Resource-driven encounters among consumers and implications for the spread of infectious disease.

Animals share a variety of common resources, which can be a major driver of conspecific encounter rates. In this work, we implement a spatially explicit mathematical model for resource visitation behaviour in order to examine how changes in resource availability can influence the rate of encounters among consumers. Using simulations and asymptotic analysis, we demonstrate that, under a reasonable set of assumptions, the relationship between resource availability and consumer conspecific encounters is not monotonic. We characterize how the maximum encounter rate and associated critical resource density depend on system parameters like consumer density and the maximum distance from which consumers can detect and respond to resources. The assumptions underlying our theoretical model and analysis are motivated by observations of large aggregations of black-backed jackals at carcasses generated by seasonal outbreaks of anthrax among herbivores in Etosha National Park, Namibia. As non-obligate scavengers, black-backed jackals use carcasses as a supplemental food resource when they are available. While jackals do not appear to acquire disease from ingesting anthrax carcasses, changes in their movement patterns in response to changes in carcass abundance do alter jackals' conspecific encounter rate in ways that may affect the transmission dynamics of other diseases, such as rabies. Our theoretical results provide a method to quantify and analyse the hypothesis that the outbreak of a fatal disease among herbivores can potentially facilitate outbreaks of an entirely different disease among jackals. By analysing carcass visitation data, we find support for our model's prediction that the number of conspecific encounters at resource sites decreases with additional increases in resource availability. Whether or not this site-dependent effect translates to an overall decrease in encounters depends, unexpectedly, on the relationship between the maximum distance of detection and the resource density.

Reassessment of HIV-1 acute phase infectivity: accounting for heterogeneity and study design with simulated cohorts.

BACKGROUND: The infectivity of the HIV-1 acute phase has been directly measured only once, from a retrospectively identified cohort of serodiscordant heterosexual couples in Rakai, Uganda. Analyses of this cohort underlie the widespread view that the acute phase is highly infectious, even more so than would be predicted from its elevated viral load, and that transmission occurring shortly after infection may therefore compromise interventions that rely on diagnosis and treatment, such as antiretroviral treatment as prevention (TasP). Here, we re-estimate the duration and relative infectivity of the acute phase, while accounting for several possible sources of bias in published estimates, including the retrospective cohort exclusion criteria and unmeasured heterogeneity in risk. METHODS AND FINDINGS: We estimated acute phase infectivity using two approaches. First, we combined viral load trajectories and viral load-infectivity relationships to estimate infectivity trajectories over the course of infection, under the assumption that elevated acute phase infectivity is caused by elevated viral load alone. Second, we estimated the relative hazard of transmission during the acute phase versus the chronic phase (RHacute) and the acute phase duration (dacute) by fitting a couples transmission model to the Rakai retrospective cohort using approximate Bayesian computation. Our model fit the data well and accounted for characteristics overlooked by previous analyses, including individual heterogeneity in infectiousness and susceptibility and the retrospective cohort's exclusion of couples that were recorded as serodiscordant only once before being censored by loss to follow-up, couple dissolution, or study termination. Finally, we replicated two highly cited analyses of the Rakai data on simulated data to identify biases underlying the discrepancies between previous estimates and our own. From the Rakai data, we estimated RHacute = 5.3 (95% credibility interval [95% CrI]: 0.79-57) and dacute = 1.7 mo (95% CrI: 0.55-6.8). The wide credibility intervals reflect an inability to distinguish a long, mildly infectious acute phase from a short, highly infectious acute phase, given the 10-mo Rakai observation intervals. The total additional risk, measured as excess hazard-months attributable to the acute phase (EHMacute) can be estimated more precisely: EHMacute = (RHacute - 1) × dacute, and should be interpreted with respect to the 120 hazard-months generated by a constant untreated chronic phase infectivity over 10 y of infection. From the Rakai data, we estimated that EHMacute = 8.4 (95% CrI: -0.27 to 64). This estimate is considerably lower than previously published estimates, and consistent with our independent estimate from viral load trajectories, 5.6 (95% confidence interval: 3.3-9.1). We found that previous overestimates likely stemmed from failure to account for risk heterogeneity and bias resulting from the retrospective cohort study design. Our results reflect the interaction between the retrospective cohort exclusion criteria and high (47%) rates of censorship amongst incident serodiscordant couples in the Rakai study due to loss to follow-up, couple dissolution, or study termination. We estimated excess physiological infectivity during the acute phase from couples data, but not the proportion of transmission attributable to the acute phase, which would require data on the broader population's sexual network structure. CONCLUSIONS: Previous EHMacute estimates relying on the Rakai retrospective cohort data range from 31 to 141. Our results indicate that these are substantial overestimates of HIV-1 acute phase infectivity, biased by unmodeled heterogeneity in transmission rates between couples and by inconsistent censoring. Elevated acute phase infectivity is therefore less likely to undermine TasP interventions than previously thought. Heterogeneity in infectiousness and susceptibility may still play an important role in intervention success and deserves attention in future analyses.

