Asymptotic behaviour of the solutions to a virus dynamics model with diffusion

Toru Sasaki, Takashi Suzuki

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Asymptotic behaviour of the solutions to a basic virus dynamics model is discussed. We consider the population of uninfected cells, infected cells, and virus particles. Diffusion effect is incorporated there. First, the Lyapunov function effective to the spatially homogeneous part (ODE model without diffusion) admits the L1 boundedness of the orbit. Then the precompactness of this orbit in the space of continuous functions is derived by the semigroup estimates. Consequently, from the invariant principle, if the basic reproductive number R0 is less than or equal to 1, each orbit converges to the disease free spatially homogeneous equilibrium, and if R0 > 1, each orbit converges to the infected spatially homogeneous equilibrium, which means that the simple diffusion does not affect the asymptotic behaviour of the solutions.

Original languageEnglish
Pages (from-to)525-541
Number of pages17
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number2
Publication statusPublished - Mar 1 2018



  • Asymptotic behaviour
  • Lyapunov functions
  • Reaction-diffution equations
  • Virus dynamics model

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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