Frequency-dependent incidence in models of sexually transmitted diseases: portrayal of pair-based transmission and effects of illness on contact behaviour

Hospital population density and risk of respiratory infection: Is close contact density dependent?

Respiratory infections acquired in hospital depend on close contact, which may be affected by hospital population density. Models of infectious disease transmission typically assume that contact rates are independent of density (frequency dependence) or proportional to it (linear density dependence), without justification. We evaluate these assumptions by measuring contact rates in hospitals under different population densities. We analysed data from a study in 15 wards in which staff, patients and visitors carried wearable sensors which detected close contacts. We proposed a general model, non-linear density dependence, and fit this to data on several types of interactions. Finally, we projected the fitted models to predict the effect of increasing population density on epidemic risk. We identified considerable heterogeneity in density dependence between wards, even those with the same medical specialty. Interactions between all persons present usually depended little on the population density. However, increasing patient density was associated with higher rates of patient contact for staff and for other patients. Simulations suggested that a 10 % increase in patient population density would carry a markedly increased risk in many wards. This study highlights the variance in density dependent dynamics and the complexity of predicting contact rates.

Parasite-induced shifts in host movement may explain the transient coexistence of high- and low-pathogenic disease strains

Many parasites induce decreased host movement, known as lethargy, which can impact disease spread and the evolution of virulence. Mathematical models have investigated virulence evolution when parasites cause host death, but disease-induced decreased host movement has received relatively less attention. Here, we consider a model where, due to the within-host parasite replication rate, an infected host can become lethargic and shift from a moving to a resting state, where it can die. We find that when the lethargy and disease-induced mortality costs to the parasites are not high, then evolutionary bistability can arise, and either moderate or high virulence can evolve depending on the initial virulence and the magnitude of mutation. These results suggest, firstly, the coexistence of strains with different virulence, which may explain the transient coexistence of low- and high-pathogenic strains of avian influenza viruses, and secondly, that medical interventions to treat the symptoms of lethargy or prevent disease-induced host deaths can result in a large jump in virulence and the rapid evolution of high virulence. In complement to existing results that show bistability when hosts are heterogeneous at the population level, we show that evolutionary bistability may arise due to transmission heterogeneity at the individual host level.

Partnership dynamics in mathematical models and implications for representation of sexually transmitted infections: a review

Mathematical models of sexually transmitted disease (STI) are increasingly relied on to inform policy, practice, and resource allocation. Because STI transmission requires sexual contact between two or more people, a model's ability to represent the dynamics of sexual partnerships can influence the validity of findings. This ability is to a large extent constrained by the model type, as different modeling frameworks vary in their capability to capture patterns of sexual contact at individual, partnership, and network levels. In this paper, we classify models into three groups: compartmental, individual-based, and statistical network models. For each framework, we describe the basic model structure and discuss key aspects of sexual partnership dynamics: how and with whom partnerships are formed, partnership duration and dissolution, and temporal overlap in partnerships (concurrency). We illustrate the potential implications of accurately accounting for partnership dynamics, but these effects depend on characteristics of both the population and pathogen; the combined impact of these partnership and epidemiologic dynamics can be difficult to predict. While each of the reviewed model frameworks may be appropriate to inform certain research or policy questions, modelers and consumers of models should carefully consider the implications of sexual partnership dynamics for the questions under study.

Uniformly accurate nonlinear transmission rate models arising from disease spread through pair contacts

We derive and asymptotically analyze mass-action models for disease spread that include transient pair formation and dissociation. Populations of unpaired susceptible individuals and infected individuals are distinguished from the population of three types of pairs of individuals: both susceptible, one susceptible and one infected, and both infected. Disease transmission can occur only within a pair consisting of one susceptible individual and one infected individual. We use perturbation expansion to formally derive uniformly valid approximations for the dynamics of the total infected and susceptible populations under different conditions including combinations of fast association, fast transmission, and fast dissociation limits. The effective equations are derived from the fundamental mass-action system without implicitly imposing transmission mechanisms, such as those used in frequency-dependent models. Our results represent submodels that show how effective nonlinear transmission can arise from pairing dynamics and are juxtaposed with density-based mass-action and frequency-based models.

