Wave propagation in a diffusive SEIR epidemic model with nonlocal reaction and standard incidence rate

Abstract

We study the existence and nonexistence of traveling waves of the reaction‐diffusion equations that describes a diffusive SEIR model with nonlocal reaction between the infected subpopulation and the susceptible subpopulation, where the total population is not constant. The existence of traveling waves depends on the basic reproduction number R0 of the corresponding ordinary differential equations and the minimal wave speed c∗. The main difficulty is the lack of order‐preserving property of our general system. Its proof is showed by constructing a closed and convex set and applying Schauder fixed point theorem. The proof of nonexistence result is obtained by two‐side Laplace transform. Finally, we present some numerical results of the minimal wave speed.

Analysis on critical waves for a diffusive epidemic model with saturating incidence rate and infinitely distributed delay

“…As in the proof of Wu et al, 12 , Theorem 3.1 we find that S is monotonically decreasing in R, ( S, Ĩ)(+∞) = (S ∞ , 0), ( S, Ĩ) ′ (±∞) = (0, 0), and…”

Traveling waves for a four‐compartment lattice epidemic system with exposed class and standard incidence

“…We would like to point out that the fourth equation of model (1.5) is coupled with the other equations, and the model studied in the current paper cannot be simplified. Although there are some works that have studied the traveling wave solution for epidemic model that R-equation cannot be decoupled, there always an assumption on the diffusion rate for the model (see, for example, condition (2.7) in Wang et al 28 and condition (20) in Wu et al 29 ). Inspired by the study of He and Tsai, 30 we will show the existence of traveling wave solutions for model (1.5) without any further condition on the diffusion rates in the current paper.…”

Public Opinion Communication Model under the Control of Official Information

“…Bentaleb and Aminie proposed a multistrain SEIR epidemic model with bilinear and nonmonotonic incident functions [22]. Wu et al proposed a nonlocalized diffusion SEIR model [23], and Liu et al proposed a new SEIR rumor propagation model that included a hesitation mechanism [24]. Zhang and Cheng established the SETQR model and used the probability theorem to derive the information propagation law [25].…”