Epidemiological Models with Non-Exponentially Distributed Disease Stages and Applications to Disease Control

SEIR epidemiological models with the inclusion of quarantine and isolation are used to study the control and intervention of infectious diseases. A simple ordinary differential equation (ODE) model that assumes exponential distribution for the latent and infectious stages is shown to be inadequate for assessing disease control strategies. By assuming arbitrarily distributed disease stages, a general integral equation model is developed, of which the simple ODE model is a special case. Analysis of the general model shows that the qualitative disease dynamics are determined by the reproductive number , which is a function of control measures. The integral equation model is shown to reduce to an ODE model when the disease stages are assumed to have a gamma distribution, which is more realistic than the exponential distribution. Outcomes of these models are compared regarding the effectiveness of various intervention policies. Numerical simulations suggest that models that assume exponential and non-exponential stage distribution assumptions can produce inconsistent predictions.     

The Effects of Vector Movement and Distribution in a Mathematical Model of Dengue Transmission

Background

Mathematical models have been used to study the dynamics of infectious disease outbreaks and predict the effectiveness of potential mass vaccination campaigns. However, models depend on simplifying assumptions to be tractable, and the consequences of making such assumptions need to be studied. Two assumptions usually incorporated by mathematical models of vector-borne disease transmission is homogeneous mixing among the hosts and vectors and homogeneous distribution of the vectors.

Methodology/Principal Findings

We explored the effects of mosquito movement and distribution in an individual-based model of dengue transmission in which humans and mosquitoes are explicitly represented in a spatial environment. We found that the limited flight range of the vector in the model greatly reduced its ability to transmit dengue among humans. A model that does not assume a limited flight range could yield similar attack rates when transmissibility of dengue was reduced by 39%. A model in which mosquitoes are distributed uniformly across locations behaves similarly to one in which the number of mosquitoes per location is drawn from an exponential distribution with a slightly higher mean number of mosquitoes per location. When the models with different assumptions were calibrated to have similar human infection attack rates, mass vaccination had nearly identical effects.

Conclusions/Significance

Small changes in assumptions in a mathematical model of dengue transmission can greatly change its behavior, but estimates of the effectiveness of mass dengue vaccination are robust to some simplifying assumptions typically made in mathematical models of vector-borne disease.     

Elucidating variations in the nucleotide sequence of Ebola virus associated with increasing pathogenicity

Background

Ebolaviruses cause a severe and often fatal haemorrhagic fever in humans, with some species such as Ebola virus having case fatality rates approaching 90%. Currently, the worst Ebola virus outbreak since the disease was discovered is occurring in West Africa. Although thought to be a zoonotic infection, a concern is that with increasing numbers of humans being infected, Ebola virus variants could be selected which are better adapted for human-to-human transmission.

Results

To investigate whether genetic changes in Ebola virus become established in response to adaptation in a different host, a guinea pig model of infection was used. In this experimental system, guinea pigs were infected with Ebola virus (EBOV), which initially did not cause disease. To simulate transmission to uninfected individuals, the virus was serially passaged five times in naïve animals. As the virus was passaged, virulence increased and clinical effects were observed in the guinea pig. An RNAseq and consensus mapping approach was then used to evaluate potential nucleotide changes in the Ebola virus genome at each passage.

Conclusions

Upon passage in the guinea pig model, EBOV become more virulent, RNA editing and also coding changes in key proteins become established. The data suggest that the initial evolutionary trajectory of EBOV in a new host can lead to a gain in virulence. Given the circumstances of the sustained transmission of EBOV in the current outbreak in West Africa, increases in virulence may be associated with prolonged and uncontrolled epidemics of EBOV.     

Quantifying Poverty as a Driver of Ebola Transmission

Background

Poverty has been implicated as a challenge in the control of the current Ebola outbreak in West Africa. Although disparities between affected countries have been appreciated, disparities within West African countries have not been investigated as drivers of Ebola transmission. To quantify the role that poverty plays in the transmission of Ebola, we analyzed heterogeneity of Ebola incidence and transmission factors among over 300 communities, categorized by socioeconomic status (SES), within Montserrado County, Liberia.

