A clarification of transmission terms in host-microparasite models: numbers, densities and areas

Individual differences in boldness influence patterns of social interactions and the transmission of cuticular bacteria among group-mates

Despite the importance of host attributes for the likelihood of associated microbial transmission, individual variation is seldom considered in studies of wildlife disease. Here, we test the influence of host phenotypes on social network structure and the likelihood of cuticular bacterial transmission from exposed individuals to susceptible group-mates using female social spiders (Stegodyphus dumicola). Based on the interactions of resting individuals of known behavioural types, we assessed whether individuals assorted according to their behavioural traits. We found that individuals preferentially interacted with individuals of unlike behavioural phenotypes. We next applied a green fluorescent protein-transformed cuticular bacterium,Pantoeasp., to individuals and allowed them to interact with an unexposed colony-mate for 24 h. We found evidence for transmission of bacteria in 55% of cases. The likelihood of transmission was influenced jointly by the behavioural phenotypes of both the exposed and susceptible individuals: transmission was more likely when exposed spiders exhibited higher 'boldness' relative to their colony-mate, and when unexposed individuals were in better body condition. Indirect transmission via shared silk took place in only 15% of cases. Thus, bodily contact appears key to transmission in this system. These data represent a fundamental step towards understanding how individual traits influence larger-scale social and epidemiological dynamics.

Limiting the spread of disease through altered migration patterns

We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations by the migration of infected individuals. We show how susceptible individuals can act collectively to limit the spread of disease during the initial phase of an epidemic by specifying the distribution that minimises the growth rate of the epidemic when the infectives are migrating so as to maximise the growth rate. We also give an explicit strategy that minimises the basic reproduction number, which is also shown be optimal in terms of the probability of extinction and total size of the epidemic.

Biannual birth pulses allow filoviruses to persist in bat populations

Filoviruses Ebolavirus (EBOV) and Marburgvirus (MARV) cause haemorrhagic fevers with high mortality rates, posing significant threats to public health. To understand transmission into human populations, filovirus dynamics within reservoir host populations must be understood. Studies have directly linked filoviruses to bats, but the mechanisms allowing viral persistence within bat populations are poorly understood. Theory suggests seasonal birthing may decrease the probability of pathogen persistence within populations, but data suggest MARV may persist within colonies of seasonally breeding Egyptian fruit bats, Rousettus aegyptiacus. I synthesize available filovirus and bat data in a stochastic compartmental model to explore fundamental questions relating to filovirus ecology: can filoviruses persist within isolated bat colonies; do critical community sizes exist; and how do host-pathogen relationships affect spillover transmission potential? Synchronous annual breeding and shorter incubation periods did not allow filovirus persistence, whereas bi-annual breeding and longer incubation periods, such as reported for Egyptian fruit bats and EBOV in experimental studies, allowed persistence in colony sizes often found in nature. Serological data support the findings, with bats from species with two annual birth pulses more likely to be seropositive (odds ratio (OR) 4.4, 95% confidence interval (CI) 2.5-8.7) than those with one, suggesting that biannual birthing is necessary for filovirus persistence.

Data-Driven Models of Foot-and-Mouth Disease Dynamics: A Review

Foot-and-mouth disease virus (FMDV) threatens animal health and leads to considerable economic losses worldwide. Progress towards minimizing both veterinary and financial impact of the disease will be made with targeted disease control policies. To move towards targeted control, specific targets and detailed control strategies must be defined. One approach for identifying targets is to use mathematical and simulation models quantified with accurate and fine-scale data to design and evaluate alternative control policies. Nevertheless, published models of FMDV vary in modelling techniques and resolution of data incorporated. In order to determine which models and data sources contain enough detail to represent realistic control policy alternatives, we performed a systematic literature review of all FMDV dynamical models that use host data, disease data or both data types. For the purpose of evaluating modelling methodology, we classified models by control strategy represented, resolution of models and data, and location modelled. We found that modelling methodology has been well developed to the point where multiple methods are available to represent detailed and contact-specific transmission and targeted control. However, detailed host and disease data needed to quantify these models are only available from a few outbreaks. To address existing challenges in data collection, novel data sources should be considered and integrated into models of FMDV transmission and control. We suggest modelling multiple endemic areas to advance local control and global control and better understand FMDV transmission dynamics. With incorporation of additional data, models can assist with both the design of targeted control and identification of transmission drivers across geographic boundaries.

Modelling the potential benefits of different strategies to control infection with Trypanosoma evansi in camels in Somaliland

Trypanosoma evansi (T. evansi), the protozoan parasitic cause of camel trypanosomosis (Surra), constitutes one of the major veterinary problems worldwide. An infectious disease model of camel trypanosomosis (Surra) was adopted from one developed for buffalo and applied to study the impact of T. evansi infection on camel production. The model contained deterministic and stochastic components and the seroprevalence based on a survey conducted in Somaliland in 2011 and 2012 to simulate and estimate the economic benefits of four different control options against T. evansi infection in camels (1, 2, 3 and 4 regimens). The mean benefit per animal of controlling surra was calculated at US$354 (the treatment of all camels biannually), US$426 (the monthly targeted treatment of clinically sick camels) and US$287 (biannual targeted treatment of seropositive camels), respectively, compared with US$137 for untreated camels. Consequently, the model predicted that the total net benefit loss to a camel herd or village that was not applying the recommended effective surra control strategy was US$115,605 (69.4 billion shilling per annum).

