Dynamics of a tick-borne disease transmission model with acquired tick resistance

Tick-borne diseases pose a potential threat to public health, and mathematical models have been developed and used to analyze the spread mechanisms of tick-borne diseases. An important host behavior, acquired tick resistance (ATR), to defend against tick infestation, has not yet been modeled and qualitatively analyzed. This paper proposes a model of tick-borne disease transmission incorporating ATR, where hosts are categorized into subgroups based on their infection status and tick bite counts. For the tick-host population model, we derive four distribution patterns of the host subpopulations and analyze the global asymptotic stability of the positive equilibrium. For the disease transmission model, we calculate the basic reproduction number and prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium. Numerical simulations illustrate that the emergence of ATR effectively reduces the number of infected hosts, while an increase in the co-feeding transmission probability leads to a rise in the number of infected ticks.