Methodology/Principal Findings

We evaluated 4,437 Ebola cases reported between February 28, 2014 and December 1, 2014 for Montserrado County to determine SES-stratified temporal trends and drivers of Ebola transmission. A dataset including dates of symptom onset, hospitalization, and death, and specified community of residence was used to stratify cases into high, middle and low SES. Additionally, information about 9,129 contacts was provided for a subset of 1,585 traced individuals. To evaluate transmission within and across socioeconomic subpopulations, as well as over the trajectory of the outbreak, we analyzed these data with a time-dependent stochastic model. Cases in the most impoverished communities reported three more contacts on average than cases in high SES communities (p<0.001). Our transmission model shows that infected individuals from middle and low SES communities were associated with 1.5 (95% CI: 1.4–1.6) and 3.5 (95% CI: 3.1–3.9) times as many secondary cases as those from high SES communities, respectively. Furthermore, most of the spread of Ebola across Montserrado County originated from areas of lower SES.

Conclusions/Significance

Individuals from areas of poverty were associated with high rates of transmission and spread of Ebola to other regions. Thus, Ebola could most effectively be prevented or contained if disease interventions were targeted to areas of extreme poverty and funding was dedicated to development projects that meet basic needs.     

Ebola in great apes – current knowledge,possibilities for vaccination,and implications for conservation and human health

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Incorporating infectious duration-dependent transmission into Bayesian epidemic models

Compartmental models are commonly used to describe the spread of infectious diseases by estimating the probabilities of transitions between important disease states. A significant challenge in fitting Bayesian compartmental models lies in the need to estimate the duration of the infectious period, based on limited data providing only symptom onset date or another proxy for the start of infectiousness. Commonly, the exponential distribution is used to describe the infectious duration, an overly simplistic approach, which is not biologically plausible. More flexible distributions can be used, but parameter identifiability and computational cost can worsen for moderately sized or large epidemics. In this article, we present a novel approach, which considers a curve of transmissibility over a fixed infectious duration. The incorporation of infectious duration-dependent (IDD) transmissibility, which decays to zero during the infectious period, is biologically reasonable for many viral infections and fixing the length of the infectious period eases computational complexity in model fitting. Through simulation, we evaluate different functional forms of IDD transmissibility curves and show that the proposed approach offers improved estimation of the time-varying reproductive number. We illustrate the benefit of our approach through a new analysis of the 1995 outbreak of Ebola Virus Disease in the Democratic Republic of the Congo.     

Power law versus exponential state transition dynamics: application to sleep-wake architecture

Background

Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot.

Methodology/Principal Findings

To characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the “incorrect” model over a range of parameters. The “zone of mimicry” of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions.

Conclusions/Significance

Recognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture.     

Predicted steady-state cell size distributions for various growth models

The question of how an individual bacterial cell grows during its life cycle remains controversial. In 1962 Collins and Richmond derived a very general expression relating the size distributions of newborn, dividing and extant cells in steady-state growth and their growth rate; it represents the most powerful framework currently available for the analysis of bacterial growth kinetics. The Collins-Richmond equation is in effect a statement of the conservation of cell numbers for populations in steady-state exponential growth. It has usually been used to calculate the growth rate from a measured cell size distribution under various assumptions regarding the dividing and newborn cell distributions, but can also be applied in reverse--to compute the theoretical cell size distribution from a specified growth law. This has the advantage that it is not limited to models in which growth rate is a deterministic function of cell size, such as in simple exponential or linear growth, but permits evaluation of far more sophisticated hypotheses. Here we employed this reverse approach to obtain theoretical cell size distributions for two exponential and six linear growth models. The former differ as to whether there exists in each cell a minimal size that does not contribute to growth, the latter as to when the presumptive doubling of the growth rate takes place: in the linear age models, it is taken to occur at a particular cell age, at a fixed time prior to division, or at division itself; in the linear size models, the growth rate is considered to double with a constant probability from cell birth, with a constant probability but only after the cell has reached a minimal size, or after the minimal size has been attained but with a probability that increases linearly with cell size. Each model contains a small number of adjustable parameters but no assumptions other than that all cells obey the same growth law. In the present article, the various growth laws are described and rigorous mathematical expressions developed to predict the size distribution of extant cells in steady-state exponential growth; in the following paper, these predictions are tested against high-quality experimental data.     

Validation of statistical models for estimating hospitalization associated with influenza and other respiratory viruses

Background

Reliable estimates of disease burden associated with respiratory viruses are keys to deployment of preventive strategies such as vaccination and resource allocation. Such estimates are particularly needed in tropical and subtropical regions where some methods commonly used in temperate regions are not applicable. While a number of alternative approaches to assess the influenza associated disease burden have been recently reported, none of these models have been validated with virologically confirmed data. Even fewer methods have been developed for other common respiratory viruses such as respiratory syncytial virus (RSV), parainfluenza and adenovirus.

