Stage-structured transmission of phocine distemper virus in the Dutch 2002 outbreak

Heterogeneities in transmission among hosts can be very important in shaping infectious disease dynamics. In mammals with strong social organization, such heterogeneities are often structured by functional stage: juveniles, subadults and adults. We investigate the importance of such stage-related heterogeneities in shaping the 2002 phocine distemper virus (PDV) outbreak in the Dutch Wadden Sea, when more than 40 per cent of the harbour seals were killed. We do this by comparing the statistical fit of a hierarchy of models with varying transmission complexity: homogeneous versus heterogeneous mixing and density- versus frequency-dependent transmission. We use the stranding data as a proxy for incidence and use Poisson likelihoods to estimate the ‘who acquires infection from whom’ (WAIFW) matrix. Statistically, the model with strong heterogeneous mixing and density-dependent transmission was found to best describe the transmission dynamics. However, patterns of incidence support a model of frequency-dependent transmission among adults and juveniles. Based on the maximum-likelihood WAIFW matrix estimates, we use the next-generation formalism to calculate an R₀ between 2 and 2.5 for the Dutch 2002 PDV epidemic.     

Estimates of the basic reproduction number for rubella using seroprevalence data and indicator-based approaches

The basic reproduction number (R₀) of an infection determines the impact of its control. For many endemic infections, R₀ is often estimated from appropriate country-specific seroprevalence data. Studies sometimes pool estimates from the same region for settings lacking seroprevalence data, but the reliability of this approach is unclear. Plausibly, indicator-based approaches could predict R₀ for such settings. We calculated R₀ for rubella for 98 settings and correlated its value against 66 demographic, economic, education, housing and health-related indicators. We also trained a random forest regression algorithm using these indicators as the input and R₀ as the output. We used the mean-square error to compare the performances of the random forest, simple linear regression and a regional averaging method in predicting R₀ using 4-fold cross validation. R₀ was <5, 5–10 and >10 for 81, 14 and 3 settings respectively, with no apparent regional differences and in the limited available data, it was usually lower for rural than urban areas. R₀ was most correlated with educational attainment, and household indicators for the Pearson and Spearman correlation coefficients respectively and with poverty-related indicators followed by the crude death rate considering the Maximum Information Coefficient, although the correlation for each was relatively weak (Pearson correlation coefficient: 0.4, 95%CI: (0.24,0.48) for educational attainment). A random forest did not perform better in predicting R₀ than simple linear regression, depending on the subsets of training indicators and studies, and neither out-performed a regional averaging approach. R₀ for rubella is typically low and using indicators to estimate its value is not straightforward. A regional averaging approach may provide as reliable an estimate of R₀ for settings lacking seroprevalence data as one based on indicators. The findings may be relevant for other infections and studies estimating the disease burden and the impact of interventions for settings lacking seroprevalence data.     

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.     

A review of data needed to parameterize a dynamic model of measles in developing countries

Background

Dynamic models of infection transmission can project future disease burden within a population. Few dynamic measles models have been developed for low-income countries, where measles disease burden is highest. Our objective was to review the literature on measles epidemiology in low-income countries, with a particular focus on data that are needed to parameterize dynamic models.

Methods

We included age-stratified case reporting and seroprevalence studies with fair to good sample sizes for mostly urban African and Indian populations. We emphasized studies conducted before widespread immunization. We summarized age-stratified attack rates and seroprevalence profiles across these populations. Using the study data, we fitted a "representative" seroprevalence profile for African and Indian settings. We also used a catalytic model to estimate the age-dependent force of infection for individual African and Indian studies where seroprevalence was surveyed. We used these data to quantify the effects of population density on the basic reproductive number R ₀.

