Traveling Waves Of A Dispersal Influenza Model Including Human Mobility

In this paper,we consider the existence and nonexistence of traveling wave solutions for an influenza transmission model incorporating human mobility both in local and nonlocal diffusion case.Firstly,we introduce the related background,including the significance of research the epidemic model,some mathematical models and main methods about analyze infectious disease.Furthermore,we propose our issue and recommend the main results.Next,we think about the existence and nonexistence of traveling wave so-lutions of a reaction-diffusion influenza transmission model including human mo-bility.We employ the Schauder's fixed point theorem combine with the upper and lower solutions method and limiting argument to investigate the existence of traveling waves.In addition,we construct suitable Lyapunov f'unctions to obtain the boundary asymptotic behavior of traveling wave solutions at+?.The nonex-istence of traveling waves is acquired by contradiction and comparison principle.Finally,we study the existence and nonexistence of traveling wave solutions for a nonlocal dispersal influenza transmission model incorporating human mobil-ity by constructing an invariant cone in a bounded domain and use the Schauder's fixed point theorem to investigate the existence of non-trivial bounded positive solutions,and then pass to the unbounded domain by a limiting argument.