Global dynamics of tick-borne diseases
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Updated: Dec 7, 2025

Tick Microbiome Characterization by Next-Generation 16S rRNA Amplicon Sequencing
Published on: August 25, 2018
Ardak Kashkynbayev1, Daiana Koptleuova1
1Department of Mathematics, Nazarbayev University, 53 Kabanbay batyr avenue, Nur-Sultan 010000, Kazakhstan.
Abstract:
A tick-borne disease model is considered with nonlinear incidence rate and piecewise constant delay of generalized type. It is known that the tick-borne diseases have their peak during certain periods due to the life cycle of ticks. Only adult ticks can bite and transmit disease. Thus, we use a piecewise constant delay to model this phenomena. The global asymptotic stability of the disease-free and endemic equilibrium is shown by constructing suitable Lyapunov functions and Lyapunov-LaSalle technique. The theoretical findings are illustrated through numerical simulations.
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