A systemic approach to assess the potential and risks of wildlife culling for infectious disease control

The maintenance of infectious diseases requires a sufficient number of susceptible hosts. Host culling is a potential control strategy for animal diseases. However, the reduction in biodiversity and increasing public concerns regarding the involved ethical issues have progressively challenged the use of wildlife culling. Here, we assess the potential of wildlife culling as an epidemiologically sound management tool, by examining the host ecology, pathogen characteristics, eco-sociological contexts, and field work constraints. We also discuss alternative solutions and make recommendations for the appropriate implementation of culling for disease control.

Large benefits to youth-focused HIV treatment-as-prevention efforts in generalized heterosexual populations: An agent-based simulation model

Predominantly heterosexual HIV-1 epidemics like those in sub-Saharan Africa continue to have high HIV incidence in young people. We used a stochastic, agent-based model for age-disparate networks to test the hypothesis that focusing uptake and retention of ART among youth could enhance the efficiency of treatment as prevention (TasP) campaigns. We used the model to identify strategies that reduce incidence to negligible levels (i.e., < 0.1 cases/100 person-years) 20-25 years after initiation of a targeted TasP campaign. The model was parameterized using behavioral, demographic, and clinical data from published papers and national reports. To keep a focus on the underlying age effects we model a generalized heterosexual population with average risks (i.e., no MSM, no PWIDs, no sex workers) and no entry of HIV+ people from other regions. The model assumes that most people (default 95%, range in variant simulations 60-95%) are "linkable"; i.e., could get linked to effective care given sufficient resources. To simplify the accounting, we assume a rapid jump in the number of people receiving treatment at the start of the TasP campaign, followed by a 2% annual increase that continues until all linkable HIV+ people have been treated. Under historical scenarios of CD4-based targeted ART allocation and current policies of untargeted (random) ART allocation, our model predicts that viral replication would need to be suppressed in 60-85% of infected people at the start of the TasP campaign to drive incidence to negligible levels. Under age-based strategies, by contrast, this percentage dropped by 18-54%, depending on the strength of the epidemic and the age target. For our baseline model, targeting those under age 30 halved the number of people who need to be treated. Age-based targeting also minimized total and time-discounted AIDS deaths over 25 years. Age-based targeting yielded benefits without being highly exclusive; in a model in which 60% of infected people were treated, ~87% and ~58% of those initiating therapy during a campaign targeting those <25 and <30 years, respectively, fell outside the target group. Sensitivity analyses revealed that youth-focused TasP is beneficial due to age-related risk factors (e.g. shorter relationship durations), and an age-specific herd immunity (ASHI) effect that protects uninfected adolescents entering the sexually active population. As testing rates increase in response to UNAIDS 90-90-90 goals, efforts to link all young people to care and treatment could contribute enormously to ending the HIV epidemic.

Why is sterility virulence most common in sexually transmitted infections? Examining the role of epidemiology

Sterility virulence, or the reduction in host fecundity due to infection, occurs in many host-pathogen systems. Notably, sterility virulence is more common for sexually transmitted infections (STIs) than for directly transmitted pathogens, while other forms of virulence tend to be limited in STIs. This has led to the suggestion that sterility virulence may have an adaptive explanation. By focusing upon finite population models, we show that the observed patterns of sterility virulence can be explained by consideration of the epidemiological differences between STIs and directly transmitted pathogens. In particular, when pathogen transmission is predominantly density invariant (as for STIs), and mortality is density dependent, sterility virulence can be favored by demographic stochasticity, whereas if pathogen transmission is predominantly density dependent, as is common for most directly transmitted pathogens, sterility virulence is disfavored. We show these conclusions can hold even if there is a weak selective advantage to sterilizing.

Infectious Disease in Wild Animal Populations: Examining Transmission and Control with Mathematical Models

The mathematical modeling of ecological interactions is an essential tool in predicting the behavior of complex systems across landscapes. The scientific literature is growing with examples of models used to explore predator-prey interactions, resource selection, population growth, and dynamics of disease transmission. These models provide managers with an efficient alternative means of testing new management and control strategies without resorting to empirical testing that is often costly, time-consuming, and impractical. This chapter presents a review of four types of mathematical models used to understand and predict the spread of infectious diseases in wild animals: compartmental, metapopulation, spatial, and contact network models. Descriptions of each model’s uses and limitations are used to provide a look at the complexities involved in modeling the spread of diseases and the trade-offs that accompany selecting one modeling approach over another. Potential avenues for the improvement and use of these models in future studies are also discussed, as are specific examples of how each type of model has improved our understanding of infectious diseases in populations of wild animals.

