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

The Impact of Host Abundance on the Epidemiology of Tick-Borne Infection

Tick-borne diseases are an increasing global public health concern due to an expanding geographical range and increase in abundance of tick-borne infectious agents. A potential explanation for the rising impact of tick-borne diseases is an increase in tick abundance which may be linked to an increase in density of the hosts on which they feed. In this study, we develop a model framework to understand the link between host density, tick demography and tick-borne pathogen epidemiology. Our model links the development of specific tick stages to the specific hosts on which they feed. We show that host community composition and host density have an impact on tick population dynamics and that this has a consequent impact on host and tick epidemiological dynamics. A key result is that our model framework can exhibit variation in host infection prevalence for a fixed density of one host type due to changes in density of other host types that support different tick life stages. Our findings suggest that host community composition may play a crucial role in explaining the variation in prevalence of tick-borne infections in hosts observed in the field.

A coupled algebraic-delay differential system modeling tick-host interactive behavioural dynamics and multi-stability

We propose a coupled system of delay-algebraic equations to describe tick attaching and host grooming behaviors in the tick-host interface, and use the model to understand how this tick-host interaction impacts the tick population dynamics. We consider two critical state variables, the loads of feeding ticks on host and the engorged ticks on the ground for ticks in a particular development stage (nymphal stage) and show that the model as a coupled system of delay differential equation and an algebraic (integral) equation may have rich structures of equilibrium states, leading to multi-stability. We perform asymptotic analyses and use the implicit function theorem to characterize the stability of these equilibrium states, and show that bi-stability and quadri-stability occur naturally in several combinations of tick attaching and host grooming behaviours. In particular, we show that in the case when host grooming is triggered by the tick biting, the system will have three stable equilibrium states including the extinction state, and two unstable equilibrium states. In addition, the two nontrivial stable equilibrium states correspond to a low attachment rate and a large number of feeding ticks, and a high attachment rate and a small number of feeding ticks, respectively.

STABILITY ANALYSIS AND OPTIMAL CONTROL OF A LYME DISEASE MODEL WITH INSECTICIDES SPRAYING AND VACCINATION

This paper studies an SIS-type Lyme transmission model incorporating insecticides spraying and vaccination as interventions. We obtain the positivity and boundedness of solutions, calculate the basic reproduction number, and discuss the global stability of disease-free and endemic equilibria when the basic reproduction number [Formula: see text] and [Formula: see text], respectively. We apply Pontryagin’s maximum principle to explore an optimal control strategy to minimize the number of infected ticks and hosts and the cost of using insecticides and vaccination. We design numerical simulations to illustrate the effectiveness of theoretical analysis.

Modeling the invasion and establishment of a tick-borne pathogen

We develop a discrete-time tick–host–pathogen model to describe the spread of a disease in a hard-bodied tick species. This model incorporates the developmental stages for a tick, the dependence of the tick life-cycle and disease transmission on host availability, and three sources of pathogen transmission. We first establish the global dynamics of the disease-free system. We then apply the model to two pathogens, Borellia burgdorferi and Anaplasma phagocytophila, using Ixodes ricinus as the tick species to study properties of the invasion and establishment of a disease numerically. In particular, we consider the basic reproduction number, which determines whether a disease can invade the tick-host system, as well as disease prevalence and time to establishment in the case of successful disease invasion. Using Monte Carlo simulations, we calculate the means of each of these disease metrics and their elasticities with respect to various model parameters. We find that increased tick survival may help enable disease invasion, decrease the time to disease establishment, and increase disease prevalence once established. In contrast, though disease invasion is sensitive to tick-to-host transmission and tick searching efficiencies, neither disease prevalence nor time to disease establishment is sensitive to these parameters. These differences emphasize the importance of developing approaches, such as the one highlighted here, that can be used to study disease dynamics beyond just pathogen invasion, including transitional and long-term dynamics.

An eco-epidemiological modeling approach to investigate dilution effect in two different tick-borne pathosystems

Disease (re)emergence appears to be driven by biodiversity decline and environmental change. As a result, it is increasingly important to study host-pathogen interactions within the context of their ecology and evolution. The dilution effect is the concept that higher biodiversity decreases pathogen transmission. It has been observed especially in zoonotic vector-borne pathosystems, yet evidence against it has been found. In particular, it is still debated how the community (dis)assembly assumptions and the degree of generalism of vectors and pathogens affect the direction of the biodiversity-pathogen transmission relationship. The aim of this study was to use empirical data and mechanistic models to investigate dilution mechanisms in two rodent-tick-pathogen systems differing in their vector degree of generalism. A community was assembled to include ecological interactions that expand from purely additive to purely substitutive. Such systems are excellent candidates to analyze the link between vector ecology, community (dis)assembly dynamics, and pathogen transmission. To base our mechanistic models on empirical data, rodent live-trapping, including tick sampling, was conducted in Wales across two seasons for three consecutive years. We have developed a deterministic single-vector, multi-host compartmental model that includes ecological relationships with non-host species, uniquely integrating theoretical and observational approaches. To describe pathogen transmission across a gradient of community diversity, the model was populated with parameters describing five different scenarios differing in ecological complexity; each based around one of the pathosystems: Ixodes ricinus (generalist tick)-Borrelia burgdorferi and I. trianguliceps (small mammals specialist tick)-Babesia microti. The results suggested that community composition and interspecific dynamics affected pathogen transmission with different dilution outcomes depending on the vector degree of generalism. The model provides evidence that dilution and amplification effects are not mutually exclusive in the same community but depend on vector ecology and the epidemiological output considered (i.e., the "risk" of interest). In our scenarios, more functionally diverse communities resulted in fewer infectious rodents, supporting the dilution effect. In the pathosystem with generalist vector we identified a hump shaped relationship between diversity and infections in hosts, while for that characterized by specialist tick, this relationship was more complex and more dependent upon specific parameter values.