Failure of Sterne- and Pasteur-like strains of Bacillus anthracis to replicate and survive in the urban bluebottle blow fly Calliphora vicina under laboratory conditions.

This study aimed to elucidate the bacteriological events occurring within the gut of Calliphora vicina, selected as the European representative of blow flies held responsible for the spread of anthrax during epidemics in certain parts of the world. Green-fluorescent-protein-carrying derivatives of Bacillus anthracis were used. These lacked either one of the virulence plasmids pXO1 and pXO2 and were infected, or not infected, with a worm intestine phage (Wip4) known to influence the phenotype and survival of the pathogen. Blood meals were prepared for the flies by inoculation of sheep blood with germinated and, in case of pXO2+ strains, encapsulated cells of the four B. anthracis strains. After being fed for 4 h an initial 10 flies were externally disinfected with peracetic acid to ensure subsequent quantitation representing ingested B. anthracis only. Following neutralization, they were crushed in sterile saline. Over each of the ensuing 7 to 10 days, 10 flies were removed and processed the same way. In the absence of Wip4, strains showed steady declines to undetectable in the total B. anthracis counts, within 7-9 days. With the phage infected strains, the falls in viable counts were significantly more rapid than in their uninfected counterparts. Spores were detectable in flies for longer periods than vegetative bacteria. In line with the findings in both biting and non-biting flies of early workers our results indicate that B. anthracis does not multiply in the guts of blow flies and survival is limited to a matter of days.

HIV sexual transmission is predominantly driven by single individuals rather than discordant couples: a model-based approach.

Understanding the relative contribution to HIV transmission from different social groups is important for public-health policy. Information about the importance of stable serodiscordant couples (when one partner is infected but not the other) relative to contacts outside of stable partnerships in spreading disease can aid in designing and targeting interventions. However, the overall importance of within-couple transmission, and the determinants and correlates of this importance, are not well understood. Here, we explore how mechanistic factors - like partnership dynamics and rates of extra-couple transmission - affect various routes of transmission, using a compartmental model with parameters based on estimates from Sub-Saharan Africa. Under our assumptions, when sampling model parameters within a realistic range, we find that infection of uncoupled individuals is usually the predominant route (median 0.62, 2.5%-97.5% quantiles: 0.26-0.88), while transmission within discordant couples is usually important, but rarely represents the majority of transmissions (median 0.33, 2.5%-97.5% quantiles: 0.10-0.67). We find a strong correlation between long-term HIV prevalence and the contact rate of uncoupled individuals, implying that this rate may be a key driver of HIV prevalence. For a given level of prevalence, we find a negative correlation between the proportion of discordant couples and the within-couple transmission rate, indicating that low discordance in a population may reflect a relatively high rate of within-couple transmission. Transmission within or outside couples and among uncoupled individuals are all likely to be important in sustaining heterosexual HIV transmission in Sub-Saharan Africa. Hence, intervention policies should be broadly targeted when practical.

A Hierarchical Distance Sampling Approach to Estimating Mortality Rates from Opportunistic Carcass Surveillance Data.

Distance sampling is widely used to estimate the abundance or density of wildlife populations. Methods to estimate wildlife mortality rates have developed largely independently from distance sampling, despite the conceptual similarities between estimation of cumulative mortality and the population density of living animals. Conventional distance sampling analyses rely on the assumption that animals are distributed uniformly with respect to transects and thus require randomized placement of transects during survey design. Because mortality events are rare, however, it is often not possible to obtain precise estimates in this way without infeasible levels of effort. A great deal of wildlife data, including mortality data, is available via road-based surveys. Interpreting these data in a distance sampling framework requires accounting for the non-uniformity sampling. Additionally, analyses of opportunistic mortality data must account for the decline in carcass detectability through time. We develop several extensions to distance sampling theory to address these problems.We build mortality estimators in a hierarchical framework that integrates animal movement data, surveillance effort data, and motion-sensor camera trap data, respectively, to relax the uniformity assumption, account for spatiotemporal variation in surveillance effort, and explicitly model carcass detection and disappearance as competing ongoing processes.Analysis of simulated data showed that our estimators were unbiased and that their confidence intervals had good coverage.We also illustrate our approach on opportunistic carcass surveillance data acquired in 2010 during an anthrax outbreak in the plains zebra of Etosha National Park, Namibia.The methods developed here will allow researchers and managers to infer mortality rates from opportunistic surveillance data.

