Dynamics of a Tick-Borne Disease Model with Birth Pulse and Pesticide Pulse at Different Moments (Journal of Nonlinear Modeling and Analysis, 2025)
Tick-borne diseases pose a potential risk to public health, which isinfluenced by the stage structure and seasonal reproduction of tick populations.In this paper, a model that explains the transmission dynamics of pathogensamong ticks and hosts is formulated and analyzed, considering birth pulse andpesticide pulse on tick population at different moments. Using the stroboscopicmapping for the disease-free system, we prove a globally asymptotically stablepositive periodic solution exists when the pulsed pesticide spraying intensity isless than a critical threshold. Applying the comparison theorem for the impulsive differential system, the conditions for global attraction of the disease-freeperiodic solution to the investigated system are given. Moreover, we demonstrate the persistence of the studied system and give numerical simulations toverify it. Ultimately, we discuss the case with multiple pesticide sprays andconclude that fewer sprays are more favorable for disease extinction.