Epidemiological uses of a population model for the tick Rhipicephalus appendiculatus

Are host control strategies effective to eradicate tick-borne diseases (TBD)?

Ticks are responsible for spreading harmful diseases including Lyme disease and tick-borne encephalitis. Understanding tick population dynamics and predicting risk of tick-borne disease insurgence helps to design preventive actions against the disease spread. Using a compartmental model describing the pathogen transmission among ticks and hosts, we study the influence of host-targeted tick control strategies with chemical insecticides on tick population and disease transmission dynamics. Our analysis shows that in areas with rapid-growing population of ticks, host-targeted controls using chemical insecticides may enhance disease persistence and even turn a disease-free area to a disease endemic area. Therefore, the complex dynamics of pathogen spread among ticks and hosts should be carefully examined when designing tick control strategies.

A stochastic epidemic model for the dynamics of two pathogens in a single tick population

Understanding tick-transmitted pathogens in tick infested areas is crucial for the development of preventive and control measures in response to the increasing cases of tick-borne diseases. A stochastic model for the dynamics of two pathogens, Rickettsia parkeri and Rickettsia amblyommii, in a single tick, Amblyomma americanum, is developed and analysed. The model, a continuous-time Markov chain, is based on a deterministic tick-borne disease model. The extinction threshold for the stochastic model is computed using the multitype branching process and conditions for pathogen extinction or persistence are presented. The probability of pathogen extinction is computed using numerical simulations and is shown to be a good estimate of the probability of extinction calculated from the branching process. A sensitivity analysis is undertaken to illustrate the relationship between co-feeding and transovarial transmission rates and the probability of pathogen extinction. Expected epidemic duration is estimated using sample paths and we show that R. amblyommii is likely to persist slightly longer than R. parkeri. Further, we estimate the duration of possible coexistence of the two pathogens.

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton-Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.

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.

Ecology and genetic variation of Amblyomma tonelliae in Argentina

The ecology of Amblyomma tonelliae (Ixodida: Ixodidae), including its seasonal distribution and the development periods of each stage, was investigated during a study carried out over two consecutive years in northwestern Argentina. In addition, the genetic variation of this tick was studied through analyses of 16S rDNA sequences. Amblyomma tonelliae has a 1-year lifecycle characterized by a long pre-moult period in larvae with no development of morphogenetic diapause. Larvae peak in abundance during late autumn and early winter; nymphs peak in abundance in spring, and adults do so from late spring to early summer. Amblyomma tonelliae shows a marked ecological preference for the driest areas of the Chaco ecoregion. In analyses of 16S rDNA sequences in genes from different populations of A. tonelliae, values for nucleotide diversity and the average number of nucleotide differences showed genetic diversity within this species to be low. No significant differences were found in comparisons among populations.

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.

Study of the life cycle of Amblyomma dubitatum (Acari: Ixodidae) based on field and laboratory data

The life cycle of Amblyomma dubitatum was described based on the seasonal distribution of all parasitic stages and the development periods of engorged ticks under different conditions of photoperiod and temperature. All stages were found active along the entire year in the study area. Larvae peaked from May to July, nymphs peaked from July to October, and females peaked from November to March. This pattern represents a life cycle with one generation per year with most of the ticks reaching adulthood during the warmest months. The analysis of the effect of the photoperiod on the development of A. dubitatum showed no indication of morphogenetic diapause. Exposure of ticks to field conditions indicates a delay in metamorphosis of immature stages, in the oviposition of females and in the incubation of eggs, which were associated with low winter temperatures. The results indicate that though A. dubitatum has a one year life cycle, more than one cohort can co-exist within the same population in a certain interval of time. Finally, the potential role of small rodents as hosts for larvae and nymphs of A. dubitatum is confirmed.

Detection and characterization of tick-borne encephalitis virus in Baltic countries and eastern Poland

Ticks were collected from the vegetation in the Baltic countries Estonia, Latvia, Lithuania and eastern Poland and analyzed for the presence of tick-borne encephalitis virus (TBEV) by amplification of the partial E and NS3 genes. In Estonia we found statistically significant differences in the TBEV prevalence between I. persulcatus and I. ricinus ticks (4.23% and 0.42%, respectively). In Latvia, the difference in TBEV prevalence between the two species was not statistically significant (1.02% for I. persulcatus and 1.51% for I. ricinus, respectively). In Lithuania and Poland TBEV was detected in 0.24% and 0.11% of I. ricinus ticks, respectively. Genetic characterization of the partial E and NS3 sequences demonstrated that the TBEV strains belonged to the European subtype in all countries, as well as to the Siberian subtype in Estonia. We also found that in areas where ranges of two tick species overlap, the TBEV subtypes may be detected not only in their natural vector, but also in sympatric tick species.

