Traveling waves in a nonlocal dispersal SIR model with nonlocal delayed transmission

Wang, Jia-Bing; Li, Wan–Tong; Yang, Fei-Ying

doi:10.1016/j.cnsns.2015.03.005

Cited by 45 publications

(33 citation statements)

References 25 publications

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“…They also obtained the existence and non-existence results of traveling wave solutions, which is related to the basic reproduction number. Li et al [12][13][14] further studied the traveling wave solutions for nonlocal delayed and nonlocal dispersal SIR model with this incidence rate. We mention that the incidence rateˇS I SCI here is an inseparable form, which is different from the other types of incidence.…”

Section: @Sxt/ @Tmentioning

confidence: 99%

“…considered the diffusive SIR epidemic model with the standard incidence rate

\{\begin{matrix} \frac{\partial S (x, t)}{\partial t} = d_{1} \frac{\partial^{2} S (x, t)}{\partial x^{2}} - \frac{β S (x, t) I (x, t)}{S (x, t) + I (x, t)}, \\ \frac{\partial I (x, t)}{\partial t} = d_{2} \frac{\partial^{2} I (x, t)}{\partial x^{2}} + \frac{β S (x, t) I (x, t)}{S (x, t) + I (x, t)} - γ I (x, t), \\ \frac{\partial R (x, t)}{\partial t} = d_{3} \frac{\partial^{2} R (x, t)}{\partial x^{2}} + γ I (x, t) . \end{matrix}

They also obtained the existence and non‐existence results of traveling wave solutions, which is related to the basic reproduction number. Li et al . further studied the traveling wave solutions for nonlocal delayed and nonlocal dispersal SIR model with this incidence rate.…”

Section: Introductionmentioning

confidence: 99%

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

Zhou

Han

Wang

2016

Math Methods in App Sciences

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In this paper, we study the traveling wave solutions of a delayed diffusive SIR epidemic model with nonlinear incidence rate and constant external supplies. We find that the existence of traveling wave solutions is determined by the basic reproduction number of the corresponding spatial‐homogenous delay differential system and the minimal wave speed. The existence is proved by applying Schauder's fixed point theorem and Lyapunov functional method. The non‐existence of traveling waves is obtained by two‐sided Laplace transform. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: @Sxt/ @Tmentioning

confidence: 99%

“…considered the diffusive SIR epidemic model with the standard incidence rate

\{\begin{matrix} \frac{\partial S (x, t)}{\partial t} = d_{1} \frac{\partial^{2} S (x, t)}{\partial x^{2}} - \frac{β S (x, t) I (x, t)}{S (x, t) + I (x, t)}, \\ \frac{\partial I (x, t)}{\partial t} = d_{2} \frac{\partial^{2} I (x, t)}{\partial x^{2}} + \frac{β S (x, t) I (x, t)}{S (x, t) + I (x, t)} - γ I (x, t), \\ \frac{\partial R (x, t)}{\partial t} = d_{3} \frac{\partial^{2} R (x, t)}{\partial x^{2}} + γ I (x, t) . \end{matrix}

Section: Introductionmentioning

confidence: 99%

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

Zhou

Han

Wang

2016

Math Methods in App Sciences

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“…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:…”

Section: Introductionmentioning

confidence: 99%

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

Tian

Yuan

2018

Math Methods in App Sciences

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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.

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“…Furthermore, the state of time delay exists universally in the objective material world [12,16]. In addition, the general incidence is more extensive to illustrate the disease spread process than the special standard incidence.…”

Section: Introductionmentioning

confidence: 99%

Traveling waves for a nonlocal dispersal SIR model equipped delay and generalized incidence

Yang¹,

Yang²,

Jiao³

2020

era

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In this paper, the existence and non-existence of traveling wave solutions are established for a nonlocal dispersal SIR model equipped delay and generalized incidence. In addition, the existence and asymptotic behaviors of traveling waves under critical wave speed are also contained. Especially, the boundedness of traveling waves is obtained completely without imposing additional conditions on the nonlinear incidence.

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Traveling waves in a nonlocal dispersal SIR model with nonlocal delayed transmission

Cited by 45 publications

References 25 publications

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

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

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

Traveling waves for a nonlocal dispersal SIR model equipped delay and generalized incidence

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