ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS TO A VIRUS DYNAMICS MODEL WITH DIFFUSION

作者：Sasaki Toru^*; Suzuki Takashi

来源：Discrete and Continuous Dynamical Systems-Series B, 2018, 23(2): 525-541.

DOI：10.3934/dcdsb.2017206

• Asymptotic behaviour
• Lyapunov functions
• reaction-diffution equations
• virus dynamics model

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 L-1 boundedness of the orbit. Then the pre-compactness 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 R-0 is less than or equal to 1, each orbit converges to the disease free spatially homogeneous equilibrium, and if R-0 > 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.

• 出版日期2018-3