Thresholds for disease persistence in models for tick-borne infections including non-viraemic transmission,extended feeding and tick aggregation

Lyme disease and Tick-Borne Encephalitis (TBE) are two emergent tick-borne diseases transmitted by the widely distributed European tick Ixodes ricinus. The life cycle of the vector and the number of hosts involved requires the development of complex models which consider different routes of pathogen transmission including those occurring between ticks that co-feed on the same host. Hence, we consider here a general model for tick-borne infections. We assumed ticks feed on two types of host species, one competent for viraemic transmission of infection, the second incompetent but included a third transmission route through non-viraemic transmission between ticks co-feeding on the same host. Since a blood meal lasts for several days these routes could lead to interesting nonlinearities in transmission rates, which may have important effects.We derive an explicit formula for the threshold for disease persistence in the case of viraemic transmission, also for the case of viraemic and non-viraemic transmission. From this formula, the effect of parameters on the persistence of infection can be determined. When only viraemic transmission occurs, we confirm that, while the density of the competent host has always a positive effect on infection persistence, the density of the incompetent host may have either a positive effect, by amplifying tick population, or a negative ("dilution") effect, by wasting tick bites on an incompetent host. With non-viraemic transmission, the "dilution" effect becomes less relevant. On the other hand, if the nonlinearity due to extended feeding is included, the dilution effect always occurs, but often at unrealistically high host densities. Finally, we incorporated the effects of tick aggregation on the hosts and correlation of tick stages and found that both had an important effect on infection persistence, if non-viraemic transmission occurred.     

Seasonal population dynamics of ticks, and their influence on infection transmission: a semi-discrete approach

A semi-discrete model for tick population dynamics is presented, whereby tick feeding is assumed to occur only during summers of each year. Conditions for existence, uniqueness, and stability of a positive equilibrium were found; the system was then studied numerically using parameter estimates calibrated for the tick Ixodes ricinus in Trentino, Italy, and the sensitivity to parameters was examined. This model was then extended to consider tick-transmitted infection of one species of hosts, while other hosts are incompetent to the infection. Assuming, for simplicity, that the infection is not affecting the total number of either hosts or ticks, a threshold condition for infection persistence was obtained. The dependence of the equilibrium infection prevalence on parameters was studied numerically; in particular, we considered how infection prevalence depends on host densities. This analysis reveals that a dilution effect occurs both for competent and for incompetent hosts. This means that, besides a lower threshold for host densities for infection to persists, there also exists an upper threshold: if host densities were higher than the upper threshold, the infection would go to extinction. Numerically, it was found that the upper threshold was not much higher than observed densities for realistic parameter values.     

Effect of deer density on tick infestation of rodents and the hazard of tick-borne encephalitis. II: population and infection models

Tick-borne encephalitis is an emerging vector-borne zoonotic disease reported in several European and Asiatic countries with complex transmission routes that involve various vertebrate host species other than a tick vector. Understanding and quantifying the contribution of the different hosts involved in the TBE virus cycle is crucial in estimating the threshold conditions for virus emergence and spread. Some hosts, such as rodents, act both as feeding hosts for ticks and reservoirs of the infection. Other species, such as deer, provide important sources of blood for feeding ticks but they do not support TBE virus transmission, acting instead as dead-end (i.e., incompetent) hosts. Here, we introduce an eco-epidemiological model to explore the dynamics of tick populations and TBE virus infection in relation to the density of two key hosts. In particular, our aim is to validate and interpret in a robust theoretical framework the empirical findings regarding the effect of deer density on tick infestation on rodents and thus TBE virus occurrence from selected European foci. Model results show hump-shaped relationships between deer density and both feeding ticks on rodents and the basic reproduction number for TBE virus. This suggests that deer may act as tick amplifiers, but may also divert tick bites from competent hosts, thus diluting pathogen transmission. However, our model shows that the mechanism responsible for the dilution effect is more complex than the simple reduction of tick burden on competent hosts. Indeed, while the number of feeding ticks on rodents may increase with deer density, the proportion of blood meals on competent compared with incompetent hosts may decrease, triggering a decline in infection. As a consequence, using simply the number of ticks per rodent as a predictor of TBE transmission potential could be misleading if competent hosts share habitats with incompetent hosts.     