Familiarity breeds contempt: combining proximity loggers and GPS reveals female white-tailed deer (Odocoileus virginianus) avoiding close contact with neighbors

Social interactions can influence infectious disease dynamics, particularly for directly transmitted pathogens. Therefore, reliable information on contact frequency within and among groups can better inform disease modeling and management. We compared three methods of assessing contact patterns: (1) space-use overlap (volume of interaction [VI]), (2) direct contact rates measured by simultaneous global positioning system (GPS) locations (<10 m apart), and (3) direct contact rates measured by proximity loggers (PLs; 1-m detection) among female white-tailed deer (Odocoileus virginianus). We calculated the PL∶GPS contact ratios to see whether both devices reveal similar contact patterns and thus predict similar pathogen transmission patterns. Contact rates measured by GPS and PLs were similarly high for two within-group dyads (pairs of deer in the same social groups). Dyads representing separate but neighboring groups (high VI) had PL∶GPS contact ratios near zero, whereas dyads further apart (intermediate VI) had higher PL∶GPS contact ratios. Social networks based on PL contacts showed the fewest connected individuals and lowest mean centrality measures; network metrics were intermediate when based on GPS contacts and greatest when based on VI. Thus, the VI network portrayed animals to be more uniformly and strongly connected than did the PL network. We conclude that simultaneous GPS locations, compared with PLs, substantially underestimate the impact of group membership on direct contact rates of female deer and make networks appear more connected. We also present evidence that deer coming within the general vicinity of each other are less likely to come in close contact if they are in neighboring social groups than deer whose home ranges overlap little if at all. Combined, these results provide evidence that direct transmission of disease agents among female and juvenile white-tailed deer is likely to be constrained both spatially and by social structure, more so than GPS data alone would suggest.

Infection dynamics in frog populations with different histories of decline caused by a deadly disease

Pathogens can drive host population dynamics. Chytridiomycosis is a fungal disease of amphibians that is caused by the fungus Batrachochytrium dendrobatidis (Bd). This pathogen has caused declines and extinctions in some host species whereas other host species coexist with Bd without suffering declines. In the early 1990s, Bd extirpated populations of the endangered common mistfrog, Litoria rheocola, at high-elevation sites, while populations of the species persisted at low-elevation sites. Today, populations have reappeared at many high-elevation sites where they presently co-exist with the fungus. We conducted a capture-mark-recapture (CMR) study of six populations of L. rheocola over 1 year, at high and low elevations. We used multistate CMR models to determine which factors (Bd infection status, site type, and season) influenced rates of frog survival, recapture, infection, and recovery from infection. We observed Bd-induced mortality of individual frogs, but did not find any significant effect of Bd infection on the survival rate of L. rheocola at the population level. Survival and recapture rates depended on site type and season. Infection rate was highest in winter when temperatures were favourable for pathogen growth, and differed among site types. The recovery rate was high (75.7-85.8%) across seasons, and did not differ among site types. The coexistence of L. rheocola with Bd suggests that (1) frog populations are becoming resistant to the fungus, (2) Bd may have evolved lower virulence, or (3) current environmental conditions may be inhibiting outbreaks of the fatal disease.

Spatial analyses of wildlife contact networks

Datasets from which wildlife contact networks of epidemiological importance can be inferred are becoming increasingly common. A largely unexplored facet of these data is finding evidence of spatial constraints on who has contact with whom, despite theoretical epidemiologists having long realized spatial constraints can play a critical role in infectious disease dynamics. A graph dissimilarity measure is proposed to quantify how close an observed contact network is to being purely spatial whereby its edges are completely determined by the spatial arrangement of its nodes. Statistical techniques are also used to fit a series of mechanistic models for contact rates between individuals to the binary edge data representing presence or absence of observed contact. These are the basis for a second measure that quantifies the extent to which contacts are being mediated by distance. We apply these methods to a set of 128 contact networks of field voles (Microtus agrestis) inferred from mark–recapture data collected over 7 years and from four sites. Large fluctuations in vole abundance allow us to demonstrate that the networks become increasingly similar to spatial proximity graphs as vole density increases. The average number of contacts, , was (i) positively correlated with vole density across the range of observed densities and (ii) for two of the four sites a saturating function of density. The implications for pathogen persistence in wildlife may be that persistence is relatively unaffected by fluctuations in host density because at low density is low but hosts move more freely, and at high density is high but transmission is hampered by local build-up of infected or recovered animals.

Costs and benefits of group living with disease: a case study of pneumonia in bighorn lambs (Ovis canadensis)

Group living facilitates pathogen transmission among social hosts, yet temporally stable host social organizations can actually limit transmission of some pathogens. When there are few between-subpopulation contacts for the duration of a disease event, transmission becomes localized to subpopulations. The number of per capita infectious contacts approaches the subpopulation size as pathogen infectiousness increases. Here, we illustrate that this is the case during epidemics of highly infectious pneumonia in bighorn lambs (Ovis canadensis). We classified individually marked bighorn ewes into disjoint seasonal subpopulations, and decomposed the variance in lamb survival to weaning into components associated with individual ewes, subpopulations, populations and years. During epidemics, lamb survival varied substantially more between ewe-subpopulations than across populations or years, suggesting localized pathogen transmission. This pattern of lamb survival was not observed during years when disease was absent. Additionally, group sizes in ewe-subpopulations were independent of population size, but the number of ewe-subpopulations increased with population size. Consequently, although one might reasonably assume that force of infection for this highly communicable disease scales with population size, in fact, host social behaviour modulates transmission such that disease is frequency-dependent within populations, and some groups remain protected during epidemic events.