Methods and Findings

We had recently conducted a prospective population-based study of virologically confirmed hospitalization for acute respiratory illnesses in persons <18 years residing in Hong Kong Island. Here we used this dataset to validate two commonly used models for estimation of influenza disease burden, namely the rate difference model and Poisson regression model, and also explored the applicability of these models to estimate the disease burden of other respiratory viruses. The Poisson regression models with different link functions all yielded estimates well correlated with the virologically confirmed influenza associated hospitalization, especially in children older than two years. The disease burden estimates for RSV, parainfluenza and adenovirus were less reliable with wide confidence intervals. The rate difference model was not applicable to RSV, parainfluenza and adenovirus and grossly underestimated the true burden of influenza associated hospitalization.

Conclusion

The Poisson regression model generally produced satisfactory estimates in calculating the disease burden of respiratory viruses in a subtropical region such as Hong Kong.     

Underestimated ranges and overlooked refuges from amphibian chytridiomycosis

Aim

Accurately documenting and predicting declines and shifts in species’ distributions is fundamental for implementing effective conservation strategies and directing future research; species distribution models (SDM) have become a powerful tool for such work. Nevertheless, much of the data used to create these models are opportunistic and often violate some of their basic assumptions. We use amphibian declines and extinctions linked to the fungus Batrachochytrium dendrobatidis (Bd) to examine how sampling biases in data collection can affect what we know of this disease and its effect on amphibians in the wild.

Location

Queensland, Australia.

Methods

We developed a distribution model for Bd incorporating known locality records for Bd and a subset of climatic variables that should correctly characterize its distribution. We tested this (original) model with additional surveys, recorded new Bd observations in novel environments and reran the distribution model. We then investigated the difference between the original and new models, and used frog abundance and infection status data from two of these new localities to look at the susceptibility of the torrent frog Litoria nannotis to chytridiomycosis.

Results

While largely correct, the original SDM underestimated the distribution of Bd; sampling in ‘unsuitable’ drier environments discovered abundant populations of susceptible frogs with pathogen prevalences of up to 100%. The validation surveys further uncovered a new population of the frog Litoria lorica coexisting with the pathogen; this species was previously believed to be an extinct rain forest endemic.

Main conclusion

Our results indicate that SDMs constructed using opportunistically collected data can be biased if species are not at equilibrium with their environment or because environmental gradients have not been adequately sampled. For disease ecology, the better estimations of pathogen distribution may lead to the discovery of new populations persisting at the edge of their range, which has important implications for the conservation of species threatened by chytridiomycosis.

     

Interaction between Ebola Virus Glycoprotein and Host Toll-Like Receptor 4 Leads to Induction of Proinflammatory Cytokines and SOCS1

Ebola virus initially targets monocytes and macrophages, which can lead to the release of proinflammatory cytokines and chemokines. These inflammatory cytokines are thought to contribute to the development of circulatory shock seen in fatal Ebola virus infections. Here we report that host Toll-like receptor 4 (TLR4) is a sensor for Ebola virus glycoprotein (GP) on virus-like particles (VLPs) and that resultant TLR4 signaling pathways lead to the production of proinflammatory cytokines and suppressor of cytokine signaling 1 (SOCS1) in a human monocytic cell line and in HEK293-TLR4/MD2 cells stably expressing the TLR4/MD2 complex. Ebola virus GP was found to interact with TLR4 by immunoprecipitation/Western blot analyses, and Ebola virus GP on VLPs was able to stimulate expression of NF-κB in a TLR4-dependent manner. Interestingly, we found that budding of Ebola virus VLPs was more pronounced in TLR4-stimulated cells than in unstimulated control cells. In sum, these findings identify the host innate immune protein TLR4 as a sensor for Ebola virus GP which may play an important role in the immunopathogenesis of Ebola virus infection.Ebola virus and Marburg virus comprise the Filoviridae family and represent important human pathogens and potential agents of bioterrorism. Currently there are no approved vaccines or specific treatments available to prevent or treat filovirus infections. The filoviruses are the cause of severe hemorrhagic disease in humans (7). Ebola virus initially targets monocytes/macrophages and dendritic cells (DCs), which can lead to the release of proinflammatory cytokines and chemokines (3, 7). A better understanding of the physical and functional interactions between Ebola virus proteins and cellular factors regulating the host innate immune response may reveal novel insights into the pathogenesis of Ebola virus and offer new strategies to inhibit Ebola virus replication.The VP40 matrix protein of Ebola virus is a key structural protein critical for budding virus-like particles (VLPs) and virion egress. Interactions between late budding domains of VP40 and specific host proteins facilitate efficient release of VLPs and infectious virus. Viral proteins other than VP40 also contribute to efficient budding of VLPs. Ebola virus glycoprotein (GP), when coexpressed with VP40, is incorporated into budding VLPs and enhances VLP egress (15), possibly by antagonizing the function of host proteins (12).Several studies have reported the induction of an innate immune response following infection or stimulation of macrophages/monocytes and DCs with Ebola virus or VLPs, respectively (2, 31). For example, incubation of Ebola virus VP40+GP VLPs with DCs led to the induction of interleukin-6 (IL-6), IL-8, NF-κB and ERK1/2 (18, 31). The triggering mechanism by which Ebola virus VLPs stimulate cytokine production is unknown. Here, we present evidence that Ebola virus VLPs stimulate induction of proinflammatory cytokines as well as SOCS1 (a ubiquitin ligase and negative feedback regulator of cytokine production) by interacting with host Toll-like receptor 4 (TLR4). Importantly, Ebola virus VP40+GP VLPs, but not VP40 VLPs, induced cytokine and SOCS1 expression in a TLR4/MD2 dependent manner both in a human monocytic cell line (THP-1 cells) and in 293T cells expressing a functional TLR4/MD2 receptor. These results indicate that the stimulation of TLR4 by Ebola virus envelope GP results in an innate host response, induction of SOCS1 protein, and potential enhancement of virus egress.     