Ticks on the Run: A Mathematical Model of Crimean-Congo Haemorrhagic Fever (CCHF)-Key Factors for Transmission

Crimean-Congo haemorrhagic fever (CCHF) is a zoonotic disease caused by the Crimean-Congo hemorrhagic fever virus (CCHFV). Ticks of the genus Hyalomma are the main vectors and represent a reservoir for the virus. CCHF is maintained in nature in an endemic vertebrate-tick-vertebrate cycle. The disease is prevalent in wide geographical areas including Asia, Africa, South-Eastern Europe and the Middle East. It is of great importance for the public health given its occasionally high case/fatality ratio of CCHFV in humans. Climate change and the detection of possible CCHFV vectors in Central Europe suggest that the establishment of the transmission in Central Europe may be possible in future. We have developed a compartment-based nonlinear Ordinary Differential Equation (ODE) system to model the disease transmission cycle including blood sucking ticks, livestock and human. Sensitivity analysis of the basic reproduction number R0 shows that decreasing the tick survival time is an efficient method to control the disease. The model supports us in understanding the influence of different model parameters on the spread of CCHFV. Tick-to-tick transmission through co-feeding and the CCHFV circulation through transstadial and transovarial transmission are important factors to sustain the disease cycle. The proposed model dynamics are calibrated through an empirical multi-country analysis and multidimensional plot reveals that the disease-parameter sets of different countries burdened with CCHF are different. This information may help decision makers to select efficient control strategies.

Long-term transmission dynamics of tick-borne diseases involving seasonal variation and co-feeding transmission

Co-feeding is a mode of pathogen transmission for a wide range of tick-borne diseases where susceptible ticks can acquire infection from co-feeding with infected ticks on the same hosts. The significance of this transmission pathway is determined by the co-occurrence of ticks at different stages in the same season. Taking this into account, we formulate a system of differential equations with tick population dynamics and pathogen transmission dynamics highly regulated by the seasonal temperature variations. We examine the global dynamics of the model systems, and show that the two important ecological and epidemiological basic reproduction numbers can be used to fully characterize the long-term dynamics, and we link these two important threshold values to efficacy of co-feeding transmission.

Host Specialisation, Immune Cross-Reaction and the Composition of Communities of Co-circulating Borrelia Strains

We use mathematical modelling to examine how microbial strain communities are structured by the host specialisation traits and antigenic relationships of their members. The model is quite general and broadly applicable, but we focus on Borrelia burgdorferi, the Lyme disease bacterium, transmitted by ticks to mice and birds. In this system, host specialisation driven by the evasion of innate immunity has been linked to multiple niche polymorphism, while antigenic differentiation driven by the evasion of adaptive immunity has been linked to negative frequency dependence. Our model is composed of two host species, one vector, and multiple co-circulating pathogen strains that vary in their host specificity and their antigenic distances from one another. We explore the conditions required to maintain pathogen diversity. We show that the combination of host specificity and antigenic differentiation creates an intricate niche structure. Unequivocal rules that relate the stability of a strain community directly to the trait composition of its members are elusive. However, broad patterns are evident. When antigenic differentiation is weak, stable communities are typically composed entirely of generalists that can exploit either host species equally well. As antigenic differentiation increases, more diverse stable communities emerge, typically around trait compositions of generalists, generalists and very similar specialists, and specialists roughly balanced between the two host species.

Dynamics of a periodic tick-borne disease model with co-feeding and multiple patches

By extending a mechanistic model for the tick-borne pathogen systemic transmission with the consideration of seasonal climate impacts, host movement as well as the co-feeding transmission route, this paper proposes a novel modeling framework for describing the spatial dynamics of tick-borne diseases. The net reproduction number for tick growth and basic reproduction number for disease transmission are derived, which predict the global dynamics of tick population growth and disease transmission. Numerical simulations not only verify the analytical results, but also characterize the contribution of co-feeding transmission route on disease prevalence in a habitat and the effect of host movement on the spatial spreading of the pathogen.

The potential impact of climate change on the transmission risk of tick-borne encephalitis in Hungary

BACKGROUND

Impact of climate change on tick-borne encephalitis (TBE) prevalence in the tick-host enzootic cycle in a given region depends on how the region-specific climate change patterns influence tick population development processes and tick-borne encephalitis virus (TBEV) transmission dynamics involving both systemic and co-feeding transmission routes. Predicting the transmission risk of TBEV in the enzootic cycle with projected climate conditions is essential for planning public health interventions including vaccination programs to mitigate the TBE incidence in the inhabitants and travelers. We have previously developed and validated a mathematical model for retroactive analysis of weather fluctuation on TBE prevalence in Hungary, and we aim to show in this research that this model provides an effective tool for projecting TBEV transmission risk in the enzootic cycle.

METHODS

Using the established model of TBEV transmission and the climate predictions of the Vas county in western Hungary in 2021-2050 and 2071-2100, we quantify the risk of TBEV transmission using a series of summative indices - the basic reproduction number, the duration of infestation, the stage-specific tick densities, and the accumulated (tick) infections due to co-feeding transmission. We also measure the significance of co-feeding transmission by observing the cumulative number of new transmissions through the non-systemic transmission route.

RESULTS

The transmission potential and the risk in the study site are expected to increase along with the increase of the temperature in 2021-2050 and 2071-2100. This increase will be facilitated by the expected extension of the tick questing season and the increase of the numbers of susceptible ticks (larval and nymphal) and the number of infected nymphal ticks co-feeding on the same hosts, leading to compounded increase of infections through the non-systemic transmission.

CONCLUSIONS

The developed mathematical model provides an effective tool for predicting TBE prevalence in the tick-host enzootic cycle, by integrating climate projection with emerging knowledge about the region-specific tick ecological and pathogen enzootic processes (through model parametrization fitting to historical data). Model projects increasing co-feeding transmission and prevalence of TBEV in a recognized TBE endemic region, so human risk of TBEV infection is likely increasing unless public health interventions are enhanced.