Social living mitigates the costs of a chronic illness in a cooperative carnivore

Infection risk is assumed to increase with social group size, and thus be a cost of group living. We assess infection risk and costs with respect to group size using data from an epidemic of sarcoptic mange (Sarcoptes scabiei) among grey wolves (Canis lupus). We demonstrate that group size does not predict infection risk and that individual costs of infection, in terms of reduced survival, can be entirely offset by having sufficient numbers of pack-mates. Infected individuals experience increased mortality hazards with increasing proportions of infected pack-mates, but healthy individuals remain unaffected. The social support of group hunting and territory defence are two possible mechanisms mediating infection costs. This is likely a common phenomenon among other social species and chronic infections, but difficult to detect in systems where infection status cannot be measured continuously over time.

Interactions between density, home range behaviors, and contact rates in the Channel Island fox (Urocyon littoralis)

Many of the mechanisms underlying density-dependent regulation of populations, including contest competition and disease spread, depend on contact among neighboring animals. Understanding how variation in population density influences the frequency of contact among neighboring animals is therefore an important aspect to understanding the mechanisms underlying, and ecological consequences of, density-dependent regulation. However, contact rates are difficult to measure in the field and may be influenced by density through multiple pathways. This study explored how local density affects contact rates among Channel Island foxes (Urocyon littoralis) through two pathways: changes in home range size and changes in home range overlap. We tracked 40 radio-collared foxes at four sites on San Clemente Island, California. Fox densities at the four sites ranged from 2.8 ± 1.28 to 42.8 ± 9.43 foxes/km². Higher fox densities were correlated with smaller home ranges (R² = 0.526, F_1,38 = 42.19, P < 0.001). Thirty foxes wore collars that also contained proximity loggers, which recorded the time and duration of occasions when collared foxes were within 5 m of one another. Contact rates between neighboring fox dyads were positively correlated with home range overlap (R² = 0.341, P = 0.008), but not fox density (R² = 0.012, P = 0.976). Individuals at high densities had more collared neighbors with overlapping home ranges (R² = 0.123, P = 0.026) but not an increase in the amount of contact between individual neighbors. This study was the first time contact rates were directly measured and compared to density and home range overlap. Results suggest that foxes exhibit a threshold in their degree of tolerance for neighbors, overlap is a reliable index of the amount of direct contact between island foxes, and disease transmission rates will likely scale with fox density.

Investment in constitutive immune function by North American elk experimentally maintained at two different population densities

Natural selection favors individuals that respond with effective and appropriate immune responses to macro or microparasites. Animals living in populations close to ecological carrying capacity experience increased intraspecific competition, and as a result are often in poor nutritional condition. Nutritional condition, in turn, affects the amount of endogenous resources that are available for investment in immune function. Our objective was to understand the relationship between immune function and density dependence mediated by trade-offs between immune function, nutritional condition, and reproduction. To determine how immune function relates to density-dependent processes, we quantified bacteria killing ability, hemolytic-complement activity, and nutritional condition of North American elk (Cervus elaphus) from populations maintained at experimentally high- and low-population densities. When compared with elk from the low-density population, those from the high-density population had higher bacteria killing ability and hemolytic-complement activity despite their lower nutritional condition. Similarly, when compared with adults, yearlings had higher bacteria killing ability, higher hemolytic-complement activity, and lower nutritional condition. Pregnancy status and lactational status did not change either measure of constitutive immunity. Density-dependent processes affected both nutritional condition and investment in constitutive immune function. Although the mechanism for how density affects immunity is ambiguous, we hypothesize two possibilities: (i) individuals in higher population densities and in poorer nutritional condition invested more into constitutive immune defenses, or (ii) had higher parasite loads causing higher induced immune responses. Those explanations are not mutually exclusive, and might be synergistic, but overall our results provide stronger support for the hypothesis that animals in poorer nutritional condition invest more in constitutive immune defenses then animals in better nutritional condition. This intriguing hypothesis should be investigated further within the larger framework of the cost and benefit structure of immune responses.

Parameter identification in a tuberculosis model for Cameroon

A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.

Effects of pond salinization on survival rate of amphibian hosts infected with the chytrid fungus

The chytrid fungus Batrachochytrium dendrobatidis has been implicated in the decline and extinction of amphibian populations worldwide, but management options are limited. Recent studies show that sodium chloride (NaCl) has fungicidal properties that reduce the mortality rates of infected hosts in captivity. We investigated whether similar results can be obtained by adding salt to water bodies in the field. We increased the salinity of 8 water bodies to 2 or 4 ppt and left an additional 4 water bodies with close to 0 ppt and monitored salinity for 18 months. Captively bred tadpoles of green and golden bell frog (Litoria aurea) were released into each water body and their development, levels of B. dendrobatidis infection, and survival were monitored at 1, 4, and 12 months. The effect of salt on the abundance of nontarget organisms was also investigated in before and after style analyses. Salinities remained constant over time with little intervention. Hosts in water bodies with 4 ppt salt had a significantly lower prevalence of chytrid infection and higher survival, following metamorphosis, than hosts in 0 ppt salt. Tadpoles in the 4 ppt group were smaller in length after 1 month in the release site than those in the 0 and 2 ppt groups, but after metamorphosis body size in all water bodies was similar . In water bodies with 4 ppt salt, the abundance of dwarf tree frogs (Litoria fallax), dragonfly larvae, and damselfly larvae was lower than in water bodies with 0 and 2 ppt salt, which could have knock-on effects for community structure. Based on our results, salt may be an effective field-based B. dendrobatidis mitigation tool for lentic amphibians that could contribute to the conservation of numerous susceptible species. However, as in all conservation efforts, these benefits need to be weighed against negative effects on both target and nontarget organisms.