Seasonal population dynamics of ticks,and its influence on infection transmission: A semi-discrete approach

In this paper, a simple semi-discrete (ticks’ feeding is assumed to occur only during the summers of each year) model for tick population dynamics is presented. Conditions for existence, uniqueness, and stability of a positive equilibrium are found; the system is then studied numerically using parameter estimates calibrated for the tick Ixodes ricinus in Trentino, Italy, and the sensitivity to parameters is examined. Then, this model is extended to consider a tick-transmitted infection of one species of hosts, while other hosts are incompetent to the infection. Assuming, for simplicity, that the infection is not affecting the total number either of hosts or ticks, a threshold condition for infection persistence is obtained. The dependence of the equilibrium infection prevalence on parameters is studied numerically; in particular, we considered how infection prevalence depends on host densities. This analysis reveals that a ‘dilution effect’ occurs both for competent and for incompetent hosts; this means that, besides a lower threshold for host densities for infection to persist, there exists also an upper threshold: if host densities were higher than the upper threshold, the infection would go to extinction. Numerically, it is found that, for realistic parameter values, the upper threshold is not much higher than observed densities.     

Ecology of Borrelia burgdorferi sensu lato in Europe: transmission dynamics in multi-host systems, influence of molecular processes and effects of climate change

The analysis of different multi-host systems suggests that even hosts that are not capable of transmitting Borrelia burgdorferi sensu lato (s.l.) to the tick vector, Ixodes ricinus, or that are secondary reservoirs for these agents contribute to the intensity of transmission and to the overall risk of Lyme borreliosis, through the process of vector augmentation and pathogen amplification. On the other hand, above certain threshold densities, or in the presence of competition with primary reservoir hosts or low attachment rate of ticks to reservoir hosts, incompetent or less competent hosts may reduce transmission through dilution. The transmission of B. burgdorferi s.l. is affected by molecular processes at the tick-host interface including mechanisms for the protection of spirochaetes against the host's immune response. Molecular biology also increasingly provides important identification tools for the study of tick-borne disease agents. Ixodes ricinus and B. burgdorferi s.l. are expanding their geographical range to northern latitudes and to higher altitudes through the effects of climate change on host populations and on tick development, survival and seasonal activity. The integration of quantitative ecology with molecular methodology is central to a better understanding of the factors that determine the main components of Lyme borreliosis eco-epidemiology and should result in more accurate predictions of the effects of climate change on the circulation of pathogens in nature.     

Persistence of Pathogens with Short Infectious Periods in Seasonal Tick Populations: The Relative Importance of Three Transmission Routes

Background

The flaviviruses causing tick-borne encephalitis (TBE) persist at low but consistent levels in tick populations, despite short infectious periods in their mammalian hosts and transmission periods constrained by distinctly seasonal tick life cycles. In addition to systemic and vertical transmission, cofeeding transmission has been proposed as an important route for the persistence of TBE-causing viruses. Because cofeeding transmission requires ticks to feed simultaneously, the timing of tick activity may be critical to pathogen persistence. Existing models of tick-borne diseases do not incorporate all transmission routes and tick seasonality. Our aim is to evaluate the influence of seasonality on the relative importance of different transmission routes by using a comprehensive mathematical model.

Methodology/Principal Findings

We developed a stage-structured population model that includes tick seasonality and evaluated the relative importance of the transmission routes for pathogens with short infectious periods, in particular Powassan virus (POWV) and the related “deer tick virus,” emergent encephalitis-causing flaviviruses in North America. We used the next generation matrix method to calculate the basic reproductive ratio and performed elasticity analyses. We confirmed that cofeeding transmission is critically important for such pathogens to persist in seasonal tick populations over the reasonable range of parameter values. At higher but still plausible rates of vertical transmission, our model suggests that vertical transmission can strongly enhance pathogen prevalence when it operates in combination with cofeeding transmission.