Saturation effects and the concurrency hypothesis: Insights from an analytic model

Sexual partnerships that overlap in time (concurrent relationships) may play a significant role in the HIV epidemic, but the precise effect is unclear. We derive edge-based compartmental models of disease spread in idealized dynamic populations with and without concurrency to allow for an investigation of its effects. Our models assume that partnerships change in time and individuals enter and leave the at-risk population. Infected individuals transmit at a constant per-partnership rate to their susceptible partners. In our idealized populations we find regions of parameter space where the existence of concurrent partnerships leads to substantially faster growth and higher equilibrium levels, but also regions in which the existence of concurrent partnerships has very little impact on the growth or the equilibrium. Additionally we find mixed regimes in which concurrency significantly increases the early growth, but has little effect on the ultimate equilibrium level. Guided by model predictions, we discuss general conditions under which concurrent relationships would be expected to have large or small effects in real-world settings. Our observation that the impact of concurrency saturates suggests that concurrency-reducing interventions may be most effective in populations with low to moderate concurrency.

The shape of the contact-density function matters when modelling parasite transmission in fluctuating populations

Models of disease transmission in a population with changing densities must assume a relation between infectious contacts and density. Typically, a choice is made between a constant (frequency-dependence) and a linear (density-dependence) contact-density function, but it is becoming increasingly clear that intermediate, nonlinear functions are more realistic. It is currently not clear, however, what the exact consequences would be of different contact-density functions in fluctuating populations. By combining field data on rodent host (Mastomys natalensis) demography, experimentally derived contact-density data, and laboratory and field data on Morogoro virus infection dynamics, we explored the effects of different contact-density function shapes on transmission dynamics and invasion/persistence. While invasion and persistence were clearly affected by the shape of the function, the effects on outbreak characteristics such as infection prevalence and seroprevalence were less obvious. This means that it may be difficult to distinguish between the different shapes based on how well models fit to real data. The shape of the transmission-density function should therefore be chosen with care, and is ideally based on existing information such as a previously quantified contact- or transmission-density relationship or the underlying biology of the host species in relation to the infectious agent.

Pair formation models for sexually transmitted infections: A primer

For modelling sexually transmitted infections, duration of partnerships can strongly influence the transmission dynamics of the infection. If partnerships are monogamous, pairs of susceptible individuals are protected from becoming infected, while pairs of infected individuals delay onward transmission of the infection as long as they persist. In addition, for curable infections re-infection from an infected partner may occur. Furthermore, interventions based on contact tracing rely on the possibility of identifying and treating partners of infected individuals. To reflect these features in a mathematical model, pair formation models were introduced to mathematical epidemiology in the 1980's. They have since been developed into a widely used tool in modelling sexually transmitted infections and the impact of interventions. Here we give a basic introduction to the concepts of pair formation models for a susceptible-infected-susceptible (SIS) epidemic. We review some results and applications of pair formation models mainly in the context of chlamydia infection.

Host heterogeneity affects both parasite transmission to and fitness on subsequent hosts

Infectious disease dynamics depend on the speed, number and fitness of parasites transmitting from infected hosts ('donors') to parasite-naive 'recipients'. Donor heterogeneity likely affects these three parameters, and may arise from variation between donors in traits including: (i) infection load, (ii) resistance, (iii) stage of infection, and (iv) previous experience of transmission. We used the Trinidadian guppy, Poecilia reticulata, and a directly transmitted monogenean ectoparasite, Gyrodactylus turnbulli, to experimentally explore how these sources of donor heterogeneity affect the three transmission parameters. We exposed parasite-naive recipients to donors (infected with a single parasite strain) differing in their infection traits, and found that donor infection traits had diverse and sometimes interactive effects on transmission. First, although transmission speed increased with donor infection load, the relationship was nonlinear. Second, while the number of parasites transmitted generally increased with donor infection load, more resistant donors transmitted more parasites, as did those with previous transmission experience. Finally, parasites transmitting from experienced donors exhibited lower population growth rates on recipients than those from inexperienced donors. Stage of infection had little effect on transmission parameters. These results suggest that a more holistic consideration of within-host processes will improve our understanding of between-host transmission and hence disease dynamics.This article is part of the themed issue 'Opening the black box: re-examining the ecology and evolution of parasite transmission'.