Adaptive modeling of viral diseases in bats with a focus on rabies

Many emerging and reemerging viruses, such as rabies, SARS, Marburg, and Ebola have bat populations as disease reservoirs. Understanding the spillover from bats to humans and other animals, and the associated health risks requires an analysis of the disease dynamics in bat populations. Traditional compartmental epizootic models, which are relatively easy to implement and analyze, usually impose unrealistic aggregation assumptions about disease-related structure and depend on parameters that frequently are not measurable in field conditions. We propose a novel combination of computational and adaptive modeling approaches that address the maintenance of emerging diseases in bat colonies through individual (intra-host) models of the response of the host to a viral challenge. The dynamics of the individual models are used to define survival, susceptibility and transmission conditions relevant to epizootics as well as to develop and parametrize models of the disease evolution into uniform and diverse populations. Applications of the proposed approach to modeling the effects of immunological heterogeneity on the dynamics of bat rabies are presented.     

Characterization and Simulation of Uncertain Frequency Distributions: Effects of Distribution Choice,Variability, Uncertainty,and Parameter Dependence

We use bootstrap simulation to characterize uncertainty in parametric distributions, including Normal, Lognormal, Gamma, Weibull, and Beta, commonly used to represent variability in probabilistic assessments. Bootstrap simulation enables one to estimate sampling distributions for sample statistics, such as distribution parameters, even when analytical solutions are not available. Using a two-dimensional framework for both uncertainty and variability, uncertainties in cumulative distribution functions were simulated. The mathematical properties of uncertain frequency distributions were evaluated in a series of case studies during which the parameters of each type of distribution were varied for sample sizes of 5, 10, and 20. For positively skewed distributions such as Lognormal, Weibull, and Gamma, the range of uncertainty is widest at the upper tail of the distribution. For symmetric unbounded distributions, such as Normal, the uncertainties are widest at both tails of the distribution. For bounded distributions, such as Beta, the uncertainties are typically widest in the central portions of the distribution. Bootstrap simulation enables complex dependencies between sampling distributions to be captured. The effects of uncertainty, variability, and parameter dependencies were studied for several generic functional forms of models, including models in which two-dimensional random variables are added, multiplied, and divided, to show the sensitivity of model results to different assumptions regarding model input distributions, ranges of variability, and ranges of uncertainty and to show the types of errors that may be obtained from mis-specification of parameter dependence. A total of 1,098 case studies were simulated. In some cases, counter-intuitive results were obtained. For example, the point value of the 95th percentile of uncertainty for the 95th percentile of variability of the product of four Gamma or Weibull distributions decreases as the coefficient of variation of each model input increases and, therefore, may not provide a conservative estimate. Failure to properly characterize parameter uncertainties and their dependencies can lead to orders-of-magnitude mis-estimates of both variability and uncertainty. In many cases, the numerical stability of two-dimensional simulation results was found to decrease as the coefficient of variation of the inputs increases. We discuss the strengths and limitations of bootstrap simulation as a method for quantifying uncertainty due to random sampling error.     