Results

The peak attack rate usually occurred at age 1 year in Africa, and 1 to 2 years in India, which is earlier than in developed countries before mass vaccination. Approximately 60% of children were seropositive for measles antibody by age 2 in Africa and India, according to the representative seroprevalence profiles. A statistically significant decline in the force of infection with age was found in 4 of 6 Indian seroprevalence studies, but not in 2 African studies. This implies that the classic threshold result describing the critical proportion immune (p _c) required to eradicate an infectious disease, p _c = 1-1/R ₀, may overestimate the required proportion immune to eradicate measles in some developing country populations. A possible, though not statistically significant, positive relation between population density and R ₀ for various Indian and African populations was also found. These populations also showed a similar pattern of waning of maternal antibodies. Attack rates in rural Indian populations show little dependence on vaccine coverage or population density compared to urban Indian populations. Estimated R ₀ values varied widely across populations which has further implications for measles elimination.

Conclusions

It is possible to develop a broadly informative dynamic model of measles transmission in low-income country settings based on existing literature, though it may be difficult to develop a model that is closely tailored to any given country. Greater efforts to collect data specific to low-income countries would aid in control efforts by allowing highly population-specific models to be developed.     

Early real-time estimation of the basic reproduction number of emerging or reemerging infectious diseases in a community with heterogeneous contact pattern: Using data from Hong Kong 2009 H1N1 Pandemic Influenza as an illustrative example

Emerging and re-emerging infections such as SARS (2003) and pandemic H1N1 (2009) have caused concern for public health researchers and policy makers due to the increased burden of these diseases on health care systems. This concern has prompted the use of mathematical models to evaluate strategies to control disease spread, making these models invaluable tools to identify optimal intervention strategies. A particularly important quantity in infectious disease epidemiology is the basic reproduction number, R_0. Estimation of this quantity is crucial for effective control responses in the early phase of an epidemic. In our previous study, an approach for estimating the basic reproduction number in real time was developed. This approach uses case notification data and the structure of potential transmission contacts to accurately estimate R₀ from the limited amount of information available at the early stage of an outbreak. Based on this approach, we extend the existing methodology; the most recent method features intra- and inter-age groups contact heterogeneity. Given the number of newly reported cases at the early stage of the outbreak, with parsimony assumptions on removal distribution and infectivity profile of the diseases, experiments to estimate real time R₀ under different levels of intra- and inter-group contact heterogeneity using two age groups are presented. We show that the new method converges more quickly to the actual value of R₀ than the previous one, in particular when there is high-level intra-group and inter-group contact heterogeneity. With the age specific contact patterns, number of newly reported cases, removal distribution, and information about the natural history of the 2009 pandemic influenza in Hong Kong, we also use the extended model to estimate R₀ and age-specific R₀.     

Fitting the HIV Epidemic in Zambia: A Two-Sex Micro-Simulation Model

Background

In describing and understanding how the HIV epidemic spreads in African countries, previous studies have not taken into account the detailed periods at risk. This study is based on a micro-simulation model (individual-based) of the spread of the HIV epidemic in the population of Zambia, where women tend to marry early and where divorces are not frequent. The main target of the model was to fit the HIV seroprevalence profiles by age and sex observed at the Demographic and Health Survey conducted in 2001.

Methods and Findings

A two-sex micro-simulation model of HIV transmission was developed. Particular attention was paid to precise age-specific estimates of exposure to risk through the modelling of the formation and dissolution of relationships: marriage (stable union), casual partnership, and commercial sex. HIV transmission was exclusively heterosexual for adults or vertical (mother-to-child) for children. Three stages of HIV infection were taken into account. All parameters were derived from empirical population-based data. Results show that basic parameters could not explain the dynamics of the HIV epidemic in Zambia. In order to fit the age and sex patterns, several assumptions were made: differential susceptibility of young women to HIV infection, differential susceptibility or larger number of encounters for male clients of commercial sex workers, and higher transmission rate. The model allowed to quantify the role of each type of relationship in HIV transmission, the proportion of infections occurring at each stage of disease progression, and the net reproduction rate of the epidemic (R ₀ = 1.95).

