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

Author:

Zhang, X, and Wu, J

Publication type:

Journal Article

Publication date:

2023-02

Journal/Series title:

Journal of Mathematical Biology

Volume:

Issue:

URL:

https://link.springer.com/article/10.1007/s00285-023-01879-8

Abstract:

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.