Preliminary analysis of an agent-based model for a tick-borne disease

Ticks have a unique life history including a distinct set of life stages and a single blood meal per life stage. This makes tick-host interactions more complex from a mathematical perspective. In addition, any model of these interactions must involve a significant degree of stochasticity on the individual tick level. In an attempt to quantify these relationships, I have developed an individual-based model of the interactions between ticks and their hosts as well as the transmission of tick-borne disease between the two populations. The results from this model are compared with those from previously published differential equation based population models. The findings show that the agent-based model produces significantly lower prevalence of disease in both the ticks and their hosts than what is predicted by a similar differential equation model.

Ecology of Amblyomma neumanni (Acari: Ixodidae)

The life cycle of Amblyomma neumanni was described studying the seasonal distribution of free-living stages and parasitic phases during two consecutive years. Development periods of engorged ticks under different photoperiod conditions were recorded. Larvae of A. neumanni have the peak of abundance in autumn. Nymphs reach the peak in winter. Females were collected on cattle from autumn to late spring. The seasonal distribution pattern of females showed a bimodal curve, with a peak in autumn and other during early and middle spring. The engorged females exposed at shortest photoperiod regimen (10 h light-14 h dark) under both laboratory and field conditions undergo morphogenetic diapause, expressed as a delay in the oviposition. It is concluded that females of A. neumanni that feed and copulate in autumn undergo morphogenetic diapause, and they will lay eggs in spring, simultaneously with the females that feed and copulate in this season. Climate niche analysis shows that adequate suitability for A. neumanni depends mainly from temperature (mean, absolute maximum and minimum, and mean temperature in wettest and driest quarters) as well as from rainfall in warmest and coldest quarters. Sequences of 16S rDNA gene belonging to different populations of A. neumanni, showed no intraspecific genetic differentiation.

Modeling and biological control of mosquitoes

Models can be useful at many different levels when considering complex issues such as biological control of mosquitoes. At an early stage, exploratory models are valuable in exploring the characteristics of an ideal biological control agent and for guidance in data collection. When more data are available, models can be used to explore alternative control strategies and the likelihood of success. There are few modeling studies that explicitly consider biological control in mosquitoes; however, there have been many theoretical studies of biological control in other insect systems and of mosquitoes and mosquito-borne diseases in general. Examples are used here to illustrate important aspects of designing, using and interpreting models. The stability properties of a model are valuable in assessing the potential of a biological control agent, but may not be relevant to a mosquito population with frequent environmental perturbations. The time scale and goal of proposed control strategies are important considerations when analyzing a model. The underlying biology of the mosquito host and the biological control agent must be carefully considered when deciding what to include in a model. Factors such as density dependent population growth in the host, the searching efficiency and aggregation of a natural enemy, and the resource base of both have been shown to influence the stability and dynamics of the interaction. Including existing mosquito control practices into a model is useful if biological control is proposed for locations with current insecticidal control. The development of Integrated Pest Management (IPM) strategies can be enhanced using modeling techniques, as a wide variety of options can be simulated and examined. Models can also be valuable in comparing alternate routes of disease transmission and to investigate the level of control needed to reduce transmission.

Modeling Tick-Borne Disease: A Metapopulation Model

Recent increases in reported outbreaks of tick-borne diseases have led to increased interest in understanding and controlling epidemics involving these transmission vectors. Mathematical disease models typically assume constant population size and spatial homogeneity. For tick-borne diseases, these assumptions are not always valid. The disease model presented here incorporates non-constant population sizes and spatial heterogeneity utilizing a system of differential equations that may be applied to a variety of spatial patches. We present analytical results for the one patch version and find parameter restrictions under which the populations and infected densities reach equilibrium. We then numerically explore disease dynamics when parameters are allowed to vary spatially and temporally and consider the effectiveness of various tick-control strategies.