Conclusions

The simulation model reproduced the dynamics of the HIV epidemic in Zambia, and fitted the age and sex pattern of HIV seroprevalence in 2001. The same model could be used to measure the effect of changing behaviour in the future.     

Contact-based transmission models in terrestrial gastropod populations infected with parasitic mites

Parasite transmission fundamentally affects the epidemiology of host-parasite systems, and is considered to be a key element in the epidemiological modelling of infectious diseases. Recent research has stressed the importance of detailed disease-specific variables involved in the transmission process. Riccardoella limacum is a hematophagous mite living in the mantle cavity of terrestrial gastropods. In this study, we experimentally examined whether the transmission success of R. limacum is affected by the contact frequency, parasite load and/or behaviour of the land snail Arianta arbustorum, a common host of R. limacum. In the experiment the transmission success was mainly affected by physical contacts among snails and slightly influenced by parasite intensity of the infected snail. Using these results we developed two different transmission models based on contact frequencies and transmission probability among host snails. As parameters for the models we used life-history data from three natural A. arbustorum populations with different population densities. Data on contact frequencies of video-recorded snail groups were used to fit the density response of the contact function, assuming either a linear relationship (model 1) or a second-degree polynomial relationship based on the ideal gas model of animal encounter (model 2). We calculated transmission coefficients (β), basic reproductive ratios (R₀) and host threshold population densities for parasite persistence in the three A. arbustorum populations. We found higher transmission coefficients (β) and larger R₀-values in model 1 than in model 2. Furthermore, the host population with the highest density showed larger R₀-values (16.47-22.59) compared to populations with intermediate (2.71-7.45) or low population density (0.75-4.10). Host threshold population density for parasite persistence ranged from 0.35 to 2.72 snails per m². Our results show that the integration of the disease-relevant biology of the organisms concerned may improve models of host-parasite dynamics.     

Sheep Movement Networks and the Transmission of Infectious Diseases

Background and Methodology

Various approaches have been used to investigate how properties of farm contact networks impact on the transmission of infectious diseases. The potential for transmission of an infection through a contact network can be evaluated in terms of the basic reproduction number, R ₀. The magnitude of R ₀ is related to the mean contact rate of a host, in this case a farm, and is further influenced by heterogeneities in contact rates of individual hosts. The latter can be evaluated as the second order moments of the contact matrix (variances in contact rates, and co-variance between contacts to and from individual hosts). Here we calculate these quantities for the farms in a country-wide livestock network: >15,000 Scottish sheep farms in each of 4 years from July 2003 to June 2007. The analysis is relevant to endemic and chronic infections with prolonged periods of infectivity of affected animals, and uses different weightings of contacts to address disease scenarios of low, intermediate and high animal-level prevalence.

Principal Findings and Conclusions

Analysis of networks of Scottish farms via sheep movements from July 2003 to June 2007 suggests that heterogeneities in movement patterns (variances and covariances of rates of movement on and off the farms) make a substantial contribution to the potential for the transmission of infectious diseases, quantified as R ₀, within the farm population. A small percentage of farms (<20%) contribute the bulk of the transmission potential (>80%) and these farms could be efficiently targeted by interventions aimed at reducing spread of diseases via animal movement.     

The basic reproduction number and the probability of extinction for a dynamic epidemic model

We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals move between populations according to a Markov transition matrix Σ and infectives can only make infectious contacts with members of their current population. Expressions for the basic reproduction number, R₀, and the probability of extinction of the epidemic are derived. It is shown that in contrast to contact distribution models, the distribution of the infectious period effects both the basic reproduction number and the probability of extinction of the epidemic in the limit as the total population size N → ∞. The interactions between the infectious period distribution and the transition matrix Σ mean that it is not possible to draw general conclusions about the effects on R₀ and the probability of extinction. However, it is shown that for n = 2, the basic reproduction number, R₀, is maximised by a constant length infectious period and is decreasing in ?, the speed of movement between the two populations.     