Managing dynamic epidemiological risks through trade

There is growing concern that trade, by connecting geographically isolated regions, unintentionally facilitates the spread of invasive pathogens and pests - forms of biological pollution that pose significant risks to ecosystem and human health. We use a bioeconomic framework to examine whether trade always increases private risks, focusing specifically on pathogen risks from live animal trade. When the pathogens have already established and traders bear some private risk, we find two results that run counter to the conventional wisdom on trade. First, uncertainty about the disease status of individual animals held in inventory may increase the incentives to trade relative to the disease-free case. Second, trade may facilitate reduced long-run disease prevalence among buyers. These results arise because disease risks are endogenous due to dynamic feedback processes involving valuable inventories, and markets facilitate the management of private risks that producers face with or without trade.

The role of antiparasite treatment experiments in assessing the impact of parasites on wildlife

It has become increasingly clear that parasites can have significant impacts on the dynamics of wildlife populations. Recently, researchers have shifted from using observational approaches to infer the impact of parasites on the health and fitness of individuals to using antiparasite drug treatments to test directly the consequences of infection. However, it is not clear the extent to which these experiments work in wildlife systems, or whether the results of these individual-level treatment experiments can predict the population-level consequences of parasitism. Here, we assess the results of treatment experiments, laying out the benefits and limitations of this approach, and discuss how they can be used to improve our understanding of the role of parasites in wildlife populations.

Seroepidemiology of leptospirosis in dogs from rural and slum communities of Los Rios Region, Chile

Background

Leptospirosis is a zoonotic disease of global importance and often neglected as a public health problem due to lack of awareness, under-diagnosis and under-reporting. Animals serve as a source of transmission through the shedding of Leptospira in their urine. Because of their proximity to humans, dogs may play a role in human infections. In order to assess and mitigate leptospirosis in dogs and the risk of transmission to humans it is important to understand the epidemiology of leptospirosis under natural conditions. This study aimed to characterize leptospirosis in owned dogs from three distinct community types. Blood, dog and household data were collected from 265 dogs in 190 households from 12 communities representing farms, rural villages, and urban slums in the Los Rios region, Chile. Serologic profiles with a 20-serovar microagglutination test panel were obtained. Binomial and multinomial logistic regression models were used to evaluate the associations between spatial, ecological, socio-economic variables and overall seropositivity as well as seropositivity to serogroup Canicola.

Results

Results from 247 dogs with no history of vaccination were used. Overall seroprevalence was 25.1% (62/247) with significant differences by community type: 10.9% (9/82) in dogs from farms, 22.3% (21/94) from rural villages, and 45.1% (32/71) from urban slums (p <0.001). This trend by community type was also observed for dogs with evidence of seropositivity to the Canicola serogroup. Factors associated with seropositive dogs included dog density and precipitation two-weeks prior to sampling. Presence of Leptospira positive puddles collected from the peri-domestic household environment was also associated with increased seropositivity.

Conclusions

Results suggest that leptospirosis is actively maintained in the dog population in this study region with notably distinct patterns by community type. Dog populations from rural villages, and urban slums in particular, showed evidence of high levels of transmission probably as a result of the combined effects of dog living conditions as well as community-level ecological and environmental factors.

Electronic supplementary material

The online version of this article (doi:10.1186/s12917-015-0341-9) contains supplementary material, which is available to authorized users.

Aggregation and environmental transmission in Chronic Wasting Disease

Disease transmission depends on the interplay between the infectious agent and the behavior of the host. Some diseases, such as Chronic Wasting Disease, can be transmitted directly between hosts as well as indirectly via the environment. The social behavior of hosts affects both of these pathways, and a successful intervention requires knowledge of the relative influence of the different etiological and behavioral aspects of the disease. We develop a strategic differential equation model for Chronic Wasting Disease and include direct and indirect transmission as well as host aggregation into our model. We calculate the basic reproduction number and perform a sensitivity analysis based on Latin hypercube sampling from published parameter values. We find conditions for the existence of an endemic equilibrium, and show that, under a certain mild assumption on parameters, the model does not exhibit a backward bifurcation or bistability. Hence, the basic reproduction number constitutes the disease elimination threshold. We find that the prevalence of the disease decreases with host aggregation and increases with the lifespan of the infectious agent in the environment.

Do open garbage dumps play a role in canine rabies transmission in Biyem-Assi health district in Cameroon?

BACKGROUND

Rabies is a neglected enzootic disease which represents a serious public health problem. In Cameroon, efforts to prevent human deaths caused by rabies are often thwarted by the lack of community awareness. The community knowledge, as well as attitudes and perception on rabies, is therefore important for both prevention of human deaths and control in animals.

METHODS

A cross-sectional study was carried out to evaluate the level of community knowledge as well as the role of open garbage dumps (OGDs) in the epidemiology of human rabies. Overall 420 heads of household were interviewed in the Biyem-Assi health district of Yaoundé. OGDs were identified through a systematic check, and household wastes they contained were characterized.

