Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 77, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2023.104041
Keywords
Time-periodic; Periodic traveling wave solutions; Critical wave speed; Influenza model; Treatment
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This paper investigates the existence and nonexistence of time-periodic traveling waves for a diffusive influenza model with treatment and seasonality. By utilizing the next generation operator theory and Schauder's fixed point theorem, the conditions for the existence of time-periodic traveling wave solutions are obtained, along with the proof of nonexistence in certain cases and exponential decay for waves with critical speed.
This paper is concerned with the existence and nonexistence of time-periodic traveling waves for a diffusive influenza model with treatment and seasonality. By using the next generation operator theory, we first get basic reproduction number R-0 for the corresponding periodic ODEs. Then, by constructing sub-and super-solutions and using Schauder's fixed point theorem, we obtain the existence of time-periodic traveling wave solutions for the system with wave speed c >c(& lowast;) and R-0 > 1. We further prove the existence of time-periodic traveling waves with wave speed c = c(& lowast;) by a delicate limitation argument. For d(u) = d(h), the nonexistence of traveling waves is proved by a contradiction argument for two cases involved with c(& lowast;) and R-0, while the exponential decay of traveling waves with the critical speed is obtained by a dynamical system approach combined with Laplace transform.
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