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

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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 R0 > 1 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 R0

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Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:729894
DOI: 10.1155/2015/729894
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