Parasites and wildlife in a changing world: The vector-host- pathogen interaction as a learning case

In the Anthropocene context, changes in climate, land use and biodiversity are considered among the most important anthropogenic factors affecting parasites-host interaction and wildlife zoonotic diseases emergence. Transmission of vector borne pathogens are particularly sensitive to these changes due to the complexity of their cycle, where the transmission of a microparasite depends on the interaction between its vector, usually a macroparasite, and its reservoir host, in many cases represented by a wildlife vertebrate. The scope of this paper focuses on the effect of some major, fast-occurring anthropogenic changes on the vectorial capacity for tick and mosquito borne pathogens. Specifically, we review and present the latest advances regarding two emerging vector-borne viruses in Europe: Tick-borne encephalitis virus (TBEV) and West Nile virus (WNV). In both cases, variation in vector to host ratio is critical in determining the intensity of pathogen transmission and consequently infection hazard for humans. Forecasting vector-borne disease hazard under the global change scenarios is particularly challenging, requiring long term studies based on a multidisciplinary approach in a One-Health framework.

Landscape structure affects the prevalence and distribution of a tick-borne zoonotic pathogen

Background

Landscape structure can affect pathogen prevalence and persistence with consequences for human and animal health. Few studies have examined how reservoir host species traits may interact with landscape structure to alter pathogen communities and dynamics. Using a landscape of islands and mainland sites we investigated how natural landscape fragmentation affects the prevalence and persistence of the zoonotic tick-borne pathogen complex Borrelia burgdorferi (sensu lato), which causes Lyme borreliosis. We hypothesized that the prevalence of B. burgdorferi (s.l.) would be lower on islands compared to the mainland and B. afzelii, a small mammal specialist genospecies, would be more affected by isolation than bird-associated B. garinii and B. valaisiana and the generalist B. burgdorferi (sensu stricto).

Methods

Questing (host-seeking) nymphal I. ricinus ticks (n = 6567) were collected from 12 island and 6 mainland sites in 2011, 2013 and 2015 and tested for B. burgdorferi (s.l.). Deer abundance was estimated using dung transects.

Results

The prevalence of B. burgdorferi (s.l.) was significantly higher on the mainland (2.5%, 47/1891) compared to island sites (0.9%, 44/4673) (P < 0.01). While all four genospecies of B. burgdorferi (s.l.) were detected on the mainland, bird-associated species B. garinii and B. valaisiana and the generalist genospecies B. burgdorferi (s.s.) predominated on islands.

Conclusion

We found that landscape structure influenced the prevalence of a zoonotic pathogen, with a lower prevalence detected among island sites compared to the mainland. This was mainly due to the significantly lower prevalence of small mammal-associated B. afzelii. Deer abundance was not related to pathogen prevalence, suggesting that the structure and dynamics of the reservoir host community underpins the observed prevalence patterns, with the higher mobility of bird hosts compared to small mammal hosts leading to a relative predominance of the bird-associated genospecies B. garinii and generalist genospecies B. burgdorferi (s.s.) on islands. In contrast, the lower prevalence of B. afzelii on islands may be due to small mammal populations there exhibiting lower densities, less immigration and stronger population fluctuations. This study suggests that landscape fragmentation can influence the prevalence of a zoonotic pathogen, dependent on the biology of the reservoir host.

Electronic supplementary material

The online version of this article (10.1186/s13071-018-3200-2) contains supplementary material, which is available to authorized users.

How ticks keep ticking in the adversity of host immune reactions

Ixodid ticks are acknowledged as one of the most important hematophagous arthropods because of their ability in transmitting a variety of tick-borne diseases. Mathematical models have been developed, based on emerging knowledge about tick ecology, pathogen epidemiology and their interface, to understand tick population dynamics and tick-borne diseases spread patterns. However, no serious effort has been made to model and assess the impact of host immunity triggered by tick feeding on the distribution of the tick population according to tick stages and on tick population extinction and persistence. Here, we construct a novel mathematical model taking into account the effect of host immunity status on tick population dynamics, and analyze the long-term behaviours of the model solutions. Two threshold values, [Formula: see text] and [Formula: see text], are introduced to measure the reproduction ratios for the tick-host interaction in the absence and presence of host immunity. We then show that these two thresholds (sometimes under additional conditions) can be used to predict whether the tick population goes extinct ([Formula: see text]) and the tick population grows without bound ([Formula: see text]). We also prove tick permanence (persistence and boundedness of the tick population) and the existence of a tick persistence equilibrium if [Formula: see text]. As the host species adjust their immunity to tick infestation levels, they form for the tick population an environment with a carrying capacity very much like that in logistic growth. Numerical results show that the host immune reactions decrease the size of the tick population at equilibrium and apparently reduce the tick-borne infection risk.

Basic reproduction number for the Brazilian Spotted Fever

Brazilian Spotted Fever (BSF) is an emerging and lethal disease in South America which basic reproduction number (R₀) is unknown. Calculating R₀ for this disease is crucial to design control interventions and prevent human deaths. BSF endemic areas are related to the presence of capybaras Hydrochoerus hydrochaeris, amplifier hosts of Rickettsia rickettsii and primary hosts of the tick Amblyomma sculptum, main vector of the agent in this area. Because of the complexity of its dynamics, we calculated R₀ for the BSF system by constructing a next-generation matrix considering different categories of vectors and hosts. Each matrix element was considered as the expected number of infected individuals of one category produced by a single infected individual of a second category. We used field and experimental data to parameterize the next-generation matrix and obtain the final calculation (R₀ ≈ 1.7). We demonstrated the low impact of the matrix elements corresponding to the transovarial transmission and the transmission from infected larvae in the maintenance of R. rickettsii. Sensitivity and elasticity analyzes were performed to quantify the perturbations of each matrix element in R₀. We noted that the elements equivalent to the number of infected attached nymphs produced by an infected capybara, and the number of infected capybaras produced by an infected attached nymph or adult are the major contributors to changes in R₀. Our results provide insights into the strategic design of preventive interventions in BSF endemic areas.