A Comparison of Two Mathematical Modeling Frameworks for Evaluating Sexually Transmitted Infection Epidemiology

BACKGROUND

Different models of sexually transmitted infections (STIs) can yield substantially different conclusions about STI epidemiology, and it is important to understand how and why models differ. Frequency-dependent models make the simplifying assumption that STI incidence is proportional to STI prevalence in the population, whereas network models calculate STI incidence more realistically by classifying individuals according to their partners' STI status.

METHODS

We assessed a deterministic frequency-dependent model approximation to a microsimulation network model of STIs in South Africa. Sexual behavior and demographic parameters were identical in the 2 models. Six STIs were simulated using each model: HIV, herpes, syphilis, gonorrhea, chlamydia, and trichomoniasis.

RESULTS

For all 6 STIs, the frequency-dependent model estimated a higher STI prevalence than the network model, with the difference between the 2 models being relatively large for the curable STIs. When the 2 models were fitted to the same STI prevalence data, the best-fitting parameters differed substantially between models, with the frequency-dependent model suggesting more immunity and lower transmission probabilities. The fitted frequency-dependent model estimated that the effects of a hypothetical elimination of concurrent partnerships and a reduction in commercial sex were both smaller than estimated by the fitted network model, whereas the latter model estimated a smaller impact of a reduction in unprotected sex in spousal relationships.

CONCLUSIONS

The frequency-dependent assumption is problematic when modeling short-term STIs. Frequency-dependent models tend to underestimate the importance of high-risk groups in sustaining STI epidemics, while overestimating the importance of long-term partnerships and low-risk groups.

Crossing the scale from within-host infection dynamics to between-host transmission fitness: a discussion of current assumptions and knowledge

The progression of an infection within a host determines the ability of a pathogen to transmit to new hosts and to maintain itself in the population. While the general connection between the infection dynamics within a host and the population-level transmission dynamics of pathogens is widely acknowledged, a comprehensive and quantitative understanding that would allow full integration of the two scales is still lacking. Here, we provide a brief discussion of both models and data that have attempted to provide quantitative mappings from within-host infection dynamics to transmission fitness. We present a conceptual framework and provide examples of studies that have taken first steps towards development of a quantitative framework that scales from within-host infections to population-level fitness of different pathogens. We hope to illustrate some general themes, summarize some of the recent advances and-maybe most importantly-discuss gaps in our ability to bridge these scales, and to stimulate future research on this important topic.

Nine challenges in incorporating the dynamics of behaviour in infectious diseases models

Traditionally, the spread of infectious diseases in human populations has been modelled with static parameters. These parameters, however, can change when individuals change their behaviour. If these changes are themselves influenced by the disease dynamics, there is scope for mechanistic models of behaviour to improve our understanding of this interaction. Here, we present challenges in modelling changes in behaviour relating to disease dynamics, specifically: how to incorporate behavioural changes in models of infectious disease dynamics, how to inform measurement of relevant behaviour to parameterise such models, and how to determine the impact of behavioural changes on observed disease dynamics.

Incorporating disease and population structure into models of SIR disease in contact networks

We consider the recently introduced edge-based compartmental models (EBCM) for the spread of susceptible-infected-recovered (SIR) diseases in networks. These models differ from standard infectious disease models by focusing on the status of a random partner in the population, rather than a random individual. This change in focus leads to simple analytic models for the spread of SIR diseases in random networks with heterogeneous degree. In this paper we extend this approach to handle deviations of the disease or population from the simplistic assumptions of earlier work. We allow the population to have structure due to effects such as demographic features or multiple types of risk behavior. We allow the disease to have more complicated natural history. Although we introduce these modifications in the static network context, it is straightforward to incorporate them into dynamic network models. We also consider serosorting, which requires using dynamic network models. The basic methods we use to derive these generalizations are widely applicable, and so it is straightforward to introduce many other generalizations not considered here. Our goal is twofold: to provide a number of examples generalizing the EBCM method for various different population or disease structures and to provide insight into how to derive such a model under new sets of assumptions.

Estimation of transmission dynamics of the Ceratomyxa shasta actinospore to the salmonid host

Transmission dynamics of the actinospore stage of Ceratomyxa shasta to the salmonid host were investigated under field and laboratory conditions. The number of parasites transmitted and the transmission rate were compared between 2 different exposure durations and also among different water velocities, by means of field exposures. Under laboratory conditions, the number of parasites transmitted and the transmission rates were compared across a broader range of water velocities and also at different water temperatures. Transmission rate was not constant over time as the number of parasites transmitted increased non-linearly between the 2 exposure durations. Transmission was also inversely related to water velocity and there was a threshold to transmission between 0·2–0·3 m s−1. Lastly, transmission rate increased with water temperature up to 18 °C then decreased at 23 °C. These experiments provide a range of values of transmission that will be incorporated into an epidemiological model to simulate the effectiveness of different management strategies. Additionally, these experiments provided novel information on the effects of environmental conditions (i.e. water velocity and water temperature) on the transmission dynamics between the salmonid host and the actinospore stage.