Conclusions/Significance

Our results demonstrate that the consistent prevalence of POWV observed in tick populations could be maintained by a combination of low vertical, intermediate cofeeding and high systemic transmission rates. When vertical transmission is weak, nymphal ticks support integral parts of the transmission cycle that are critical for maintaining the pathogen. We also extended the model to pathogens that cause chronic infections in hosts and found that cofeeding transmission could contribute to elevating prevalence even in these systems. Therefore, the common assumption that cofeeding transmission is not relevant in models of chronic host infection, such as Lyme disease, could lead to underestimating pathogen prevalence.     

Attachment site selection of ticks on roe deer, <Emphasis Type="Italic">Capreolus capreolus</Emphasis>

The spatio-temporal attachment site patterns of ticks feeding on their hosts can be of significance if co-feeding transmission (i.e. from tick to tick without a systemic infection of the host) of pathogens affects the persistence of a given disease. Using tick infestation data on roe deer, we analysed preferred attachment sites and niche width of Ixodes ticks (larvae, nymphs, males, females) and investigated the degree of inter- and intrastadial aggregation. The different development stages showed rather consistent attachment site patterns and relative narrow feeding site niches. Larvae were mostly found on the head and on the front legs of roe deer, nymphs reached highest densities on the head and highest adult densities were found on the neck of roe deer. The tick stages feeding (larvae, nymphs, females) on roe deer showed high degrees of intrastadial spatial aggregation, whereas males did not. Male ticks showed large feeding site overlap with female ticks. Feeding site overlap between larval-female and larval-nymphal ticks did occur especially during the months May–August on the head and front legs of roe deer and might allow pathogen transmission via co-feeding. Tick density, niche width and niche overlap on roe deer are mainly affected by seasonality, reflecting seasonal activity and abundance patterns of ticks. Since different tick development stages occur spatially and temporally clustered on roe deer, transmission experiments of tick-borne pathogens are urgently needed.     

The Relationship between Host Lifespan and Pathogen Reservoir Potential: An Analysis in the System Arabidopsis thaliana-Cucumber mosaic virus

Identification of the determinants of pathogen reservoir potential is central to understand disease emergence. It has been proposed that host lifespan is one such determinant: short-lived hosts will invest less in costly defenses against pathogens, so that they will be more susceptible to infection, more competent as sources of infection and/or will sustain larger vector populations, thus being effective reservoirs for the infection of long-lived hosts. This hypothesis is sustained by analyses of different hosts of multihost pathogens, but not of different genotypes of the same host species. Here we examined this hypothesis by comparing two genotypes of the plant Arabidopsis thaliana that differ largely both in life-span and in tolerance to its natural pathogen Cucumber mosaic virus (CMV). Experiments with the aphid vector Myzus persicae showed that both genotypes were similarly competent as sources for virus transmission, but the short-lived genotype was more susceptible to infection and was able to sustain larger vector populations. To explore how differences in defense against CMV and its vector relate to reservoir potential, we developed a model that was run for a set of experimentally-determined parameters, and for a realistic range of host plant and vector population densities. Model simulations showed that the less efficient defenses of the short-lived genotype resulted in higher reservoir potential, which in heterogeneous host populations may be balanced by the longer infectious period of the long-lived genotype. This balance was modulated by the demography of both host and vector populations, and by the genetic composition of the host population. Thus, within-species genetic diversity for lifespan and defenses against pathogens will result in polymorphisms for pathogen reservoir potential, which will condition within-population infection dynamics. These results are relevant for a better understanding of host-pathogen co-evolution, and of the dynamics of pathogen emergence.     

Impact of biodiversity and seasonality on Lyme-pathogen transmission

Lyme disease imposes increasing global public health challenges. To better understand the joint effects of seasonal temperature variation and host community composition on the pathogen transmission, a stage-structured periodic model is proposed by integrating seasonal tick development and activity, multiple host species and complex pathogen transmission routes between ticks and reservoirs. Two thresholds, one for tick population dynamics and the other for Lyme-pathogen transmission dynamics, are identified and shown to fully classify the long-term outcomes of the tick invasion and disease persistence. Seeding with the realistic parameters, the tick reproduction threshold and Lyme disease spread threshold are estimated to illustrate the joint effects of the climate change and host community diversity on the pattern of Lyme disease risk. It is shown that climate warming can amplify the disease risk and slightly change the seasonality of disease risk. Both the “dilution effect” and “amplification effect” are observed by feeding the model with different possible alternative hosts. Therefore, the relationship between the host community biodiversity and disease risk varies, calling for more accurate measurements on the local environment, both biotic and abiotic such as the temperature and the host community composition.     

