• The first model exploring female tick selection preference impacts on dynamics. • A novel model stratifying questing adult ticks by sex and mating status. • A proof of the Allee effect due to low mating probability at low tick loads. • A proof of bi-stability arising from female tick selection preference. • A new analytic formula for the male-female ratio, validated by field data. A correlation analysis of the Gulf Coast tick ( Amblyomma maculatum Koch ) count data collected in 1985, 1987, and 1991 from the Shay Ranch in Refugio County Texas demonstrated host selection preference by questing females to the host cattle with feeding/fed male ticks. Here, we develop a novel mathematical model to incorporate this host selection preference, and we use this model to explore the male-female ratio of feeding ticks at the equilibrium state, and to describe the impact of the selection preference by female ticks on mating, reproduction success, and tick population dynamics. The model set-up involves the stratification of questing adult ticks by sex and mating status, and stratification of hosts infested by different categories of ticks. Our equilibrium state analysis illustrates Allee effects due to low mating probability with a small number of ticks distributed over a large number of hosts, where the infestation-free equilibrium is always asymptotically stable. We also give conditions for the existence of infestation-establishment equilibria, in terms of the maximum number of eggs reproduced and survived during the tick life cycle, the adult tick questing rate, and the host selection preference. The model set-up and the established male-female ratio at the equilibrium state provide insight into tactics for tick population suppression strategies. This study also suggests many topics for future studies on a system of delay differential equations with complex nonlinearities due to host selection preference.
Zhang et al. (2026) studied this question.