Effect of Climate and Land Use on the Spatio-Temporal Variability of Tick-Borne Bacteria in Europe

The incidence of tick-borne diseases caused by Borrelia burgdorferi sensu lato, Anaplasma phagocytophilum and Rickettsia spp. has been rising in Europe in recent decades. Early pre-assessment of acarological hazard still represents a complex challenge. The aim of this study was to model Ixodes ricinus questing nymph density and its infection rate with B. burgdorferi s.l., A. phagocytophilum and Rickettsia spp. in five European countries (Italy, Germany, Czech Republic, Slovakia, Hungary) in various land cover types differing in use and anthropisation (agricultural, urban and natural) with climatic and environmental factors (Normalized Difference Vegetation Index (NDVI), Normalized Difference Water Index (NDWI), Land Surface Temperature (LST) and precipitation). We show that the relative abundance of questing nymphs was significantly associated with climatic conditions, such as higher values of NDVI recorded in the sampling period, while no differences were observed among land use categories. However, the density of infected nymphs (DIN) also depended on the pathogen considered and land use. These results contribute to a better understanding of the variation in acarological hazard for Ixodes ricinus transmitted pathogens in Central Europe and provide the basis for more focused ecological studies aimed at assessing the effect of land use in different sites on tick–host pathogens interaction.

Effects of conservation management of landscapes and vertebrate communities on Lyme borreliosis risk in the United Kingdom

Landscape change and altered host abundance are major drivers of zoonotic pathogen emergence. Conservation and biodiversity management of landscapes and vertebrate communities can have secondary effects on vector-borne pathogen transmission that are important to assess. Here we review the potential implications of these activities on the risk of Lyme borreliosis in the United Kingdom. Conservation management activities include woodland expansion, management and restoration, deer management, urban greening and the release and culling of non-native species. Available evidence suggests that increasing woodland extent, implementing biodiversity policies that encourage ecotonal habitat and urban greening can increase the risk of Lyme borreliosis by increasing suitable habitat for hosts and the tick vectors. However, this can depend on whether deer population management is carried out as part of these conservation activities. Exclusion fencing or culling deer to low densities can decrease tick abundance and Lyme borreliosis risk. As management actions often constitute large-scale perturbation experiments, these hold great potential to understand underlying drivers of tick and pathogen dynamics. We recommend integrating monitoring of ticks and the risk of tick-borne pathogens with conservation management activities. This would help fill knowledge gaps and the production of best practice guidelines to reduce risks.

This article is part of the themed issue ‘Conservation, biodiversity and infectious disease: scientific evidence and policy implications’.

[Pathogenic mechanisms of Tick-borne Flaviviruses]

Many tick-borne flaviviruses causes fatal encephalitis in humans and animals with severe sequelae. However, it remains unclear how viral replication and pathogenicity contribute to the neurologic manifestations. In this paper, I summarized the specific replication mechanism of tick-borne flaviviruses in neurons and their effect on the pathogenicity of neurological disease. Our findings of the unique virus-host interaction in central nerve system will improve further understanding of the molecular mechanisms of viral replication and the pathogenicity of neurotropic viruses.

CRITICAL CONTACT RATE FOR VECTOR–HOST–PATHOGEN OSCILLATION INVOLVING CO-FEEDING AND DIAPAUSE

We consider the dynamic vector–host–pathogen interaction motivated by tick-borne diseases such as tick-borne encephalitis and Lyme disease. We stratify the vector population in terms of the stage before and after the vector’s contact with hosts when co-feeding transmission may take place, and we also consider the case where vector development may involve two time lags due to normal development and diapause. We derive threshold conditions for disease persistence and for nonlinear oscillations in the vector population and in the diseased vector and host populations. Our objective here is to use a simple mechanistic dynamic model to show that diapause and co-feeding transmission may generate periodic and irregular oscillations even when seasonal variations of the environmental conditions are ignored. These oscillations are not necessary in synchrony with the seasonality of vector development, and hence complicated oscillatory patterns of vector-borne disease dynamics in the field and surveillance observations should be expected.

[Tick-borne encephalitis]

Tick-borne encephalitis virus (TBEV) belongs to the Flaviviridae family and Flavivirus genus. TBEV is maintained in transmission cycles between Ixodid ticks and wild mammalian hosts, particularly rodents. A wide range of animal species are also infected with TBEV by the bite of infected ticks, and TBEV infection causes fatal encephalitis in humans. TBEV is endemic widely in the Eurasian continent, and more than 10,000 cases of the disease are reported annually. In Japan, the 1st confirmed case of TBE was reported in the southern area of Hokkaido in 1993, and after 20 years, the 2nd to 4th cases were reported in Hokkaido in 2016 and 2017. Our sero-epizootiological survey indicated endemic foci of TBEV are widely distributed in Hokkaido and that those of TBEV or tick-borne flavivirus outside Hokkaido. In this review, I introduced recent topics of TBEV including newly developed diagnostic methods, epidemiology and pathogenesis of TBEV.

Ticks infected via co-feeding transmission can transmit Lyme borreliosis to vertebrate hosts

Vector-borne pathogens establish systemic infections in host tissues to maximize transmission to arthropod vectors. Co-feeding transmission occurs when the pathogen is transferred between infected and naive vectors that feed in close spatiotemporal proximity on a host that has not yet developed a systemic infection. Borrelia afzelii is a tick-borne spirochete bacterium that causes Lyme borreliosis (LB) and is capable of co-feeding transmission. Whether ticks that acquire LB pathogens via co-feeding are actually infectious to vertebrate hosts has never been tested. We created nymphs that had been experimentally infected as larvae with B. afzelii via co-feeding or systemic transmission, and compared their performance over one complete LB life cycle. Co-feeding nymphs had a spirochete load that was 26 times lower than systemic nymphs but both nymphs were highly infectious to mice (i.e., probability of nymph-to-host transmission of B. afzelii was ~100%). The mode of transmission had no effect on the other infection phenotypes of the LB life cycle. Ticks that acquire B. afzelii via co-feeding transmission are highly infectious to rodents, and the resulting rodent infection is highly infectious to larval ticks. This is the first study to show that B. afzelii can use co-feeding transmission to complete its life cycle.