Population dynamics of plant-parasite interactions: thresholds for invasion

Thresholds are derived for the invasion of plant populations by parasites. The theory is developed for a generic model that takes into account two features characteristic of plant-parasite interactions: a dual source of inoculum (infection from primary or externally introduced inoculum and secondary infection from contact between susceptible and infected host tissue) and a host response to infection load. Each of the threshold criteria is shown to be the sum of the individual components for primary and secondary infection. This indicates that if parasite invasion is not possible through primary or secondary infection alone, when the two modes of transmission are combined, the parasite may be able to invade. The invasion criteria demonstrate that there is a threshold population of susceptible hosts below which the parasite is unable to invade. If there are nonlinearities in the population dynamics (arising through either the transmission process or the host response), there are also threshold densities for the infected hosts and parasite populations below which invasion does not occur. The implications of the results for the control of plant disease are discussed.     

Maternal antibodies contribute to sex-based difference in hantavirus transmission dynamics

Individuals often differ in their ability to transmit disease and identifying key individuals for transmission is a major issue in epidemiology. Male hosts are often thought to be more important than females for parasite transmission and persistence. However, the role of infectious females, particularly the transient immunity provided to offspring through maternal antibodies (MatAbs), has been neglected in discussions about sex-biased infection transmission. We examined the effect of host sex upon infection dynamics of zoonotic Puumala hantavirus (PUUV) in semi-natural, experimental populations of bank vole (Myodes glareolus). Populations were founded with either females or males that were infected with PUUV, whereas the other sex was immunized against PUUV infection. The likelihood of the next generation being infected was lower when the infected founders were females, underlying the putative importance of adult males in PUUV transmission and persistence in host populations. However, we show that this effect probably results from transient immunity that infected females provide to their offspring, rather than any sex-biased transmission efficiency per se. Our study proposes a potential contrasting nature of female and male hosts in the transmission dynamics of hantaviruses.     

Effect of host populations on the intensity of ticks and the prevalence of tick-borne pathogens: how to interpret the results of deer exclosure experiments

Deer are important blood hosts for feeding Ixodes ricinus ticks but they do not support transmission of many tick-borne pathogens, so acting as dead-end transmission hosts. Mathematical models show their role as tick amplifiers, but also suggest that they dilute pathogen transmission, thus reducing infection prevalence. Empirical evidence for this is conflicting: experimental plots with deer removal (i.e. deer exclosures) show that the effect depends on the size of the exclosure. Here we present simulations of dynamic models that take into account different tick stages, and several host species (e.g. rodents) that may move to and from deer exclosures; models were calibrated with respect to Ixodes ricinus ticks and tick-borne encephalitis (TBE) in Trentino (northern Italy). Results show that in small exclosures, the density of rodent-feeding ticks may be higher inside than outside, whereas in large exclosures, a reduction of such tick density may be reached. Similarly, TBE prevalence in rodents decreases in large exclosures and may be slightly higher in small exclosures than outside them. The density of infected questing nymphs inside small exclosures can be much higher, in our numerical example almost twice as large as that outside, leading to potential TBE infection risk hotspots.     

The influence of host competition and predation on tick densities and management implications

Host community composition and biodiversity can limit and regulate tick abundance which can have profound impacts on the incidence and severity of tick-borne diseases. Our understanding of the relationship between host community composition and tick abundance is still very limited. Here, we present a novel mathematical model of a stage-structured tick population to study the influence of host behaviour and competition in the presence of heterospecifics and the influence of host predation on tick densities. We examine the influence of specific changes in biodiversity that modify the competition among and the predation on small and large host populations. We find that increasing biodiversity will not always reduce tick populations, but depends on changes in species composition affecting the degree and type competition among hosts, and the host the predation is acting on. With indirect competition, tick densities are not regulated by increasing biodiversity; however, with direct competition, increased biodiversity will regulate tick densities. Generally, we find that biodiversity will regulate tick densities when it affects tick-host encounter rates. We also find that predation on small hosts have a limited influence on reducing tick populations, but when the predation was on large hosts this increased the magnitude of tick population oscillations. Our results have tick-management implications: while controlling large host populations (e.g. deer) and adult ticks will decrease tick densities, measures that directly control the nymph ticks could also be effective.     

