Open AccessGlobal dynamics of tick-borne diseases
Author(s) -
Ardak Kashkynbayev,
Daiana Koptleuova
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020225
Subject(s) - piecewise , tick , lyapunov function , constant (computer programming) , mathematics , nonlinear system , exponential stability , basic reproduction number , control theory (sociology) , biology , computer science , mathematical analysis , physics , ecology , medicine , control (management) , artificial intelligence , population , environmental health , quantum mechanics , programming language
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.