RESULTS

Although 66.9% of respondents have knowledge on stray dogs, only 35% of respondents knew the role of OGDs in the increase of stray dog population. Overall OGDs consisted of fermentable wastes. Nutrition places for stray dogs were wild garbage dumps (68.1%), markets (18.3%), and houses (13.6%). The feeding behavior of stray dogs correlated significantly with the human rabies transmission (χ (2)=154.12, df=4, p<0.05).

CONCLUSION

Most participants knew that rabies could be transmitted by a dog bite as well as the measures to be taken in this type of situation. Increased knowledge of respondents on rabies showed OGDs and stray dogs as significant risk factors for canine rabies in Biyem-Assi health district.

Density-related effects on the infectivity and aggressiveness of a sterilising smut in a wild population of Digitaria sanguinalis

Understanding host-pathogen evolutionary dynamics needs characterisation and quantification of processes occurring at many spatiotemporal scales. With this aim, the effects of smut on a naturally infected population of the summer annual Digitaria sanguinalis were followed for 4 years in an uncropped field. The main purpose of the study was to quantify the effects of within-population density on the infectivity and the aggressiveness of the pathogen in a range of densities that occurred naturally. The infectivity-related variable measured was the proportion of smutted plants at the end of each growing season; proportions were analysed using a generalised linear model with a binomial distribution considering the year, the density and their interaction as effects. The aggressiveness-related variables chosen were the number of smutted inflorescences per plant and per area, obtained over the last 2 years; they were analysed by means of ancova considering disease status (seeded or smutted), year, density and all the interactions between them. Although the disease is monocyclic, results showed clearly that infectivity increased with plant density. The number of inflorescences per plant was 1.5 times higher in smutted plants than in healthy plants throughout the range of densities. This variable declined when density increased, but as the infectivity increased at a higher rate, the aggressiveness also increased with density. The surprising results on infectivity are discussed in the context of current knowledge of plant-pathogen interaction dynamics, as well as neighbour effects on pathogen aggressiveness. Moreover, the results could be useful to develop weed biological control strategies.

Spatial dynamics of bovine tuberculosis in the Autonomous Community of Madrid, Spain (2010-2012)

Progress in control of bovine tuberculosis (bTB) is often not uniform, usually due to the effect of one or more sometimes unknown epidemiological factors impairing the success of eradication programs. Use of spatial analysis can help to identify clusters of persistence of disease, leading to the identification of these factors thus allowing the implementation of targeted control measures, and may provide some insights of disease transmission, particularly when combined with molecular typing techniques. Here, the spatial dynamics of bTB in a high prevalence region of Spain were assessed during a three year period (2010-2012) using data from the eradication campaigns to detect clusters of positive bTB herds and of those infected with certain Mycobacterium bovis strains (characterized using spoligotyping and VNTR typing). In addition, the within-herd transmission coefficient (β) was estimated in infected herds and its spatial distribution and association with other potential outbreak and herd variables was evaluated. Significant clustering of positive herds was identified in the three years of the study in the same location ("high risk area"). Three spoligotypes (SB0339, SB0121 and SB1142) accounted for >70% of the outbreaks detected in the three years. VNTR subtyping revealed the presence of few but highly prevalent strains within the high risk area, suggesting maintained transmission in the area. The spatial autocorrelation found in the distribution of the estimated within-herd transmission coefficients in herds located within distances <14 km and the results of the spatial regression analysis, support the hypothesis of shared local factors affecting disease transmission in farms located at a close proximity.

Immuno-epidemiological modeling of HIV-1 predicts high heritability of the set-point virus load, while selection for CTL escape dominates virulence evolution

It has been suggested that HIV-1 has evolved its set-point virus load to be optimized for transmission. Previous epidemiological models and studies into the heritability of set-point virus load confirm that this mode of adaptation within the human population is feasible. However, during the many cycles of replication between infection of a host and transmission to the next host, HIV-1 is under selection for escape from immune responses, and not transmission. Here we investigate with computational and mathematical models how these two levels of selection, within-host and between-host, are intertwined. We find that when the rate of immune escape is comparable to what has been observed in patients, immune selection within hosts is dominant over selection for transmission. Surprisingly, we do find high values for set-point virus load heritability, and argue that high heritability estimates can be caused by the 'footprints' left by differing hosts' immune systems on the virus.

Responses of small mammals to habitat fragmentation: epidemiological considerations for rodent-borne hantaviruses in the Americas

Rodent-borne hantaviruses are a group of zoonotic agents that cause hemorrhagic fever in humans. The transmission of hantaviruses among rodent hosts may be higher with the increase of reservoir host abundance in a given area (density-dependent transmission) and with the decrease of small mammal diversity (dilution effect phenomenon). These population and community parameters may be modified by habitat fragmentation; however, studies that focus on fragmentation and its effect on hantavirus infection risk are scarce. To further understanding of this issue, we assessed some population and community responses of rodents that may increase the risk for hantavirus transmission among wildlife hosts in the Americas. We conducted a meta-analysis of published studies to assess the responses of small mammals to fragmentation of native habitats, relative to patch size. Our analyses included five countries and 14 case studies for abundance of reservoir hosts (8 species) and 15 case studies for species richness. We found that a reduction of patch area due to habitat fragmentation is associated with increased reservoir host abundances and decreased small mammal richness, which is mainly due to the loss of non-host small mammals. According to these results, habitat fragmentation in the Americas should be considered as an epidemiological risk factor for hantavirus transmission to humans. These findings are important to assess potential risk of infection when fragmentation of native habitats occurs.

