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Global dynamics of tick-borne diseases

  • Received: 11 March 2020 Accepted: 29 May 2019 Published: 05 June 2020
  • 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.

    Citation: Ardak Kashkynbayev, Daiana Koptleuova. Global dynamics of tick-borne diseases[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 4064-4079. doi: 10.3934/mbe.2020225

    Related Papers:

  • 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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