Traveling waves for a nonlocal dispersal SIR model with delay and external supplies

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

“…On the other hand, if R 0 = + > 1 and c ∈ (0, c * ), or R 0 ≤ 1, then there exists no nontrivial and nonnegative traveling wave solution (S, E, I, R) satisfying the asymptotic boundary conditions (15). Remark 2.1.…”

“…Theorem 4.1. If R 0 = + ≤ 1, then there exists no nontrivial and nonnegative traveling wave solution (S, E, I, R) of system (11) to (14) satisfying the asymptotic boundary conditions (15).…”

“…Proof. Suppose for the contrary that (S(x + ct), E(x + ct), I(x + ct), R(x + ct)) is a traveling wave solution of (11) to (14) satisfying the asymptotic boundary conditions (15). Since…”

“…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

“…Thus, it is necessary to consider models taking the vital dynamics into account. Therefore, Li et al [16,17], Fu [18], and Zhang et al [19] considered the following delayed diffusive SIR epidemic models with external supplies 8 < :…”