Infections with varying contact rates: application to varicella

We develop methods for the analysis of infectious disease data when age-specific contact rates vary over time. Our methods are valid when contact rates vary slowly on the time scale of the infection process, and are applicable to a variety of data types including serial seroprevalence surveys and case reports. The methods exploit approximate endemic equilibria, and require numerical solution of an associated integral equation in age and time. We also estimate summary statistics such as time-dependent analogs of the basic reproduction number and critical immunization threshold. We illustrate the methods with data on varicella (chickenpox) in the United Kingdom.     

Updating age-specific contact structures to match evolving demography in a dynamic mathematical model of tuberculosis vaccination

We investigated the effects of updating age-specific social contact matrices to match evolving demography on vaccine impact estimates. We used a dynamic transmission model of tuberculosis in India as a case study. We modelled four incremental methods to update contact matrices over time, where each method incorporated its predecessor: fixed contact matrix (M0), preserved contact reciprocity (M1), preserved contact assortativity (M2), and preserved average contacts per individual (M3). We updated the contact matrices of a deterministic compartmental model of tuberculosis transmission, calibrated to epidemiologic data between 2000 and 2019 derived from India. We additionally calibrated the M0, M2, and M3 models to the 2050 TB incidence rate projected by the calibrated M1 model. We stratified age into three groups, children (<15y), adults (≥15y, <65y), and the elderly (≥65y), using World Population Prospects demographic data, between which we applied POLYMOD-derived social contact matrices. We simulated an M72-AS01_E-like tuberculosis vaccine delivered from 2027 and estimated the per cent TB incidence rate reduction (IRR) in 2050 under each update method. We found that vaccine impact estimates in all age groups remained relatively stable between the M0–M3 models, irrespective of vaccine-targeting by age group. The maximum difference in impact, observed following adult-targeted vaccination, was 7% in the elderly, in whom we observed IRRs of 19% (uncertainty range 13–32), 20% (UR 13–31), 22% (UR 14–37), and 26% (UR 18–38) following M0, M1, M2 and M3 updates, respectively. We found that model-based TB vaccine impact estimates were relatively insensitive to demography-matched contact matrix updates in an India-like demographic and epidemiologic scenario. Current model-based TB vaccine impact estimates may be reasonably robust to the lack of contact matrix updates, but further research is needed to confirm and generalise this finding.     

A method to relate StarTrack® measurements to R50 variations in clinical linacs

The relation between the data recorded with any device for the daily checking of the behavior of a clinical linac and the reference magnitudes to be monitored may be unknown. An experimental method relating the energy stability of the electron beam measured with StarTrack^® to the R₅₀ beam quality index is proposed. The bending magnet current is varied producing a change in the exit energy window and, therefore, a modification of the R₅₀ value. For different values of this current, the output data of StarTrack^® and the R₅₀, obtained from depth doses measured in a water phantom are determined. A linear fit between both sets of data allows the identification of the StarTrack^® output that provides the best way to obtain the quality index R₅₀, for each beam nominal energy. Using these fits, an historical datum series is used to analyze the method proposed in the daily quality control.The ouput data of the StarTrack^® and the R₅₀ values show a good linear correlation. It is possible to establish a methodology that allows the monitoring of R₅₀ by direct use of the daily quality control data measured with StarTrack^®.A method to monitor R₅₀ in the daily quality control using the StarTrack^® device has been developed. The method may be applied to similar devices in which the statistical control variable does not show a linear behavior with R₅₀.     