Effects of experimental exclusion of scavengers from carcasses of anthrax-infected herbivores on Bacillus anthracis sporulation, survival, and distribution.

Scavenging of anthrax carcasses has long been hypothesized to play a critical role in the production of the infectious spore stage of Bacillus anthracis after host death, though empirical studies assessing this are lacking. We compared B. anthracis spore production, distribution, and survival at naturally occurring anthrax herbivore carcasses that were either experimentally caged to exclude vertebrate scavengers or left unmanipulated. We found no significant effect of scavengers on soil spore density (P > 0.05). Soil stained with terminally hemorrhaged blood and with nonhemorrhagic fluids exhibited high levels of B. anthracis spore contamination (ranging from 10(3) to 10(8) spores/g), even in the absence of vertebrate scavengers. At most of the carcass sites, we also found that spore density in samples taken from hemorrhagic-fluid-stained soil continued to increase for >4 days after host death. We conclude that scavenging by vertebrates is not a critical factor in the life cycle of B. anthracis and that anthrax control measures relying on deterrence or exclusion of vertebrate scavengers to prevent sporulation are unlikely to be effective.

Extra-couple HIV transmission in sub-Saharan Africa: a mathematical modelling study of survey data.

BACKGROUND: The proportion of heterosexual HIV transmission in sub-Saharan Africa that occurs within cohabiting partnerships, compared with that in single people or extra-couple relationships, is widely debated. We estimated the proportional contribution of different routes of transmission to new HIV infections. As plans to use antiretroviral drugs as a strategy for population-level prevention progress, understanding the importance of different transmission routes is crucial to target intervention efforts. METHODS: We built a mechanistic model of HIV transmission with data from Demographic and Health Surveys (DHS) for 2003-2011, of 27,201 cohabiting couples (men aged 15-59 years and women aged 15-49 years) from 18 sub-Saharan African countries with information about relationship duration, age at sexual debut, and HIV serostatus. We combined this model with estimates of HIV survival times and country-specific estimates of HIV prevalence and coverage of antiretroviral therapy (ART). We then estimated the proportion of recorded infections in surveyed cohabiting couples that occurred before couple formation, between couple members, and because of extra-couple intercourse. FINDINGS: In surveyed couples, we estimated that extra-couple transmission accounted for 27-61% of all HIV infections in men and 21-51% of all those in women, with ranges showing intercountry variation. We estimated that in 2011, extra-couple transmission accounted for 32-65% of new incident HIV infections in men in cohabiting couples, and 10-47% of new infections in women in such couples. Our findings suggest that transmission within couples occurs largely from men to women; however, the latter sex have a very high-risk period before couple formation. INTERPRETATION: Because of the large contribution of extra-couple transmission to new HIV infections, interventions for HIV prevention should target the general sexually active population and not only serodiscordant couples. FUNDING: US National Institutes of Health, US National Science Foundation, and J S McDonnell Foundation.

How to make epidemiological training infectious.

Modern infectious disease epidemiology builds on two independently developed fields: classical epidemiology and dynamical epidemiology. Over the past decade, integration of the two fields has increased in research practice, but training options within the fields remain distinct with few opportunities for integration in the classroom. The annual Clinic on the Meaningful Modeling of Epidemiological Data (MMED) at the African Institute for Mathematical Sciences has begun to address this gap. MMED offers participants exposure to a broad range of concepts and techniques from both epidemiological traditions. During MMED 2010 we developed a pedagogical approach that bridges the traditional distinction between classical and dynamical epidemiology and can be used at multiple educational levels, from high school to graduate level courses. The approach is hands-on, consisting of a real-time simulation of a stochastic outbreak in course participants, including realistic data reporting, followed by a variety of mathematical and statistical analyses, stemming from both epidemiological traditions. During the exercise, dynamical epidemiologists developed empirical skills such as study design and learned concepts of bias while classical epidemiologists were trained in systems thinking and began to understand epidemics as dynamic nonlinear processes. We believe this type of integrated educational tool will prove extremely valuable in the training of future infectious disease epidemiologists. We also believe that such interdisciplinary training will be critical for local capacity building in analytical epidemiology as Africa continues to produce new cohorts of well-trained mathematicians, statisticians, and scientists. And because the lessons draw on skills and concepts from many fields in biology--from pathogen biology, evolutionary dynamics of host--pathogen interactions, and the ecology of infectious disease to bioinformatics, computational biology, and statistics--this exercise can be incorporated into a broad array of life sciences courses.