DYNAMICS ANALYSIS OF A VACCINATION MODEL FOR HPV TRANSMISSION

A new deterministic model for the transmission dynamics of human papillomavirus (HPV) and related cancers, in the presence of the Gardasil vaccine (which targets four HPV types), is presented. In the absence of routine vaccination in the community, the model is shown to undergo the phenomenon of backward bifurcation. This phenomenon, which has important consequences on the feasibility of effective disease control in the community, arises due to the re-infection of recovered individuals. For the special case when backward bifurcation does not occur, the disease-free equilibrium (DFE) of the model is shown to be globally-asymptotically stable (GAS) if the associated reproduction number is less than unity. The model with vaccination is also rigorously analyzed. Numerical simulations of the model with vaccination show that, with the assumed 90% efficacy of the Gardasil vaccine, the effective community-wide control of the four Gardasil-preventable HPV types is feasible if the Gardasil coverage rate is high enough (in the range 78–88%).

Complex system modelling for veterinary epidemiology

The use of mathematical models has a long tradition in infectious disease epidemiology. The nonlinear dynamics and complexity of pathogen transmission pose challenges in understanding its key determinants, in identifying critical points, and designing effective mitigation strategies. Mathematical modelling provides tools to explicitly represent the variability, interconnectedness, and complexity of systems, and has contributed to numerous insights and theoretical advances in disease transmission, as well as to changes in public policy, health practice, and management. In recent years, our modelling toolbox has considerably expanded due to the advancements in computing power and the need to model novel data generated by technologies such as proximity loggers and global positioning systems. In this review, we discuss the principles, advantages, and challenges associated with the most recent modelling approaches used in systems science, the interdisciplinary study of complex systems, including agent-based, network and compartmental modelling. Agent-based modelling is a powerful simulation technique that considers the individual behaviours of system components by defining a set of rules that govern how individuals ("agents") within given populations interact with one another and the environment. Agent-based models have become a recent popular choice in epidemiology to model hierarchical systems and address complex spatio-temporal dynamics because of their ability to integrate multiple scales and datasets.

Modeling the potential impact of host population survival on the evolution of M. tuberculosis latency

Tuberculosis (TB) is an infectious disease with a peculiar feature: Upon infection with the causative agent, Mycobacterium Tuberculosis (MTB), most hosts enter a latent state during which no transmission of MTB to new hosts occurs. Only a fraction of latently infected hosts develop TB disease and can potentially infect new hosts. At first glance, this seems like a waste of transmission potential and therefore an evolutionary suboptimal strategy for MTB. It might be that the human immune response keeps MTB in check in most hosts, thereby preventing it from achieving its evolutionary optimum. Another possible explanation is that long latency and progression to disease in only a fraction of hosts are evolutionary beneficial to MTB by allowing it to persist better in small host populations. Given that MTB has co-evolved with human hosts for millenia or longer, it likely encountered small host populations for a large share of its evolutionary history and had to evolve strategies of persistence. Here, we use a mathematical model to show that indeed, MTB persistence is optimal for an intermediate duration of latency and level of activation. The predicted optimal level of activation is above the observed value, suggesting that human co-evolution has lead to host immunity, which keeps MTB below its evolutionary optimum.

Horizontal transmission of a parasite is influenced by infected host phenotype and density

Transmission is a key determinant of parasite fitness, and understanding the dynamics of transmission is fundamental to the ecology and evolution of host-parasite interactions. Successful transmission is often reliant on contact between infected individuals and susceptible hosts. The social insects consist of aggregated groups of genetically similar hosts, making them particularly vulnerable to parasite transmission. Here we investigate how the ratio of infected to susceptible individuals impacts parasite transmission, using the honey bee, Apis mellifera and its microsporidian parasite Nosema ceranae. We used 2 types of infected hosts found simultaneously in colonies; sterile female workers and sexual males. We found a higher ratio of infected to susceptible individuals in groups resulted in a greater proportion of susceptibles becoming infected, but this effect was non-linear and interestingly, the ratio also affected the spore production of infected individuals. The transmission level was much greater in an experiment where the infected individuals were drones than in an experiment where they were workers, suggesting drones may act as intracolonial 'superspreaders'. Understanding the subtleties of transmission and how it is influenced by the phenotype of the infected/susceptible individuals is important for understanding pathogen transmission at population level, and for optimum targeting of parasite control strategies.

Epidemic process over the commute network in a metropolitan area

An understanding of epidemiological dynamics is important for prevention and control of epidemic outbreaks. However, previous studies tend to focus only on specific areas, indicating that application to another area or intervention strategy requires a similar time-consuming simulation. Here, we study the epidemic dynamics of the disease-spread over a commute network, using the Tokyo metropolitan area as an example, in an attempt to elucidate the general properties of epidemic spread over a commute network that could be used for a prediction in any metropolitan area. The model is formulated on the basis of a metapopulation network in which local populations are interconnected by actual commuter flows in the Tokyo metropolitan area and the spread of infection is simulated by an individual-based model. We find that the probability of a global epidemic as well as the final epidemic sizes in both global and local populations, the timing of the epidemic peak, and the time at which the epidemic reaches a local population are mainly determined by the joint distribution of the local population sizes connected by the commuter flows, but are insensitive to geographical or topological structure of the network. Moreover, there is a strong relation between the population size and the time that the epidemic reaches this local population and we are able to determine the reason for this relation as well as its dependence on the commute network structure and epidemic parameters. This study shows that the model based on the connection between the population size classes is sufficient to predict both global and local epidemic dynamics in metropolitan area. Moreover, the clear relation of the time taken by the epidemic to reach each local population can be used as a novel measure for intervention; this enables efficient intervention strategies in each local population prior to the actual arrival.

