A seasonal matrix population model for ixodid ticks with complex life histories and limited host availability

Many vector-borne diseases are sensitive to changes in land use and climate; hence, it is important to understand the factors that govern the vector populations. Ixodid ticks, which serve as vectors for multiple diseases, have a slow life cycle compared with many of their hosts. The observable questing population represents only a fraction of the total tick population and may include overlapping cohorts in each stage. The duration of each life stage (larvae, nymph, and adult) is variable and depends on factors such as the seasonal timing of questing, development, and host availability. Mathematical models are therefore essential to mediate how complex life cycle transitions and host interactions underpin the seasonal dynamics of the questing tick population. In this study, we develop a seasonal matrix population model for ixodid ticks feeding on a small and large host. The model has 17 stages representing the main life history stages (eggs, larvae, nymphs, and adults) combined with status of feeding, seasonal timing of feeding, and overwintering. The probability of finding a host depends on tick instar and host type, and density regulation is incorporated through limited host capacity. Using a life history representing Ixodes ricinus in Northern Europe as a baseline, we extract seasonal numbers of different parts of the tick population and calculate life history outcomes such as generation time and mean and variance of lifespan and of lifetime reproductive output. These results are compared with an alternative scenario of a southern life history. Secondly, we investigate (1) effects of seasonality in the small host availability on the seasonal numbers of tick stages and (2) effects of varying host availability and utilization of small versus large hosts by larvae and nymphs, on the seasonal numbers of questing ticks. Our results suggest that the small host availability is an important regulating factor through the feeding of larvae. Our model incorporates complex mechanisms underlying the seasonal composition of the tick population. It can be applied to different ixodid tick species and provides a framework for future investigations into intra- and interspecific variation in life history and population dynamics.