Bifurcations and dynamics of a Filippov epidemic model with joint threshold control policy and vector preference

Threshold interventions are essential for the targeted control of infectious diseases, but their effectiveness can be strongly influenced by vector preference, which is often neglected in existing non-smooth dynamic models. Accordingly, this study investigates the impact of vector preference on threshold control strategies. We develop a Filippov model with vector preference and a joint threshold policy, where interventions are triggered when the combined proportion of susceptible and infected hosts exceeds a critical level. We theoretically analyze the existence of sliding regions, the existence and stability of regular equilibria and pseudo-equilibria, as well as discontinuity-induced bifurcation phenomena. Our results reveal that vector preference can induce diverse equilibrium states. In particular, preference for susceptible hosts allows the coexistence of up to five equilibria, leading to various bistability and possible tristability. Numerical simulations further show that without preference the threshold level directly determines whether early intervention is triggered. Preference for susceptible hosts markedly increases threshold sensitivity and readily induces multistability, allowing disease persistence even when the basic reproduction number is below one; thus, effective control requires targeting the critical threshold rather than merely lowering it. In contrast, preference for infected hosts yields a more monotonic response and facilitates stable disease suppression over a broader range of threshold values. These results indicate that precise threshold setting is essential for effective disease control across different host preference patterns.