Bovine tuberculosis: within-herd transmission models to support and direct the decision-making process

Use of mathematical models to study the transmission dynamics of infectious diseases is becoming increasingly common in veterinary sciences. However, modeling chronic infectious diseases such as bovine tuberculosis (bTB) is particularly challenging due to the substantial uncertainty associated with the epidemiology of the disease. Here, the methodological approaches used to model bTB and published in the peer-reviewed literature in the last decades were reviewed with a focus on the impact that the models' assumptions may have had on their results, such as the assumption of density vs. frequency-dependent transmission, the existence of non-infectious and non-detectable stages, and the effect of extrinsic sources of infection (usually associated with wildlife reservoirs). Although all studies suggested a relatively low rate of within-herd transmission of bTB when test-and-cull programs are in place, differences in the estimated length of the infection stages, sensitivity and specificity of the tests used and probable type of transmission (density or frequency dependent) were observed. Additional improvements, such as exploring the usefulness of contact-networks instead of assuming homogeneous mixing of animals, may help to build better models that can help to design, evaluate and monitor control and eradication strategies against bTB.

Transmission of chronic wasting disease in Wisconsin white-tailed deer: implications for disease spread and management

Few studies have evaluated the rate of infection or mode of transmission for wildlife diseases, and the implications of alternative management strategies. We used hunter harvest data from 2002 to 2013 to investigate chronic wasting disease (CWD) infection rate and transmission modes, and address how alternative management approaches affect disease dynamics in a Wisconsin white-tailed deer population. Uncertainty regarding demographic impacts of CWD on cervid populations, human and domestic animal health concerns, and potential economic consequences underscore the need for strategies to control CWD distribution and prevalence. Using maximum-likelihood methods to evaluate alternative multi-state deterministic models of CWD transmission, harvest data strongly supports a frequency-dependent transmission structure with sex-specific infection rates that are two times higher in males than females. As transmissible spongiform encephalopathies are an important and difficult-to-study class of diseases with major economic and ecological implications, our work supports the hypothesis of frequency-dependent transmission in wild deer at a broad spatial scale and indicates that effective harvest management can be implemented to control CWD prevalence. Specifically, we show that harvest focused on the greater-affected sex (males) can result in stable population dynamics and control of CWD within the next 50 years, given the constraints of the model. We also provide a quantitative estimate of geographic disease spread in southern Wisconsin, validating qualitative assessments that CWD spreads relatively slowly. Given increased discovery and distribution of CWD throughout North America, insights from our study are valuable to management agencies and to the general public concerned about the impacts of CWD on white-tailed deer populations.

Elevation, temperature, and aquatic connectivity all influence the infection dynamics of the amphibian chytrid fungus in adult frogs

Infectious diseases can cause population declines and even extinctions. The amphibian chytrid fungus, Batrachochytrium dendrobatidis (Bd), has caused population declines and extinctions in amphibians on most continents. In the tropics, research on the dynamics of this disease has focused on amphibian populations in mountainous areas. In most of these areas, high and low elevation sites are connected by an assemblage of streams that may transport the infectious stage of the pathogen from high to low elevations, and, also, this pathogen, which grows well at cool temperatures, may persist better in cooler water flowing from high elevations. Thus, the dynamics of disease at low elevation sites without aquatic connections to higher elevation sites, i.e., non-contiguous low elevation sites, may differ from dynamics at contiguous low elevation sites. We sampled adult common mistfrogs (Litoria rheocola) at six sites of three types: two at high (> 400m) elevations, two at low elevations contiguous with high elevation streams, and two at low elevations non-contiguous with any high elevation site. Adults were swabbed for Bd diagnosis from June 2010 to June 2011 in each season, over a total of five sampling periods. The prevalence of Bd fluctuated seasonally and was highest in winter across all site types. Site type significantly affected seasonal patterns of prevalence of Bd. Prevalence remained well above zero throughout the year at the high elevation sites. Prevalence declined to lower levels in contiguous low sites, and reached near-zero at non-contiguous low sites. Patterns of air temperature fluctuation were very similar at both the low elevation site types, suggesting that differences in water connectivity to high sites may have affected the seasonal dynamics of Bd prevalence between contiguous and non-contiguous low elevation site types. Our results also suggest that reservoir hosts may be important in the persistence of disease at low elevations.

