Dynamics of a Tick-Borne Disease Model with Birth Pulse and Pesticide Pulse at Different Moments
Year: 2025
Journal of Nonlinear Modeling and Analysis, Vol. 7 (2025), Iss. 1 : pp. 111–134
Abstract
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2025.111
Journal of Nonlinear Modeling and Analysis, Vol. 7 (2025), Iss. 1 : pp. 111–134
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Tick-borne disease stage structure double pulse stability permanence.
Author Details
Shuyu Yan Email
Xue Zhang Email