TRAVELING WAVE SOLUTION FOR A DIFFUSION SEIR EPIDEMIC MODEL WITH SELF-PROTECTION AND TREATMENT

A reaction-diffusion SEIR model, including the self-protection for susceptible individuals, treatments for infectious individuals and constant recruitment, is introduced. The existence of traveling wave solution, which is determined by the basic reproduction number R-0 and wave speed c, is firstly proved as R-0 > 1 and c >= c* via the Schauder fixed point theorem, where c* is minimal wave speed. Asymptotic behavior of traveling wave solution at infinity is also proved by applying the Lyapunov functional. Furthermore, when R-0 <= 1 or R-0 > 1 with c is an element of (0, c*), we derive the non-existence of traveling wave solution with utilizing two-sides Laplace transform. We take advantage of numerical simulations to indicate the existence of traveling wave, and show that self-protection and treatment can reduce the spread speed at last.