The evolution of covert,silent infection as a parasite strategy

Many parasites and pathogens cause silent/covert infections in addition to the more obvious infectious disease-causing pathology. Here, we consider how assumptions concerning superinfection, protection and seasonal host birth and transmission rates affect the evolution of such covert infections as a parasite strategy. Regardless of whether there is vertical infection or effects on sterility, overt infection is always disadvantageous in relatively constant host populations unless it provides protection from superinfection. If covert infections are protective, all individuals will enter the covert stage if there is enough vertical transmission, and revert to overt infections after a ‘latent’ period (susceptible, exposed, infected epidemiology). Seasonal variation in transmission rates selects for non-protective covert infections in relatively long-lived hosts with low birth rates typical of many mammals. Variable host population density caused by seasonal birth rates may also select for covert transmission, but in this case it is most likely in short-lived fecund hosts. The covert infections of some insects may therefore be explained by their outbreak population dynamics. However, our models consistently predict proportions of covert infection, which are lower than some of those observed in nature. Higher proportions of covert infection may occur if there is a direct link between covert infection and overt transmission success, the covert infection is protective or the covert state is the result of suppression by the host. Relatively low proportions of covert transmission may, however, be explained as a parasite strategy when transmission opportunities vary.     

Stage-structured infection transmission and a spatial epidemic: a model for Lyme disease

A greater understanding of the rate at which emerging disease advances spatially has both ecological and applied significance. Analyzing the spread of vector-borne disease can be relatively complex when the vector's acquisition of a pathogen and subsequent transmission to a host occur in different life stages. A contemporary example is Lyme disease. A long-lived tick vector acquires infection during the larval blood meal and transmits it as a nymph. We present a reaction-diffusion model for the ecological dynamics governing the velocity of the current epidemic's spread. We find that the equilibrium density of infectious tick nymphs (hence the risk of human disease) can depend on density-independent survival interacting with biotic effects on the tick's stage structure. The local risk of infection reaches a maximum at an intermediate level of adult tick mortality and at an intermediate rate of juvenile tick attacks on mammalian hosts. If the juvenile tick attack rate is low, an increase generates both a greater density of infectious nymphs and an increased spatial velocity. However, if the juvenile attack rate is relatively high, nymph density may decline while the epidemic's velocity still increases. Velocities of simulated two-dimensional epidemics correlate with the model pathogen's basic reproductive number (R0), but calculating R0 involves parameters of both host infection dynamics and the vector's stage-structured dynamics.     

The role of deer in facilitating the spatial spread of the pathogen Borrelia burgdorferi

Borrelia burgdorferi is a vector-bourne zoonosis which propagates in wild populations of rodents and deer. The latter are incompetent for the pathogen but are required for the life cycle of hard-backed ticks which act as a vector for the pathogen. Increasing the diversity of hosts has previously suggested the presence of a ‘dilution effect’ in which such an increase reduces successful pathogen transmission as it increases the chance that a tick will encounter an incompetent host. This paper will produce a model which shows that whilst a dilution effect is possible for a system in which deer are the only incompetent host, this effect is not likely to be strong. Extending the population dynamics to include movement of deer into regions previously only inhabited by competent hosts, we find that, although ticks come in with the deer, there is a significant time lag before Borrelia appears.     

