Traveling waves in a Kermack–Mckendrick epidemic model with diffusion and latent period

Critical traveling waves in a diffusive disease model

“…We prove that F is compact with respect to the norm | · | µ in B µ (R, R 2 ). The proof can be carried out by the similar argument as that in [16,Lemma 3.5] or [21,Lemma 3.7]. For completeness, we give the details here.…”

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

“…Furthermore, there does not exist any nontrivial and nonnegative traveling wave solution for this system if c < c * or R 0 = ∕( + ) ≤ 1. More works have been done to get the existence of traveling waves in other cases, refer to, eg, the standard incidence rate SI∕(S + I) in Wang et al, 5 a saturating incidence rate SI∕(1 + kI) in Xu, 6 Michaelis-Menten-type incidence rate SI∕(1 + b(S + I + R)) in Chapwanya et al, 7 general nonlinear incidence rates in other studies, [8][9][10][11] nonlocal reaction terms in other studies, [12][13][14] and nonlocal diffusion terms in Li et al 15 and Yang et al 16 Recently, Tian and Yuan 17 considered the following SEIR model:…”

Traveling wave solutions for a delayed diffusive SIR epidemic model with nonlinear incidence rate and external supplies

“…Accordingly, by using Schauder's fixed point theorem and Laplace transform, Wang and Wu studied the existence and non‐existence of traveling wave solutions for the diffusive epidemic model with nonlocal and delayed disease transmission, and obtained the similar results that correspond to Hosono and Ilyas's conclusions. Note that the incidence rate in these two models are bilinear term β S I , after then, there have been numerous researches focusing on the traveling wave solutions for (delayed) diffusive epidemic models with nonlinear incidence rate, such as incidence rate and general form f ( S ) g ( I ).…”