the dynamic network. Thus our moment closure approximation is very flexible in the kinds of network models it can approximate. Received: 26 August 2001 / Revised version: 15 March 2002 / Published online: 23 August 2002 C.T.B. was supported by the NSF. Key words or phrases: Moment closure approximation – Network model – Pair approximation – Sexually transmitted diseases – Steady/casual partnership network     

Non-linear transmission and simple models for bovine tuberculosis

1.  A new model is presented for a possum–tuberculosis (TB) system ( Trichosurus vulpecula – Mycobacterium bovis ) that is both realistic and parsimonious. The model includes a phenomenological treatment of heterogeneity of risk for susceptible hosts, similar to that used in insect host–parasitoid systems.
2.  Parameter values for the model reflect current knowledge and differ significantly from those in other recent models of this system. Associated with these structural and parametric changes are substantially different predictions for the dynamics and control of TB in possums.
3.  The model predictions include (i) only limited host suppression due to the disease (< 10%, cf. several earlier simple models for TB in both possums and badgers); (ii) asymptotically stable disease dynamics (cf. homogeneous-mixing models that predict either extremely weak stability such that disease fails to recover when host density is temporarily reduced, or oscillatory behaviour and potential elimination of disease following such a perturbation); (iii) TB that is harder to control than in the homogeneous-mixing model equivalents, in line with practical experience; and (iv) a threshold host density for disease elimination that differs substantially from the host equilibrium density in the presence of disease.
4.  Homogeneous-mixing models are unable to reproduce this behaviour, whatever parameter values are chosen. Heterogeneous-mixing models with non-linear transmission may therefore be worth consideration in other endemic wildlife disease systems, as is now commonplace for insect–parasitoid and insect–pathogen ones.