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- W2550414334 abstract "This paper is devoted to the study of the wave propagation in a reaction-convection infectious disease model with a spatio-temporal delay. Previous numerical studies have demonstrated the existence of traveling wave fronts for the system and obtained a critical value c ⁎ , which is the minimal wave speed of the traveling waves. In the present paper, we provide a complete and rigorous proof. To overcome the difficulty due to the lack of monotonicity for the system, we construct a pair of upper and lower solutions, and then apply the Schauder fixed point theorem to establish the existence of a nonnegative solution for the wave equation on a bounded interval. Moreover, we use a limiting argument and in turn generate the solution on the unbounded interval R . In particular, by constructing a suitable Lyapunov functional, we further show that the traveling wave solution converges to the epidemic equilibrium point as t = + ∞ ." @default.
- W2550414334 created "2016-11-30" @default.
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- W2550414334 date "2017-05-01" @default.
- W2550414334 modified "2023-09-26" @default.
- W2550414334 title "Wave propagation in an infectious disease model" @default.
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- W2550414334 doi "https://doi.org/10.1016/j.jmaa.2016.11.051" @default.
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