@Article{JNMA-7-1,
author = {Yan, Shuyu and Zhang, Xue},
title = {Dynamics of a Tick-Borne Disease Model with Birth Pulse and Pesticide Pulse at Different Moments},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2025},
volume = {7},
number = {1},
pages = {111--134},
abstract = {<p style="text-align: justify;">Tick-borne diseases pose a potential risk to public health, which is
influenced by the stage structure and seasonal reproduction of tick populations.
In this paper, a model that explains the transmission dynamics of pathogens
among ticks and hosts is formulated and analyzed, considering birth pulse and
pesticide pulse on tick population at different moments. Using the stroboscopic
mapping for the disease-free system, we prove a globally asymptotically stable
positive periodic solution exists when the pulsed pesticide spraying intensity is
less than a critical threshold. Applying the comparison theorem for the impulsive differential system, the conditions for global attraction of the disease-free
periodic solution to the investigated system are given. Moreover, we demonstrate the persistence of the studied system and give numerical simulations to
verify it. Ultimately, we discuss the case with multiple pesticide sprays and
conclude that fewer sprays are more favorable for disease extinction.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2025.111},
url = {https://global-sci.com/article/91684/dynamics-of-a-tick-borne-disease-model-with-birth-pulse-and-pesticide-pulse-at-different-moments}
}