A [P]NAD-based method to identify and quantitate long residence time enoyl-acyl carrier protein reductase inhibitors

The classical methods for quantifying drug–target residence time (t_R) use loss or regain of enzyme activity in progress curve kinetic assays. However, such methods become imprecise at very long residence times, mitigating the use of alternative strategies. Using the NAD(P)H-dependent FabI enoyl-acyl carrier protein (enoyl-ACP) reductase as a model system, we developed a Penefsky column-based method for direct measurement of t_R, where the off-rate of the drug was determined with radiolabeled [adenylate-³²P]NAD(P⁺) cofactor. In total, 23 FabI inhibitors were analyzed, and a mathematical model was used to estimate limits to the t_R values of each inhibitor based on percentage drug–target complex recovery following gel filtration. In general, this method showed good agreement with the classical steady-state kinetic methods for compounds with t_R values of 10 to 100 min. In addition, we were able to identify seven long t_R inhibitors (100–1500 min) and to accurately determine their t_R values. The method was then used to measure t_R as a function of temperature, an analysis not previously possible using the standard kinetic approach due to decreased NAD(P)H stability at elevated temperatures. In general, a 4-fold difference in t_R was observed when the temperature was increased from 25 to 37 °C.     

H3N2v and Other Influenza Epidemic Risk Based on Age-Specific Estimates of Sero-Protection and Contact Network Interactions

Cases of a novel swine-origin influenza A(H3N2) variant (H3N2v) have recently been identified in the US, primarily among children. We estimated potential epidemic attack rates (ARs) based on age-specific estimates of sero-susceptibility and social interactions. A contact network model previously established for the Greater Vancouver Area (GVA), Canada was used to estimate average epidemic (infection) ARs for the emerging H3N2v and comparator viruses (H1N1pdm09 and an extinguished H3N2 seasonal strain) based on typical influenza characteristics, basic reproduction number (R₀), and effective contacts taking into account age-specific sero-protection rates (SPRs). SPRs were assessed in sera collected from the GVA in 2009 or earlier (pre-H1N1pdm09) and fall 2010 (post-H1N1pdm09, seasonal A/Brisbane/10/2007(H3N2), and H3N2v) by hemagglutination inhibition (HI) assay. SPR was assigned per convention based on proportion with HI antibody titre ≥40 (SPR40). Recognizing that the HI titre ≥40 was established as the 50%sero-protective threshold we also explored for ½SPR40, SPR80 and a blended gradient defined as: ¼SPR20, ½SPR40, ¾SPR80, SPR160. Base case analysis assumed R₀ = 1.40, but we also explored R₀ as high as 1.80. With R₀ = 1.40 and SPR40, simulated ARs were well aligned with field observations for H1N1pdm09 incidence (AR: 32%), sporadic detections without a third epidemic wave post-H1N1pdm09 (negligible AR<0.1%) as well as A/Brisbane/10/2007(H3N2) seasonal strain extinction and antigenic drift replacement (negligible AR<0.1%). Simulated AR for the novel swine-origin H3N2v was 6%, highest in children 6–11years (16%). However, with modification to SPR thresholds per above, H3N2v AR ≥20% became possible. At SPR40, H3N2v AR ≥10%, ≥15% or ≥30%, occur if R₀≥1.48, ≥1.56 or ≥1.86, respectively. Based on conventional assumptions, the novel swine-origin H3N2v does not currently pose a substantial pandemic threat. If H3N2v epidemics do occur, overall community ARs are unlikely to exceed typical seasonal influenza experience. However risk assessment may change with time and depends crucially upon the validation of epidemiological features of influenza, notably the serologic correlate of protection and R₀.     

Spatial Distribution of Potential in a Flat Cell: Application to the Catfish Horizontal Cell Layers