Modeling the effects of variable feeding patterns of larval ticks on the transmission of Borrelia lusitaniae and Borrelia afzelii

Spirochetes belonging to the Borrelia burgdoferi sensu lato (sl) group cause Lyme Borreliosis (LB), which is the most commonly reported vector-borne zoonosis in Europe. B. burgdorferi sl is maintained in nature in a complex cycle involving Ixodes ricinus ticks and several species of vertebrate hosts. The transmission dynamics of B. burgdorferi sl is complicated by the varying competence of animals for different genospecies of spirochetes that, in turn, vary in their capability of causing disease. In this study, a set of difference equations simplifying the complex interaction between vectors and their hosts (competent and not for Borrelia) is built to gain insights into conditions underlying the dominance of B. lusitaniae (transmitted by lizards to susceptible ticks) and the maintenance of B. afzelii (transmitted by wild rodents) observed in a study area in Tuscany, Italy. Findings, in agreement with field observations, highlight the existence of a threshold for the fraction of larvae feeding on rodents below which the persistence of B. afzelii is not possible. Furthermore, thresholds change as nonlinear functions of the expected number of nymph bites on mice, and the transmission and recovery probabilities. In conclusion, our model provided an insight into mechanisms underlying the relative frequency of different Borrelia genospecies, as observed in field studies.

Transmission dynamics and control of Rickettsia rickettsii in populations of Hydrochoerus hydrochaeris and Amblyomma sculptum

BACKGROUND

Brazilian Spotted Fever (BSF), caused by the bacterium Rickettsia rickettsii, is the tick-borne disease that generates the largest number of human deaths in the world. In Brazil, the current increase of BSF human cases has been associated with the presence and expansion of capybaras Hydrochoerus hydrochaeris, which act as primary hosts for the tick Amblyomma sculptum, vector of the R. rickettsii in this area.

METHODS

We proposed a semi-discrete-time stochastic model to evaluate the role of capybaras in the transmission dynamics of R. rickettsii. Through a sensitivity analysis, we identified the parameters with significant influence on the R. rickettsii establishment. Afterward, we implemented the Gillespie's algorithm to simulate the impact of potential public health interventions to prevent BSF human cases.

RESULTS

The introduction of a single infected capybara with at least one infected attached tick is enough to trigger the disease in a non-endemic area. We found that to avoid the formation of new BSF-endemic areas, it is crucial to impede the emigration of capybaras from endemic areas by reducing their birth rate by more than 58%. Model results were corroborated by ex-situ data generated from field studies, and this supports our proposal to prevent BSF human cases by implementing control strategies focused on capybaras.

CONCLUSION

The proposed stochastic model illustrates how strategies for the control and prevention of vector-borne infectious diseases can be focused on amplifier hosts management practices. This work provides a basis for future prevention strategies for other neglected vector-borne diseases.

Modeling Lyme disease transmission

Lyme disease, a typical tick-borne disease, imposes increasing global public health challenges. A growing body of theoretical models have been proposed to better understand various factors determining the disease risk, which not only enrich our understanding on the ecological cycle of disease transmission but also promote new theoretical developments on model formulation, analysis and simulation. In this paper, we provide a review about the models and results we have obtained recently on modeling and analyzing Lyme disease transmission, with the purpose to highlight various aspects in the ecological cycle of disease transmission to be incorporated, including the growth of ticks with different stages in the life cycle, the seasonality, host diversity, spatial disease pattern due to host short distance movement and bird migration, co-infection with other tick-borne pathogens, and climate change impact.

Heterogeneity in the abundance and distribution of Ixodes ricinus and Borrelia burgdorferi (sensu lato) in Scotland: implications for risk prediction

BACKGROUND

Cases of Lyme borreliosis, a vector-borne zoonosis caused by bacteria in the Borrelia burgdorferi (sensu lato) species group, have increased in recent years in Europe. Knowledge of environmental factors associated with abundance of the tick vector Ixodes ricinus and the pathogen B. burgdorferi (s.l.) is of interest to understand responses to environmental changes, predict variation in risk and to inform management interventions.

METHODS

Nineteen woodland sites across Scotland were surveyed in 2012 for B. burgdorferi (s.l.) infection in questing I. ricinus nymphs (n = 200 per site), deer abundance and vegetation. Climatic factors were extracted for each site. Six additional sites were surveyed for questing nymphs in both 2012 and 2013 (n = 200 per site and year) to test for variation in B. burgdorferi (s.l.) prevalence between years.

RESULTS

The mean prevalence of B. burgdorferi (s.l.) across 19 sites was 1.7% (95% CI: 1.4-2.2%; range 0-6%), all four genospecies known to be present in the UK were detected: B. garinii, B. afzelii, B. burgdorferi (sensu stricto) and B. valaisiana. A higher prevalence of B. burgdorferi (s.l.), higher densities of nymphs and higher densities of infected nymphs were found at sites with warmer climates, estimated with growing degree-days. No association between infection prevalence in nymphs and woodland type (semi-natural mixed vs coniferous) or deer density was found. At six sites sampled in 2012 and 2013, there was a significant increase in B. afzelli prevalence at two sites and a decrease in B. garinii prevalence at one site.