Black-backed jackal exposure to rabies virus, canine distemper virus, and Bacillus anthracis in Etosha National Park, Namibia.

Canine distemper virus (CDV) and rabies virus (RABV) occur worldwide in wild carnivore and domestic dog populations and pose threats to wildlife conservation and public health. In Etosha National Park (ENP), Namibia, anthrax is endemic and generates carcasses frequently fed on by an unusually dense population of black-backed jackals (Canis mesomelas). Using serology, phylogenetic analyses (on samples obtained from February 2009-July 2010), and historical mortality records (1975-2011), we assessed jackal exposure to Bacillus anthracis (BA; the causal bacterial agent of anthrax), CDV, and RABV. Prevalence of antibodies against BA (95%, n = 86) and CDV (71%, n = 80) was relatively high, while that of antibodies against RABV was low (9%, n = 81). Exposure to BA increased significantly with age, and all animals >6 mo old were antibody-positive. As with BA, prevalence of antibodies against CDV increased significantly with age, with similar age-specific trends during both years of the study. No significant effect of age was found on the prevalence of antibodies against RABV. Three of the seven animals with antibodies against RABV were monitored for more than 1 yr after sampling and showed no signs of active infection. Mortality records revealed that rabid animals are destroyed nearly every year inside the ENP tourist camps. Phylogenetic analyses demonstrated that jackal RABV in ENP is part of the same transmission cycle as other dog-jackal RABV cycles in Namibia.

Distribution and molecular evolution of bacillus anthracis genotypes in Namibia.

The recent development of genetic markers for Bacillus anthracis has made it possible to monitor the spread and distribution of this pathogen during and between anthrax outbreaks. In Namibia, anthrax outbreaks occur annually in the Etosha National Park (ENP) and on private game and livestock farms. We genotyped 384 B. anthracis isolates collected between 1983-2010 to identify the possible epidemiological correlations of anthrax outbreaks within and outside the ENP and to analyze genetic relationships between isolates from domestic and wild animals. The isolates came from 20 animal species and from the environment and were genotyped using a 31-marker multi-locus-VNTR-analysis (MLVA) and, in part, by twelve single nucleotide polymorphism (SNP) markers and four single nucleotide repeat (SNR) markers. A total of 37 genotypes (GT) were identified by MLVA, belonging to four SNP-groups. All GTs belonged to the A-branch in the cluster- and SNP-analyses. Thirteen GTs were found only outside the ENP, 18 only within the ENP and 6 both inside and outside. Genetic distances between isolates increased with increasing time between isolations. However, genetic distance between isolates at the beginning and end of the study period was relatively small, indicating that while the majority of GTs were only found sporadically, three genetically close GTs, accounting for more than four fifths of all the ENP isolates, appeared dominant throughout the study period. Genetic distances among isolates were significantly greater for isolates from different host species, but this effect was small, suggesting that while species-specific ecological factors may affect exposure processes, transmission cycles in different host species are still highly interrelated. The MLVA data were further used to establish a model of the probable evolution of GTs within the endemic region of the ENP. SNR-analysis was helpful in correlating an isolate with its source but did not elucidate epidemiological relationships.

The importance of age dependent mortality and the extrinsic incubation period in models of mosquito-borne disease transmission and control.

Nearly all mathematical models of vector-borne diseases have assumed that vectors die at constant rates. However, recent empirical research suggests that mosquito mortality rates are frequently age dependent. This work develops a simple mathematical model to assess how relaxing the classical assumption of constant mortality affects the predicted effectiveness of anti-vectorial interventions. The effectiveness of mosquito control when mosquitoes die at age dependent rates was also compared across different extrinsic incubation periods. Compared to a more realistic age dependent model, constant mortality models overestimated the sensitivity of disease transmission to interventions that reduce mosquito survival. Interventions that reduce mosquito survival were also found to be slightly less effective when implemented in systems with shorter EIPs. Future transmission models that examine anti-vectorial interventions should incorporate realistic age dependent mortality rates.