Evidence of the importance of host habitat use in predicting the dilution effect of wild boar for deer exposure to Anaplasma spp

Foci of tick-borne pathogens occur at fine spatial scales, and depend upon a complex arrangement of factors involving climate, host abundance and landscape composition. It has been proposed that the presence of hosts that support tick feeding but not pathogen multiplication may dilute the transmission of the pathogen. However, models need to consider the spatial component to adequately explain how hosts, ticks and pathogens are distributed into the landscape. In this study, a novel, lattice-derived, behavior-based, spatially-explicit model was developed to test how changes in the assumed perception of different landscape elements affect the outcome of the connectivity between patches and therefore the dilution effect. The objective of this study was to explain changes in the exposure rate (ER) of red deer to Anaplasma spp. under different configurations of suitable habitat and landscape fragmentation in the presence of variable densities of the potentially diluting host, wild boar. The model showed that the increase in habitat fragmentation had a deep impact on Habitat Sharing Ratio (HSR), a parameter describing the amount of habitat shared by red deer and wild boar, weighted by the probability of the animals to remain together in the same patch (according to movement rules), the density of ticks and the density of animals at a given vegetation patch, and decreased the dilution effect of wild boar on deer Anaplasma ER. The model was validated with data collected on deer, wild boar and tick densities, climate, landscape composition, host vegetation preferences and deer seropositivity to Anaplasma spp. (as a measure of ER) in 10 study sites in Spain. However, although conditions were appropriate for a dilution effect, empirical results did not show a decrease in deer ER in sites with high wild boar densities. The model showed that the HSR was the most effective parameter to explain the absence of the dilution effect. These results suggest that host habitat usage may weaken the predicted dilution effect for tick-borne pathogens and emphasize the importance of the perceptual capabilities of different hosts in different landscapes and habitat fragmentation conditions for predictions of dilution effects.     

Ecological drivers of African swine fever virus persistence in wild boar populations: Insight for control

Environmental sources of infection can play a primary role in shaping epidemiological dynamics; however, the relative impact of environmental transmission on host‐pathogen systems is rarely estimated. We developed and fit a spatially explicit model of African swine fever virus (ASFV) in wild boar to estimate what proportion of carcass‐based transmission is contributing to the low‐level persistence of ASFV in Eastern European wild boar. Our model was developed based on ecological insight and data from field studies of ASFV and wild boar in Eastern Poland. We predicted that carcass‐based transmission would play a substantial role in persistence, especially in low‐density host populations where contact rates are low. By fitting the model to outbreak data using approximate Bayesian computation, we inferred that between 53% and 66% of transmission events were carcass‐based that is, transmitted through contact of a live host with a contaminated carcass. Model fitting and sensitivity analyses showed that the frequency of carcass‐based transmission increased with decreasing host density, suggesting that management policies should emphasize the removal of carcasses and consider how reductions in host densities may drive carcass‐based transmission. Sensitivity analyses also demonstrated that carcass‐based transmission is necessary for the autonomous persistence of ASFV under realistic parameters. Autonomous persistence through direct transmission alone required high host densities; otherwise re‐introduction of virus periodically was required for persistence when direct transmission probabilities were moderately high. We quantify the relative role of different persistence mechanisms for a low‐prevalence disease using readily collected ecological data and viral surveillance data. Understanding how the frequency of different transmission mechanisms vary across host densities can help identify optimal management strategies across changing ecological conditions.     

Impact of the experimental removal of lizards on Lyme disease risk

The distribution of vector meals in the host community is an important element of understanding and predicting vector-borne disease risk. Lizards (such as the western fence lizard; Sceloporus occidentalis) play a unique role in Lyme disease ecology in the far-western United States. Lizards rather than mammals serve as the blood meal hosts for a large fraction of larval and nymphal western black-legged ticks (Ixodes pacificus--the vector for Lyme disease in that region) but are not competent reservoirs for the pathogen, Borrelia burgdorferi. Prior studies have suggested that the net effect of lizards is to reduce risk of human exposure to Lyme disease, a hypothesis that we tested experimentally. Following experimental removal of lizards, we documented incomplete host switching by larval ticks (5.19%) from lizards to other hosts. Larval tick burdens increased on woodrats, a competent reservoir, but not on deer mice, a less competent pathogen reservoir. However, most larvae failed to find an alternate host. This resulted in significantly lower densities of nymphal ticks the following year. Unexpectedly, the removal of reservoir-incompetent lizards did not cause an increase in nymphal tick infection prevalence. The net result of lizard removal was a decrease in the density of infected nymphal ticks, and therefore a decreased risk to humans of Lyme disease. Our results indicate that an incompetent reservoir for a pathogen may, in fact, increase disease risk through the maintenance of higher vector density and therefore, higher density of infected vectors.