CONCLUSIONS

This study highlights challenges for the prediction of risk of Lyme borreliosis, reflecting the sensitivity of both pathogen and vector ecology to habitat, host and climatic factors. Significant changes in the prevalence of individual genospecies at sites monitored across time are likely to be due to variability in the host community composition between years. Our results indicate the importance of monitoring dynamic variables such as reservoir host populations as well as climate and habitat factors over multiple years, to identify environmental factors associated with Lyme borreliosis risk.

Past and future perspectives on mathematical models of tick-borne pathogens

Ticks are vectors of pathogens which are important both with respect to human health and economically. They have a complex life cycle requiring several blood meals throughout their life. These blood meals take place on different individual hosts and potentially on different host species. Their life cycle is also dependent on environmental conditions such as the temperature and habitat type. Mathematical models have been used for the more than 30 years to help us understand how tick dynamics are dependent on these environmental factors and host availability. In this paper, we review models of tick dynamics and summarize the main results. This summary is split into two parts, one which looks at tick dynamics and one which looks at tick-borne pathogens. In general, the models of tick dynamics are used to determine when the peak in tick densities is likely to occur in the year and how that changes with environmental conditions. The models of tick-borne pathogens focus more on the conditions under which the pathogen can persist and how host population densities might be manipulated to control these pathogens. In the final section of the paper, we identify gaps in the current knowledge and future modelling approaches. These include spatial models linked to environmental information and Geographic Information System maps, and development of new modelling techniques which model tick densities per host more explicitly.

Stability and persistence in ODE models for populations with many stages

A model of ordinary differential equations is formulated for populations which are structured by many stages. The model is motivated by ticks which are vectors of infectious diseases, but is general enough to apply to many other species. Our analysis identifies a basic reproduction number that acts as a threshold between population extinction and persistence. We establish conditions for the existence and uniqueness of nonzero equilibria and show that their local stability cannot be expected in general. Boundedness of solutions remains an open problem though we give some sufficient conditions.

Host preferences of immature Dermacentor reticulatus (Acari: Ixodidae) in a forest habitat in Germany

Dermacentor reticulatus is widespread throughout Europe and is expanding its range in several European countries. It is associated with a number of different pathogens. Its role in the transmission of disease to humans is currently small; however, it might play an important role in the maintenance of pathogens in enzootic cycles. The ecology of D. reticulatus, especially of the immatures, is not well known. In this study, ticks from small mammals, caught in a capture-mark-release study between May 2012 and October 2014 in a unique woodland area close to Karlsruhe, Germany, were collected. The main host species trapped were the yellow-necked mouse (Apodemus flavicollis) and the bank vole (Myodes glareolus). Small mammal populations showed high variability in their density between the study years, which is probably due to harsh winter conditions in 2012/2013 and missing mast leading to high winter mortality. Larvae and nymphs of D. reticulatus were predominantly found in July and August, respectively, and the infestation rates among the different small mammal species suggest a host preference of D. reticulatus for M. glareolus.

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.

Pattern of tick aggregation on mice: larger than expected distribution tail enhances the spread of tick-borne pathogens

The spread of tick-borne pathogens represents an important threat to human and animal health in many parts of Eurasia. Here, we analysed a 9-year time series of Ixodes ricinus ticks feeding on Apodemus flavicollis mice (main reservoir-competent host for tick-borne encephalitis, TBE) sampled in Trentino (Northern Italy). The tail of the distribution of the number of ticks per host was fitted by three theoretical distributions: Negative Binomial (NB), Poisson-LogNormal (PoiLN), and Power-Law (PL). The fit with theoretical distributions indicated that the tail of the tick infestation pattern on mice is better described by the PL distribution. Moreover, we found that the tail of the distribution significantly changes with seasonal variations in host abundance. In order to investigate the effect of different tails of tick distribution on the invasion of a non-systemically transmitted pathogen, we simulated the transmission of a TBE-like virus between susceptible and infective ticks using a stochastic model. Model simulations indicated different outcomes of disease spreading when considering different distribution laws of ticks among hosts. Specifically, we found that the epidemic threshold and the prevalence equilibria obtained in epidemiological simulations with PL distribution are a good approximation of those observed in simulations feed by the empirical distribution. Moreover, we also found that the epidemic threshold for disease invasion was lower when considering the seasonal variation of tick aggregation.

Our work analyses a 9-year time series of tick co-feeding patterns on Yellow-necked mice. Our data shows a strong heterogeneity, where most mice are parasitised by a small number of ticks while few host a much larger number. We describe the number of ticks per host by the commonly used Negative Binomial model, by the Poisson-LogNormal model, and we propose the Power Law model as an alternative. In our data, the last model seems to better describe the strong heterogeneity. In order to understand the epidemiological consequences, we use a computational model to reproduce a peculiar way of transmission, observed in some cases in nature, where uninfected ticks acquire an infection by feeding on a host where infected ticks are present, without any remarkable epidemiological involvement of the host itself. In particular, we are interested in determining the conditions leading to pathogen spread. We observe that the effective transmission of this infection in nature is highly dependent on the capability of the implemented model to describe the tick burden. In addition, we also consider seasonal changes in tick aggregation on mice, showing its influence on the spread of the infection.

Delay differential systems for tick population dynamics

Ticks play a critical role as vectors in the transmission and spread of Lyme disease, an emerging infectious disease which can cause severe illness in humans or animals. To understand the transmission dynamics of Lyme disease and other tick-borne diseases, it is necessary to investigate the population dynamics of ticks. Here, we formulate a system of delay differential equations which models the stage structure of the tick population. Temperature can alter the length of time delays in each developmental stage, and so the time delays can vary geographically (and seasonally which we do not consider). We define the basic reproduction number [Formula: see text] of stage structured tick populations. The tick population is uniformly persistent if [Formula: see text] and dies out if [Formula: see text]. We present sufficient conditions under which the unique positive equilibrium point is globally asymptotically stable. In general, the positive equilibrium can be unstable and the system show oscillatory behavior. These oscillations are primarily due to negative feedback within the tick system, but can be enhanced by the time delays of the different developmental stages.

