Unraveling the seasonal dynamics of ixodid ticks: A flexible matrix population model with delayed life history effects

Many vector-borne diseases are sensitive to changes in land use and climate, making it crucial to understand the factors that govern the vector populations. Ixodid ticks, which serve as vectors for multiple diseases, have a slow life cycle compared to many of their hosts. The duration of each active life stage (larvae, nymph, adult) varies greatly and depends on factors such as timing of questing and development, host availability throughout the seasons, and photoperiod-related behavioral and developmental diapause. Importantly, the observable questing population only represents a fraction of the total tick population and may include overlapping generations in each stage. Mathematical models are therefore essential to understand how complex life cycle transitions and host interactions impact the dynamics of the tick population. In this study, we present a flexible seasonal matrix model for ixodid ticks that feed on small and large hosts varying in seasonal availability. This model incorporates the delayed life history effects of overwintering and seasonal timing of feeding, density regulation through limited host capacity, and scramble competition among larvae and nymphs for small hosts. We extract the equilibrium seasonal numbers of questing, feeding, and emerging ticks for each life stage, as well as the seasonal patterns of host use. We also calculate key life history characteristics including the mean generation time, stable stage structure, and reproductive values. The baseline model represents a northern life history of the sheep tick (Ixodes ricinus) feeding on a seasonal small host and constant large host, which is compared to a scenario without host seasonality and a scenario representing a southern ecosystem. Our findings support the importance of small hosts in regulating tick populations, and highlight that feeding of larvae is a critical transition. Our analyses shed light on the complex mechanisms underlying the seasonal composition of the questing population, with its important implications for disease risk. The model can be applied to other ixodid tick species and provides a framework for future investigations into population dynamics under various tick and host scenarios.