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A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations

Author

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  • José Paulo Carvalho dos Santos
  • Lislaine Cristina Cardoso
  • Evandro Monteiro
  • Nelson H. T. Lemes

Abstract

This paper shows that the epidemic model, previously proposed under ordinary differential equation theory, can be generalized to fractional order on a consistent framework of biological behavior. The domain set for the model in which all variables are restricted is established. Moreover, the existence and stability of equilibrium points are studied. We present the proof that endemic equilibrium point when reproduction number is locally asymptotically stable. This result is achieved using the linearization theorem for fractional differential equations. The global asymptotic stability of disease-free point, when , is also proven by comparison theory for fractional differential equations. The numeric simulations for different scenarios are carried out and data obtained are in good agreement with theoretical results, showing important insight about the use of the fractional coupled differential equations set to model babesiosis disease and tick populations.

Suggested Citation

  • José Paulo Carvalho dos Santos & Lislaine Cristina Cardoso & Evandro Monteiro & Nelson H. T. Lemes, 2015. "A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-10, July.
    • Handle: RePEc:hin:jnlaaa:729894
    DOI: 10.1155/2015/729894
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    Cited by:

    1. Tirumalasetty Chiranjeevi & Raj Kumar Biswas, 2017. "Discrete-Time Fractional Optimal Control," Mathematics, MDPI, vol. 5(2), pages 1-12, April.
    2. Vassili N. Kolokoltsov, 2023. "On the Control over the Distribution of Ticks Based on the Extensions of the KISS Model," Mathematics, MDPI, vol. 11(2), pages 1-25, January.
    3. Cardoso, Lislaine Cristina & Camargo, Rubens Figueiredo & dos Santos, Fernando Luiz Pio & Dos Santos, José Paulo Carvalho, 2021. "Global stability analysis of a fractional differential system in hepatitis B," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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