An analytical solution is obtained for the three-dimensional spatial distribution of potential inside a flat cell, such as the layer of horizontal cells, as a function of its geometry and resistivity characteristics. It was found that, within a very large range of parameter values, the potential is given by [Formula: see text] where r = ρ/ρ₀, = z/ρ₀, ρ = (R_i/R_m)·ρ₀, δ = h/ρ₀; K is a constant; J is the assumed synaptic current; ρ, z are cylindrical coordinates; ρ₀ is the radius of the synaptic area of excitation; h is the cell thickness; and R_i, R_m are the intracellular and membrane resistivities, respectively. Formula A closely fits data for the spatial decay of potential which were obtained from the catfish internal and external horizontal cells. It predicts a decay which is exponential down to about 40% of the maximum potential but is much slower than exponential below that level, a characteristic also exhibited by the data. Such a feature in the decay mode allows signal integration over the large retinal areas which have been observed experimentally both at the horizontal and ganglion cell stages. The behavior of the potential distribution as a function of the flat cell parameters is investigated, and it is found that for the range of the horizontal cell thicknesses (10-50 μ) the decay rate depends solely on the ratio R_m/R_i. Data obtained from both types of horizontal cells by varying the diameter of the stimulating spot and for three widely different intensity levels were closely fitted by equation A. In the case of the external horizontal cell, the fit for different intensities was obtained by varying the ratio R_m/R_i; in the case of the internal horizontal cell it was found necessary, in order to fit the data for different intensities, to vary the assumed synaptic current J.     

Vector borne diseases on an urban environment: The effects of heterogeneity and human circulation

We study the effect of human circulation and host/vector heterogeneities on the onset of epidemics of arboviruses. From a meta-population dynamics based on the classical Bailey–Dietz model, we derive a multi-group model under three assumptions: (i) fast host sojourn time-scale; (ii) mosquitoes do not move; (iii) time homogeneity and strong connectivity of human circulation. Within this modelling framework, three different kinds of R₀ appear: (i) the “true” or “global” R₀—derived from the corresponding next generation matrix; (ii) the uniform R₀—obtained if the patches are taken homogeneous; (iii) the local R₀s—obtained if the patches are disconnected. We show that there is relevant epidemiological information associated to all of them. In particular, they can be used to understand the effects of changing the circulation on the value of the global R₀. We also present additional results on the effects on R₀ of different vector control policies, and a simulation with data from the city of Rio de Janeiro, Brazil.     

The impact of network clustering and assortativity on epidemic behaviour

Epidemic models have successfully included many aspects of the complex contact structure apparent in real-world populations. However, it is difficult to accommodate variations in the number of contacts, clustering coefficient and assortativity. Investigations of the relationship between these properties and epidemic behaviour have led to inconsistent conclusions and have not accounted for their interrelationship. In this study, simulation is used to estimate the impact of social network structure on the probability of an SIR (susceptible-infective-removed) epidemic occurring and, if it does, the final size. Increases in assortativity and clustering coefficient are associated with smaller epidemics and the impact is cumulative. Derived values of the basic reproduction ratio (R₀) over networks with the highest property values are more than 20% lower than those derived from simulations with zero values of these network properties.     

Estimating Dengue Transmission Intensity from Sero-Prevalence Surveys in Multiple Countries

Background

Estimates of dengue transmission intensity remain ambiguous. Since the majority of infections are asymptomatic, surveillance systems substantially underestimate true rates of infection. With advances in the development of novel control measures, obtaining robust estimates of average dengue transmission intensity is key for assessing both the burden of disease from dengue and the likely impact of interventions.

Methodology/Principal Findings

The force of infection (λ) and corresponding basic reproduction numbers (R₀) for dengue were estimated from non-serotype (IgG) and serotype-specific (PRNT) age-stratified seroprevalence surveys identified from the literature. The majority of R₀ estimates ranged from 1–4. Assuming that two heterologous infections result in complete immunity produced up to two-fold higher estimates of R₀ than when tertiary and quaternary infections were included. λ estimated from IgG data were comparable to the sum of serotype-specific forces of infection derived from PRNT data, particularly when inter-serotype interactions were allowed for.

Conclusions/Significance

Our analysis highlights the highly heterogeneous nature of dengue transmission. How underlying assumptions about serotype interactions and immunity affect the relationship between the force of infection and R₀ will have implications for control planning. While PRNT data provides the maximum information, our study shows that even the much cheaper ELISA-based assays would provide comparable baseline estimates of overall transmission intensity which will be an important consideration in resource-constrained settings.