Harnessing Case Isolation and Ring Vaccination to Control Ebola

As a devastating Ebola outbreak in West Africa continues, non-pharmaceutical control measures including contact tracing, quarantine, and case isolation are being implemented. In addition, public health agencies are scaling up efforts to test and deploy candidate vaccines. Given the experimental nature and limited initial supplies of vaccines, a mass vaccination campaign might not be feasible. However, ring vaccination of likely case contacts could provide an effective alternative in distributing the vaccine. To evaluate ring vaccination as a strategy for eliminating Ebola, we developed a pair approximation model of Ebola transmission, parameterized by confirmed incidence data from June 2014 to January 2015 in Liberia and Sierra Leone. Our results suggest that if a combined intervention of case isolation and ring vaccination had been initiated in the early fall of 2014, up to an additional 126 cases in Liberia and 560 cases in Sierra Leone could have been averted beyond case isolation alone. The marginal benefit of ring vaccination is predicted to be greatest in settings where there are more contacts per individual, greater clustering among individuals, when contact tracing has low efficacy or vaccination confers post-exposure protection. In such settings, ring vaccination can avert up to an additional 8% of Ebola cases. Accordingly, ring vaccination is predicted to offer a moderately beneficial supplement to ongoing non-pharmaceutical Ebola control efforts.     

How Methodologic Differences Affect Results of Economic Analyses: A Systematic Review of Interferon Gamma Release Assays for the Diagnosis of LTBI

Introduction

Cost effectiveness analyses (CEA) can provide useful information on how to invest limited funds, however they are less useful if different analysis of the same intervention provide unclear or contradictory results. The objective of our study was to conduct a systematic review of methodologic aspects of CEA that evaluate Interferon Gamma Release Assays (IGRA) for the detection of Latent Tuberculosis Infection (LTBI), in order to understand how differences affect study results.

Methods

A systematic review of studies was conducted with particular focus on study quality and the variability in inputs used in models used to assess cost-effectiveness. A common decision analysis model of the IGRA versus Tuberculin Skin Test (TST) screening strategy was developed and used to quantify the impact on predicted results of observed differences of model inputs taken from the studies identified.

Results

Thirteen studies were ultimately included in the review. Several specific methodologic issues were identified across studies, including how study inputs were selected, inconsistencies in the costing approach, the utility of the QALY (Quality Adjusted Life Year) as the effectiveness outcome, and how authors choose to present and interpret study results. When the IGRA versus TST test strategies were compared using our common decision analysis model predicted effectiveness largely overlapped.

Implications

Many methodologic issues that contribute to inconsistent results and reduced study quality were identified in studies that assessed the cost-effectiveness of the IGRA test. More specific and relevant guidelines are needed in order to help authors standardize modelling approaches, inputs, assumptions and how results are presented and interpreted.     

A Small Community Model for the Transmission of Infectious Diseases: Comparison of School Closure as an Intervention in Individual-Based Models of an Influenza Pandemic

Background

In the absence of other evidence, modelling has been used extensively to help policy makers plan for a potential future influenza pandemic.

Method

We have constructed an individual based model of a small community in the developed world with detail down to exact household structure obtained from census collection datasets and precise simulation of household demographics, movement within the community and individual contact patterns. We modelled the spread of pandemic influenza in this community and the effect on daily and final attack rates of four social distancing measures: school closure, increased case isolation, workplace non-attendance and community contact reduction. We compared the modelled results of final attack rates in the absence of any interventions and the effect of school closure as a single intervention with other published individual based models of pandemic influenza in the developed world.

Results

We showed that published individual based models estimate similar final attack rates over a range of values for R₀ in a pandemic where no interventions have been implemented; that multiple social distancing measures applied early and continuously can be very effective in interrupting transmission of the pandemic virus for R₀ values up to 2.5; and that different conclusions reached on the simulated benefit of school closure in published models appear to result from differences in assumptions about the timing and duration of school closure and flow-on effects on other social contacts resulting from school closure.

Conclusion

Models of the spread and control of pandemic influenza have the potential to assist policy makers with decisions about which control strategies to adopt. However, attention needs to be given by policy makers to the assumptions underpinning both the models and the control strategies examined.     

On the HIV Incubation Distribution Under AZT Treatment

Assuming some general models for the HIV epidemic, in this paper I derive the HIV incubation distributions under AZT treatment. It is shown that under some conditions, these probability distributions are mixtures of some generalized Gamma distributions and products of generalized Gamma distributions.