Shaping zoonosis risk: landscape ecology vs. landscape attractiveness for people, the case of tick-borne encephalitis in Sweden

BACKGROUND

In this paper, the hazard and exposure concepts from risk assessment are applied in an innovative approach to understand zoonotic disease risk. Hazard is here related to the landscape ecology determining where the hosts, vectors and pathogens are and, exposure is defined as the attractiveness and accessibility to hazardous areas. Tick-borne encephalitis in Sweden was used as a case study.

METHODS

Three boosted regression tree models are compared: a hazard model, an exposure model and a global model which combines the two approaches.

RESULTS

The global model offers the best predictive power and the most accurate modelling. The highest probabilities were found in easy-to-reach places with high landscape diversity, holiday houses, waterbodies and, well-connected forests of oak, birch or pine, with open-area in their ecotones, a complex shape, numerous clear-cuts and, a variation in tree height.

CONCLUSION

While conditions for access and use of hazardous areas are quite specific to Scandinavia, this study offers promising perspectives to improve our understanding of the distribution of zoonotic and vector-borne diseases in diverse contexts.

Does biodiversity protect humans against infectious disease?

Control of human infectious disease has been promoted as a valuable ecosystem service arising from the conservation of biodiversity. There are two commonly discussed mechanisms by which biodiversity loss could increase rates of infectious disease in a landscape. First, loss of competitors or predators could facilitate an increase in the abundance of competent reservoir hosts. Second, biodiversity loss could disproportionately affect non-competent, or less competent reservoir hosts, which would otherwise interfere with pathogen transmission to human populations by, for example, wasting the bites of infected vectors. A negative association between biodiversity and disease risk, sometimes called the "dilution effect hypothesis," has been supported for a few disease agents, suggests an exciting win-win outcome for the environment and society, and has become a pervasive topic in the disease ecology literature. Case studies have been assembled to argue that the dilution effect is general across disease agents. Less touted are examples in which elevated biodiversity does not affect or increases infectious disease risk for pathogens of public health concern. In order to assess the likely generality of the dilution effect, we review the association between biodiversity and public health across a broad variety of human disease agents. Overall, we hypothesize that conditions for the dilution effect are unlikely to be met for most important diseases of humans. Biodiversity probably has little net effect on most human infectious diseases but, when it does have an effect, observation and basic logic suggest that biodiversity will be more likely to increase than to decrease infectious disease risk.

Developing a temperature-driven map of the basic reproductive number of the emerging tick vector of Lyme disease Ixodes scapularis in Canada

A mechanistic model of the tick vector of Lyme disease, Ixodes scapularis, was adapted to a deterministic structure. Using temperature normals smoothed by Fourier analysis to generate seasonal temperature-driven development rates and host biting rates, and a next generation matrix approach, the model was used to obtain values for the basic reproduction number (R(0)) for I. scapularis at locations in southern Canada where the tick is established and emerging. The R(0) at Long Point, Point Pelee and Chatham sites where I. scapularis are established, was estimated at 1.5, 3.19 and 3.65, respectively. The threshold temperature conditions for tick population survival (R(0)=1) were shown to be the same as those identified using the mechanistic model (2800-3100 cumulative annual degree days >0°C), and a map of R(0) for I. scapularis, the first such map for an arthropod vector, was drawn for Canada east of the Rocky Mountains. This map supports current risk assessments for Lyme disease risk emergence in Canada. Sensitivity analysis identified host abundance, tick development rates and summer temperatures as highly influential variables in the model, which is consistent with our current knowledge of the biology of this tick. The development of a deterministic model for I. scapularis that is capable of providing values for R(0) is a key step in our evolving ability to develop tools for assessment of Lyme disease risk emergence and for development of public health policies on surveillance, prevention and control.

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.

Pangloss revisited: a critique of the dilution effect and the biodiversity-buffers-disease paradigm

The twin concepts of zooprophylaxis and the dilution effect originated with vector-borne diseases (malaria), were driven forward by studies on Lyme borreliosis and have now developed into the mantra "biodiversity protects against disease". The basic idea is that by diluting the assemblage of transmission-competent hosts with non-competent hosts, the probability of vectors feeding on transmission-competent hosts is reduced and so the abundance of infected vectors is lowered. The same principle has recently been applied to other infectious disease systems--tick-borne, insect-borne, indirectly transmitted via intermediate hosts, directly transmitted. It is claimed that the presence of extra species of various sorts, acting through a variety of distinct mechanisms, causes the prevalence of infectious agents to decrease. Examination of the theoretical and empirical evidence for this hypothesis reveals that it applies only in certain circumstances even amongst tick-borne diseases, and even less often if considering the correct metric--abundance rather than prevalence of infected vectors. Whether dilution or amplification occurs depends more on specific community composition than on biodiversity per se. We warn against raising a straw man, an untenable argument easily dismantled and dismissed. The intrinsic value of protecting biodiversity and ecosystem function outweighs this questionable utilitarian justification.

Saturation deficit and deer density affect questing activity and local abundance of Ixodes ricinus (Acari, Ixodidae) in Italy

The wood tick Ixodes ricinus, one of the most common arthropod-borne disease vectors, is of increasing relevance for human and animal health in Europe. The aim of this study was to determine the relative contribution of several abiotic and biotic factors potentially affecting questing activity and local abundance of I. ricinus in Italy, considering the scale at which these factors interact with the host-seeking ticks. Within EDEN, a large-scale EU collaborative project on eco-epidemiology of vector-borne diseases, we collected questing ticks for three consecutive years using a standard protocol at eleven sites in the Italian Alps and Apennines. A total of 25 447 I. ricinus were collected. All sites showed the same annual pattern of tick activity (bimodal for nymphs and unimodal for larvae and adults), although the abundance of nymphs was statistically different between sites and years. A Generalized Linear Mixed Model and a Linear Mixed Model fitted to data for nymphs, showed that while the principal variables affecting the local abundance of questing ticks were saturation deficit (an index combining temperature and relative humidity) and red deer density, the most important variable affecting questing nymph activity was saturation deficit. As for the timing of seasonal emergence, we confirmed that the threshold temperature at this latitude for larvae is 10°C (mean maximum) while that for nymphs is 8°C.