Density thresholds for Mopeia virus invasion and persistence in its host Mastomys natalensis

Well-established theoretical models predict host density thresholds for invasion and persistence of parasites with a density-dependent transmission. Studying such thresholds in reality, however, is not obvious because it requires long-term data for several fluctuating populations of different size. We developed a spatially explicit and individual-based SEIR model of Mopeia virus in multimammate mice Mastomys natalensis. This is an interesting model system for studying abundance thresholds because the host is the most common African rodent, populations fluctuate considerably and the virus is closely related to Lassa virus but non-pathogenic to humans so can be studied safely in the field. The simulations show that, while host density clearly is important, sharp thresholds are only to be expected for persistence (and not for invasion), since at short time-spans (as during invasion), stochasticity is determining. Besides host density, also the spatial extent of the host population is important. We observe the repeated local occurrence of herd immunity, leading to a decrease in transmission of the virus, while even a limited amount of dispersal can have a strong influence in spreading and re-igniting the transmission. The model is most sensitive to the duration of the infectious stage, the size of the home range and the transmission coefficient, so these are important factors to determine experimentally in the future.

Optimizing reactive responses to outbreaks of immunizing infections: balancing case management and vaccination

For vaccine-preventable infections, immunization generally needs to be supplemented by palliative care of individuals missed by the vaccination. Costs and availability of vaccine doses and palliative care vary by disease and by region. In many situations, resources for delivery of palliative care are independent of resources required for vaccination; however we also need to consider the conservative scenario where there is some trade-off between efforts, which is of potential relevance for resource-poor settings. We formulate an SEIR model that includes those two control strategies – vaccination and palliative care. We consider their relative merit and optimal allocation in the context of a highly efficacious vaccine, and under the assumption that palliative care may reduce transmission. We investigate the utility of a range of mixed or pure strategies that can be implemented after an epidemic has started, and look for rule-of-thumb principles of how best to reduce the burden of disease during an acute outbreak over a spectrum of vaccine-preventable infections. Intuitively, we expect the best strategy to initially focus on vaccination, and enhanced palliative care after the infection has peaked, but a number of plausible realistic constraints for control result in important qualifications on the intervention strategy. The time in the epidemic when one should switch strategy depends sensitively on the relative cost of vaccine to palliative care, the available budget, and . Crucially, outbreak response vaccination may be more effective in managing low- diseases, while high scenarios enhance the importance of routine vaccination and case management.

Sociality, density-dependence and microclimates determine the persistence of populations suffering from a novel fungal disease, white-nose syndrome

Disease has caused striking declines in wildlife and threatens numerous species with extinction. Theory suggests that the ecology and density-dependence of transmission dynamics can determine the probability of disease-caused extinction, but few empirical studies have simultaneously examined multiple factors influencing disease impact. We show, in hibernating bats infected with Geomyces destructans, that impacts of disease on solitary species were lower in smaller populations, whereas in socially gregarious species declines were equally severe in populations spanning four orders of magnitude. However, as these gregarious species declined, we observed decreases in social group size that reduced the likelihood of extinction. In addition, disease impacts in these species increased with humidity and temperature such that the coldest and driest roosts provided initial refuge from disease. These results expand our theoretical framework and provide an empirical basis for determining which host species are likely to be driven extinct while management action is still possible.

Comparability of results from pair and classical model formulations for different sexually transmitted infections

The "classical model" for sexually transmitted infections treats partnerships as instantaneous events summarized by partner change rates, while individual-based and pair models explicitly account for time within partnerships and gaps between partnerships. We compared predictions from the classical and pair models over a range of partnership and gap combinations. While the former predicted similar or marginally higher prevalence at the shortest partnership lengths, the latter predicted self-sustaining transmission for gonorrhoea (GC) and Chlamydia (CT) over much broader partnership and gap combinations. Predictions on the critical level of condom use (C(c)) required to prevent transmission also differed substantially when using the same parameters. When calibrated to give the same disease prevalence as the pair model by adjusting the infectious duration for GC and CT, and by adjusting transmission probabilities for HIV, the classical model then predicted much higher C(c) values for GC and CT, while C(c) predictions for HIV were fairly close. In conclusion, the two approaches give different predictions over potentially important combinations of partnership and gap lengths. Assuming that it is more correct to explicitly model partnerships and gaps, then pair or individual-based models may be needed for GC and CT since model calibration does not resolve the differences.