Modeling seasonal behavior changes and disease transmission with application to chronic wasting disease

Behavior and habitat of wildlife animals change seasonally according to environmental conditions. Mathematical models need to represent this seasonality to be able to make realistic predictions about the future of a population and the effectiveness of human interventions. Managing and modeling disease in wild animal populations requires particular care in that disease transmission dynamics is a critical consideration in the etiology of both human and animal diseases, with different transmission paradigms requiring different disease risk management strategies. Since transmission of infectious diseases among wildlife depends strongly on social behavior, mechanisms of disease transmission could also change seasonally. A specific consideration in this regard confronted by modellers is whether the contact rate between individuals is density-dependent or frequency-dependent. We argue that seasonal behavior changes could lead to a seasonal shift between density and frequency dependence. This hypothesis is explored in the case of chronic wasting disease (CWD), a fatal disease that affects deer, elk and moose in many areas of North America. Specifically, we introduce a strategic CWD risk model based on direct disease transmission that accounts for the seasonal change in the transmission dynamics and habitats occupied, guided by information derived from cervid ecology. The model is composed of summer and winter susceptible-infected (SI) equations, with frequency-dependent and density-dependent transmission dynamics, respectively. The model includes impulsive birth events with density-dependent birth rate. We determine the basic reproduction number as a weighted average of two seasonal reproduction numbers. We parameterize the model from data derived from the scientific literature on CWD and deer ecology, and conduct global and local sensitivity analyses of the basic reproduction number. We explore the effectiveness of different culling strategies for the management of CWD: although summer culling seems to be an effective disease eradication strategy, the total culling rate is limited by the requirement to preserve the herd.

Mapping the distribution of the main host for plague in a complex landscape in Kazakhstan: An object-based approach using SPOT-5 XS, Landsat 7 ETM+, SRTM and multiple Random Forests

Plague is a zoonotic infectious disease present in great gerbil populations in Kazakhstan. Infectious disease dynamics are influenced by the spatial distribution of the carriers (hosts) of the disease. The great gerbil, the main host in our study area, lives in burrows, which can be recognized on high resolution satellite imagery. In this study, using earth observation data at various spatial scales, we map the spatial distribution of burrows in a semi-desert landscape.

The study area consists of various landscape types. To evaluate whether identification of burrows by classification is possible in these landscape types, the study area was subdivided into eight landscape units, on the basis of Landsat 7 ETM+ derived Tasselled Cap Greenness and Brightness, and SRTM derived standard deviation in elevation.

In the field, 904 burrows were mapped. Using two segmented 2.5 m resolution SPOT-5 XS satellite scenes, reference object sets were created. Random Forests were built for both SPOT scenes and used to classify the images. Additionally, a stratified classification was carried out, by building separate Random Forests per landscape unit.

Burrows were successfully classified in all landscape units. In the ‘steppe on floodplain’ areas, classification worked best: producer's and user's accuracy in those areas reached 88% and 100%, respectively. In the ‘floodplain’ areas with a more heterogeneous vegetation cover, classification worked least well; there, accuracies were 86 and 58% respectively. Stratified classification improved the results in all landscape units where comparison was possible (four), increasing kappa coefficients by 13, 10, 9 and 1%, respectively.

In this study, an innovative stratification method using high- and medium resolution imagery was applied in order to map host distribution on a large spatial scale. The burrow maps we developed will help to detect changes in the distribution of great gerbil populations and, moreover, serve as a unique empirical data set which can be used as input for epidemiological plague models. This is an important step in understanding the dynamics of plague.

Nearest-neighbor interactions, habitat fragmentation, and the persistence of host-pathogen systems

Spatial interactions are known to promote stability and persistence in enemy-victim interactions if instability and extinction occur in well-mixed settings. We investigate the effect of spatial interactions in the opposite case, where populations can persist in well-mixed systems. A stochastic agent-based model of host-pathogen dynamics is considered that describes nearest-neighbor interactions in an undivided habitat. Contrary to previous notions, we find that in this setting, spatial interactions in fact promote extinction. The reason is that, in contrast to the mass-action system, the outcome of the nearest-neighbor model is governed by dynamics in small "local neighborhoods." This is an abstraction that describes interactions in a minimal grid consisting of an individual plus its nearest neighbors. The small size of this characteristic scale accounts for the higher extinction probabilities. Hence, nearest-neighbor interactions in a continuous habitat lead to outcomes reminiscent of a fragmented habitat, which is underlined further with a metapopulation model that explicitly assumes habitat fragmentation. Beyond host-pathogen dynamics, axiomatic modeling shows that our results hold for generic enemy-victim interactions under specified assumptions. These results are used to interpret a set of published experiments that provide a first step toward model testing and are discussed in the context of the literature.

The scaling of contact rates with population density for the infectious disease models

Contact rates and patterns among individuals in a geographic area drive transmission of directly-transmitted pathogens, making it essential to understand and estimate contacts for simulation of disease dynamics. Under the uniform mixing assumption, one of two mechanisms is typically used to describe the relation between contact rate and population density: density-dependent or frequency-dependent. Based on existing evidence of population threshold and human mobility patterns, we formulated a spatial contact model to describe the appropriate form of transmission with initial growth at low density and saturation at higher density. We show that the two mechanisms are extreme cases that do not capture real population movement across all scales. Empirical data of human and wildlife diseases indicate that a nonlinear function may work better when looking at the full spectrum of densities. This estimation can be applied to large areas with population mixing in general activities. For crowds with unusually large densities (e.g., transportation terminals, stadiums, or mass gatherings), the lack of organized social contact structure deviates the physical contacts towards a special case of the spatial contact model - the dynamics of kinetic gas molecule collision. In this case, an ideal gas model with van der Waals correction fits well; existing movement observation data and the contact rate between individuals is estimated using kinetic theory. A complete picture of contact rate scaling with population density may help clarify the definition of transmission rates in heterogeneous, large-scale spatial systems.