Minimal wave speed and traveling wave in nonlocal dispersion SIS epidemic model with delay

Rassim Darazirar; Rasha M. Yaseen; Ahmed A. Mohsen; Aziz Khan; Thabet Abdeljawad

doi:10.1186/s13661-025-02055-1

Minimal wave speed and traveling wave in nonlocal dispersion SIS epidemic model with delay

Rassim Darazirar
, Rasha M. Yaseen
, Ahmed A. Mohsen^*
, Aziz Khan
, Thabet Abdeljawad^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

This study examines traveling wave solutions of the SIS epidemic model with nonlocal dispersion and delay. The research shows that a key factor in determining whether traveling waves exist is the basic reproduction number R0. In particular, the system permits nontrivial traveling wave solutions for σ≥σ∗ for R0>1, whereas there are no such solutions for σ<σ∗. This is because there is a minimal wave speed σ∗>0. On the other hand, there are no traveling wave solutions when R0≤1. In conclusion, we provide several numerical simulations that illustrate the existence of TWS.

Original language	English
Article number	67
Journal	Boundary Value Problems
Volume	2025
Issue number	1
DOIs	https://doi.org/10.1186/s13661-025-02055-1
Publication status	Published - Dec 2025
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Basic reproduction number
Minimal wave speed
SIS model
Traveling waves

Access to Document

10.1186/s13661-025-02055-1

Cite this

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title = "Minimal wave speed and traveling wave in nonlocal dispersion SIS epidemic model with delay",

abstract = "This study examines traveling wave solutions of the SIS epidemic model with nonlocal dispersion and delay. The research shows that a key factor in determining whether traveling waves exist is the basic reproduction number R0. In particular, the system permits nontrivial traveling wave solutions for σ≥σ∗ for R0>1, whereas there are no such solutions for σ<σ∗. This is because there is a minimal wave speed σ∗>0. On the other hand, there are no traveling wave solutions when R0≤1. In conclusion, we provide several numerical simulations that illustrate the existence of TWS.",

keywords = "Basic reproduction number, Minimal wave speed, SIS model, Traveling waves",

author = "Rassim Darazirar and Yaseen, \{Rasha M.\} and Mohsen, \{Ahmed A.\} and Aziz Khan and Thabet Abdeljawad",

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T1 - Minimal wave speed and traveling wave in nonlocal dispersion SIS epidemic model with delay

AU - Darazirar, Rassim

AU - Yaseen, Rasha M.

AU - Mohsen, Ahmed A.

AU - Khan, Aziz

AU - Abdeljawad, Thabet

N1 - Publisher Copyright: © The Author(s) 2025.

PY - 2025/12

Y1 - 2025/12

N2 - This study examines traveling wave solutions of the SIS epidemic model with nonlocal dispersion and delay. The research shows that a key factor in determining whether traveling waves exist is the basic reproduction number R0. In particular, the system permits nontrivial traveling wave solutions for σ≥σ∗ for R0>1, whereas there are no such solutions for σ<σ∗. This is because there is a minimal wave speed σ∗>0. On the other hand, there are no traveling wave solutions when R0≤1. In conclusion, we provide several numerical simulations that illustrate the existence of TWS.

AB - This study examines traveling wave solutions of the SIS epidemic model with nonlocal dispersion and delay. The research shows that a key factor in determining whether traveling waves exist is the basic reproduction number R0. In particular, the system permits nontrivial traveling wave solutions for σ≥σ∗ for R0>1, whereas there are no such solutions for σ<σ∗. This is because there is a minimal wave speed σ∗>0. On the other hand, there are no traveling wave solutions when R0≤1. In conclusion, we provide several numerical simulations that illustrate the existence of TWS.

KW - Basic reproduction number

KW - Minimal wave speed

KW - SIS model

KW - Traveling waves

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VL - 2025

JO - Boundary Value Problems

JF - Boundary Value Problems

IS - 1

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ER -

Minimal wave speed and traveling wave in nonlocal dispersion SIS epidemic model with delay

Abstract

UN SDGs

Keywords

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