Social behavior drives the dynamics of respiratory disease in threatened tortoises

Since the early 1990s, morbidity and mortality in tortoise populations have been associated with a transmissible, mycoplasmal upper respiratory tract disease (URTD). Although the etiology, transmission, and diagnosis of URTD have been extensively studied, little is known about the dynamics of disease transmission in free-ranging tortoise populations. To understand the transmission dynamics of Mycoplasma agassizii, the primary etiological agent of URTD in wild tortoise populations, we studied 11 populations of free-ranging gopher tortoises (Gopherus polyphemus; n = 1667 individuals) over five years and determined their exposure to the pathogen by serology, by clinical signs, and by detection of the pathogen in nasal lavages. Adults tortoises (n = 759) were 11 times more likely to be seropositive than immature animals (n = 242) (odds ratio = 10.6, 95% CI = 5.7-20, P < 0.0001). Nasal discharge was observed in only 1.4% (4/296) of immature tortoises as compared with 8.6% (120/1399) of adult tortoises. Nasal lavages from all juvenile tortoises (n = 283) were negative by PCR for mycoplasmal pathogens associated with URTD. We tested for spatial segregation among tortoise burrows by size class and found no consistent evidence of clustering of either juveniles or adults. We suggest that the social behavior of tortoises plays a critical role in the spread of URTD in wild populations, with immature tortoises having minimal interactions with adult tortoises, thereby limiting their exposure to the pathogen. These findings may have broader implications for modeling horizontally transmitted diseases in other species with limited parental care and emphasize the importance of incorporating animal behavior parameters into disease transmission studies to better characterize the host-pathogen dynamics.

Sickness behaviour acting as an evolutionary trap? Male house finches preferentially feed near diseased conspecifics

Host behaviour towards infectious conspecifics is a crucial yet overlooked component of pathogen dynamics. Selection is expected to favour individuals who can recognize and avoid infected conspecifics in order to reduce their own risk of infection. However, evidence is scarce and limited to species employing chemical cues. Here, we experimentally examine whether healthy captive house finches (Carpodacus mexicanus) preferentially forage near a same-sex, healthy conspecific versus one infected with the directly transmissible pathogen Mycoplasma gallisepticum (MG), which causes lethargy and visible conjunctivitis. Interestingly, male house finches strongly preferred feeding near diseased conspecifics, while females showed no preference. This sex difference appeared to be the result of lower aggression rates in diseased males, but not in females. The reduced aggression of diseased males may act as an 'evolutionary trap' by presenting a historically beneficial behavioural cue in the context of a new environment, which now includes a recently emerged, potentially fatal pathogen. Since MG can be directly transmitted during feeding, healthy males may inadvertently increase their risk of contracting MG. This behaviour is likely to significantly contribute to the continued persistence of MG epidemics in wild populations.

Wildlife cancer: a conservation perspective

Until recently, cancer in wildlife was not considered to be a conservation concern. However, with the identification of Tasmanian devil facial tumour disease, sea turtle fibropapillomatosis and sea lion genital carcinoma, it has become apparent that neoplasia can be highly prevalent and have considerable effects on some species. It is also clear that anthropogenic activities contribute to the development of neoplasia in wildlife species, such as beluga whales and bottom-dwelling fish, making them sensitive sentinels of disturbed environments.