Comparative population dynamics of a generalist (Ixodes ricinus) and specialist tick (I. hexagonus) species from European hedgehogs

Although the population dynamics of the tick Ixodes ricinus are relatively well studied, those of other Western European tick species are largely unknown. Moreover, there is very little information related to the interactions between I. ricinus and other ticks. Such knowledge, however, is of special interest in respect to the epidemiology of tick-borne pathogens such as Borrelia spp. We compared the dynamics of the generalist I. ricinus with the nest-dwelling hedgehog specialist, I. hexagonus. Both species were collected from hedgehogs from a naturally infested experimental population between 2006 and 2008. Ticks were collected once a month from March to October from each hedgehog counted and the life history stage and species determined. All hedgehogs harboured both tick species. Nymphs, females and males of I. ricinus showed clear bimodal seasonal distributions with peaks in spring and autumn, while larvae peaked only in summer. The density of I. hexagonus life stages was low during the whole investigation period and seasonal fluctuations of population density were much weaker compared to I. ricinus. Nymphs and larvae showed comparatively little change in population size and no consistent period of peak density. Females showed a single peak in summer and males were found only occasionally on hedgehogs. We suggest density-dependent mechanisms regulating the population density of the specialist I. hexagonus but not of the generalist I. ricinus.

Investigating the persistence of tick-borne pathogens via the R0model

In the epidemiology of infectious diseases, the basic reproduction number, R0, has a number of important applications, most notably it can be used to predict whether a pathogen is likely to become established, or persist, in a given area. We used the R0model to investigate the persistence of 3 tick-borne pathogens;Babesia microti, Anaplasma phagocytophilumandBorrelia burgdorferisensu lato in anApodemus sylvaticus-Ixodes ricinussystem. The persistence of these pathogens was also determined empirically by screening questing ticks and wood mice by PCR. All 3 pathogens behaved differently in response to changes in the proportion of transmission hosts on whichI. ricinusfed, the efficiency of transmission between the host and ticks and the abundance of larval and nymphal ticks found on small mammals. Empirical data supported theoretical predictions of the R0model. The transmission pathway employed and the duration of systemic infection were also identified as important factors responsible for establishment or persistence of tick-borne pathogens in a given tick-host system. The current study demonstrates how the R0model can be put to practical use to investigate factors affecting tick-borne pathogen persistence, which has important implications for animal and human health worldwide.

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.

A clear and present danger: tick-borne diseases in Europe

Ticks can transmit a variety of viruses, bacteria or parasites that can cause serious infections or conditions in humans and animals. While tick-borne diseases are becoming an increasing and serious problem in Europe, tick-borne diseases are also responsible for major depressions in livestock production and mortality in sub-Saharan Africa, Latin America and Asia. This review will focus on the most important circulating tick-transmitted pathogens in Europe (Borrelia spp., Anaplasma phagocytophilum, Babesia spp., tick-borne encephalitis virus, Rickettsia spp. and Crimean-Congo hemorrhagic fever virus).

A model for the transmission dynamics of Orientia tsutsugamushi among its natural reservoirs

The bacteria Orientia tsutsugamushi is the causative agent of scrub typhus, a prevalent disease in Asian countries that can affect humans and which shows an alarming increase of cases during the last years, especially in rural areas. Unfortunately, there is no vaccine for scrub typhus, and antibiotic treatments successfully used in the past appear to be inefficient to treat some strains of O. tsutsugamushi. We introduce a mathematical model that approximates the dynamics of the bacteria among its natural reservoirs. After computing the basic reproductive number from the proposed model, we explore its sensitivity to the parameter values that may be affected by application of control measures. This theoretical model may be of interest to pest managers as well as health authorities interested in gaining insight into the public management of the disease, through a better understanding of its qualitative dynamics.

Transmission dynamics of Borrelia lusitaniae and Borrelia afzelii among Ixodes ricinus, lizards, and mice in Tuscany, central Italy

To estimate the basic reproduction number (R(0)) of Borrelia lusitaniae and Borrelia afzelii, we formulated a mathematical model considering the interactions among the tick vector, vertebrate hosts, and pathogens in a 500-ha enclosed natural reserve on Le Cerbaie hills, Tuscany, central Italy. In the study area, Ixodes ricinus were abundant and were found infected by B. lusitaniae and B. afzelii. Lizards (Podarcis spp.) and mice (Apodemus spp.), respectively, are the reservoir hosts of these two Borrelia burgdorferi sensu lato (s.l.) genospecies and compete for immature ticks. B. lusitaniae R(0) estimation is in agreement with field observations, indicating the maintenance and diffusion of this genospecies in the study area, where lizards are abundant and highly infested by I. ricinus immature stages. In fact, B. lusitaniae shows a focal distribution in areas where the tick vector and the vertebrate reservoir coexist. Mouse population dynamics and their relatively low suitability as hosts for nymphs seem to determine, on the other hand, a less efficient transmission of B. afzelii, whose R(0) differs between scenarios in the study area. Considering host population dynamics, the proposed model suggests that, given a certain combination of the two host population sizes, both spirochete genospecies can coexist in our study area. Additional incompetent hosts for B. burgdorferi s.l. have a negative effect on B. afzelii maintenance, whose R(0) results > 1 only with high mouse population densities and/or low lizards abundance, but they do not seem to influence B. lusitaniae transmission cycle on Le Cerbaie. Secondly, our model confirms the importance of nymphs' infestation, of host population density and diversity, and spirochetes host association for the maintenance of the transmission cycle of B. burgdorferi s.l.