Controlling nosocomial infection based on structure of hospital social networks

Nosocomial infection (i.e. infection in healthcare facilities) raises a serious public health problem, as implied by the existence of pathogens characteristic to healthcare facilities such as methicillin-resistant Staphylococcus aureus and hospital-mediated outbreaks of influenza and severe acute respiratory syndrome. For general communities, epidemic modeling based on social networks is being recognized as a useful tool. However, disease propagation may occur in a healthcare facility in a manner different from that in a urban community setting due to different network architecture. We simulate stochastic susceptible-infected-recovered dynamics on social networks, which are based on observations in a hospital in Tokyo, to explore effective containment strategies against nosocomial infection. The observed social networks in the hospital have hierarchical and modular structure in which dense substructure such as departments, wards, and rooms, are globally but only loosely connected, and do not reveal extremely right-skewed distributions of the number of contacts per individual. We show that healthcare workers, particularly medical doctors, are main vectors (i.e. transmitters) of diseases on these networks. Intervention methods that restrict interaction between medical doctors and their visits to different wards shrink the final epidemic size more than intervention methods that directly protect patients, such as isolating patients in single rooms. By the same token, vaccinating doctors with priority rather than patients or nurses is more effective. Finally, vaccinating individuals with large betweenness centrality (frequency of mediating connection between pairs of individuals along the shortest paths) is superior to vaccinating ones with large connectedness to others or randomly chosen individuals, which was suggested by previous model studies.

Eating yourself sick: transmission of disease as a function of foraging ecology

Species interactions may profoundly influence disease outbreaks. However, disease ecology has only begun to integrate interactions between hosts and their food resources (foraging ecology) despite that hosts often encounter their parasites while feeding. A zooplankton-fungal system illustrated this central connection between foraging and transmission. Using experiments that varied food density for Daphnia hosts, density of fungal spores and body size of Daphnia, we produced mechanistic yet general models for disease transmission rate based on broadly applicable components of feeding biology. Best performing models could explain why prevalence of infection declined at high food density and rose sharply as host size increased (a pattern echoed in nature). In comparison, the classic mass-action model for transmission performed quite poorly. These foraging-based models should broadly apply to systems in which hosts encounter parasites while eating, and they will catalyse future integration of the roles of Daphnia as grazer and host.

Within-host dynamics of an intestinal pathogen of bumble bees

The success of a pathogen depends not only on its transmission to new hosts, but also on its ability to colonize and persist within its current host. Studies of within-host dynamics have focused on only a few diseases of humans, whereas little is known about the factors that influence pathogen populations as they develop inside non-human hosts. Here, we investigate pathogen dynamics occurring within bumble bees (Bombus impatiens) infected by the gut trypanosome Crithidia bombi. Infection by C. bombi showed several features characteristic of vertebrate diseases, including a rapid initial increase in infection intensity, marked oscillations in parasitaemia, and the stimulation of a systemic immune response in infected bees. Within-host dynamics generated substantial variation in the infectiousness and flower-visiting behaviour of bumble bees. Changes in bee foraging that arise from infection may influence the probability of C. bombi transmission between bees at flowers.

Superspreading and the effect of individual variation on disease emergence

From Typhoid Mary to SARS, it has long been known that some people spread disease more than others. But for diseases transmitted via casual contact, contagiousness arises from a plethora of social and physiological factors, so epidemiologists have tended to rely on population averages to assess a disease's potential to spread. A new analysis of outbreak data shows that individual differences in infectiousness exert powerful influences on the epidemiology of ten deadly diseases. SARS and measles (and perhaps avian influenza) show strong tendencies towards ‘superspreading events’ that can ignite explosive epidemics — but this same volatility makes outbreaks more likely to fizzle out. Smallpox and pneumonic plague, two potential bioterrorism agents, show steadier growth but still differ markedly from the traditional average-based view. These findings are relevant to how emerging diseases are detected and controlled.

Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups^1,2. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, R₀, which is defined as the mean number of infections caused by an infected individual in a susceptible population^3,4. Population estimates of R₀ can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of severe acute respiratory syndrome (SARS) by numerous ‘superspreading events’ in which certain individuals infected unusually large numbers of secondary cases^5,6,7,8,9,10. For diseases transmitted by non-sexual direct contacts, such as SARS or smallpox, individual variation is difficult to measure empirically, and thus its importance for outbreak dynamics has been unclear^2,10,11. Here we present an integrated theoretical and statistical analysis of the influence of individual variation in infectiousness on disease emergence. Using contact tracing data from eight directly transmitted diseases, we show that the distribution of individual infectiousness around R₀ is often highly skewed. Model predictions accounting for this variation differ sharply from average-based approaches, with disease extinction more likely and outbreaks rarer but more explosive. Using these models, we explore implications for outbreak control, showing that individual-specific control measures outperform population-wide measures. Moreover, the dramatic improvements achieved through targeted control policies emphasize the need to identify predictive correlates of higher infectiousness. Our findings indicate that superspreading is a normal feature of disease spread, and to frame ongoing discussion we propose a rigorous definition for superspreading events and a method to predict their frequency.

Measuring the transmission dynamics of a sexually transmitted disease

Sexually transmitted diseases (STDs) occur throughout the animal kingdom and are generally thought to affect host population dynamics and evolution very differently from other directly transmitted infectious diseases. In particular, STDs are not thought to have threshold densities for persistence or to be able to regulate host population density independently; they may also have the potential to cause host extinction. However, these expectations follow from a theory that assumes that the rate of STD spread depends on the proportion (rather than the density) of individuals infected in a population. We show here that this key assumption ("frequency dependence"), which has not previously been tested in an animal STD system, is invalid in a simple and general experimental model. Transmission of an STD in the two-spot ladybird depended more on the density of infected individuals in the study population than on their frequency. We argue that, in this system, and in many other animal STDs in which population density affects sexual contact rate, population dynamics may exhibit some characteristics that are normally reserved for diseases with density-dependent transmission.

Should we expect population thresholds for wildlife disease?

Host population thresholds for the invasion or persistence of infectious disease are core concepts of disease ecology and underlie disease control policies based on culling and vaccination. However, empirical evidence for these thresholds in wildlife populations has been sparse, although recent studies have begun to address this gap. Here, we review the theoretical bases and empirical evidence for disease thresholds in wildlife. We see that, by their nature, these thresholds are rarely abrupt and always difficult to measure, and important facets of wildlife ecology are neglected by current theories. Empirical studies seeking to identify disease thresholds in wildlife encounter recurring obstacles of small sample sizes and confounding factors. Disease control policies based solely on threshold targets are rarely warranted, but management to reduce abundance of susceptible hosts can be effective.

Species Coexistence and Periodicity in Host-Host-Pathogen Models

Models for the transmission of an infectious disease in one and two host populations with and without self-regulation are analyzed. Many unusual behaviors such as multiple positive equilibria and periodic solutions occur in previous models that use the mass-action (density-dependent) incidence. In contrast, the models formulated using the frequency-dependent (standard) incidence have the behavior of a classic endemic model, since below the threshold, the disease dies out, and above the threshold, the disease persists and the infectious fractions approach an endemic equilibrium. The results given here reinforce previous examples in which there are major differences in behavior between models using mass-action and frequency-dependent incidences.

Plant venereal diseases: insights from a messy metaphor

The concept of plant venereal disease is examined from definitional, operational and axiomatic viewpoints. The transmission of many plant pathogens occurs during the flowering phase and is effected either by pollinators or by wind dispersal of spores from inflorescences. Attraction of insects by pseudo-flowers or sugary secretions also serves to spread many diseases. Given the diversity of processes involved, a simple all-encompassing parallel with animal venereal diseases is not possible. Operationally establishing the routes of disease transmission, as well as quantifying the relative magnitudes of these different routes, remains critical for understanding disease dynamics and controlling spread in agricultural contexts. From an axiomatic viewpoint, sexually transmitted diseases are characterized by frequency-dependent transmission, transmission in the adult stage, and by virulence effects involving sterility rather than mortality. These characteristics serve to differentiate the dynamics and evolution of sexually transmitted diseases from that of other diseases and are features that are also shared by many pollinator-transmitted diseases. However, the majority of plant diseases that involve the reproductive structures show a rich biology that defies easy categorization. The experimental convenience of plants and their pathogens is likely to play an important role in understanding the evolution of disease traits, irrespective of what descriptive terms are applied to the natural history of the transmission process.

The effect of treatment on pathogen virulence

The optimal virulence of a pathogen is determined by a trade-off between maximizing the rate of transmission and maximizing the duration of infectivity. Treatment measures such as curative therapy and case isolation exert selective pressure by reducing the duration of infectivity, reducing the value of duration-increasing strategies to the pathogen and favoring pathogen strategies that maximize the rate of transmission. We extend the trade-off models of previous authors, and represents the reproduction number of the pathogen as a function of the transmissibility, host contact rate, disease-induced mortality, recovery rate, and treatment rate, each of which may be influenced by the virulence. We find that when virulence is subject to a transmissibility-mortality trade-off, treatment can lead to an increase in optimal virulence, but that in other scenarios (such as the activity-recovery trade-off) treatment decreases the optimal virulence. Paradoxically, when levels of treatment rise with pathogen virulence, increasing control efforts may raise predicted levels of optimal virulence. Thus we show that conflict can arise between the epidemiological benefits of treatment and the evolutionary risks of heightened virulence.