Persistence and extinction of a stochastic SVI epidemic model with standard incidence and reaction–diffusion

Tan Su; Yonggui Kao; Daqing Jiang

doi:10.1016/j.aml.2025.109579

Persistence and extinction of a stochastic SVI epidemic model with standard incidence and reaction–diffusion

Tan Su
, Yonggui Kao^*
, Daqing Jiang

^*Corresponding author for this work

Harbin Institute of Technology Weihai

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

Abstract

Considering the important effects of population diffusion and vaccine ineffectiveness on disease transmission, a stochastic SVI (Susceptible–Vaccinated–Infected) epidemic model with reaction–diffusion is mainly investigated in this paper. We prove the existence of the unique global positive strong solution by an innovative variable transformation. The sufficient conditions for disease persistence and exponential extinction are also established by suitable Lyapunov functions.

Original language	English
Article number	109579
Journal	Applied Mathematics Letters
Volume	168
DOIs	https://doi.org/10.1016/j.aml.2025.109579
State	Published - Sep 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

Exponential extinction
Persistence
Reaction–diffusion
Stochastic epidemic model

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10.1016/j.aml.2025.109579

Cite this

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title = "Persistence and extinction of a stochastic SVI epidemic model with standard incidence and reaction–diffusion",

abstract = "Considering the important effects of population diffusion and vaccine ineffectiveness on disease transmission, a stochastic SVI (Susceptible–Vaccinated–Infected) epidemic model with reaction–diffusion is mainly investigated in this paper. We prove the existence of the unique global positive strong solution by an innovative variable transformation. The sufficient conditions for disease persistence and exponential extinction are also established by suitable Lyapunov functions.",

keywords = "Exponential extinction, Persistence, Reaction–diffusion, Stochastic epidemic model",

author = "Tan Su and Yonggui Kao and Daqing Jiang",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Ltd",

year = "2025",

month = sep,

doi = "10.1016/j.aml.2025.109579",

language = "英语",

volume = "168",

journal = "Applied Mathematics Letters",

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TY - JOUR

T1 - Persistence and extinction of a stochastic SVI epidemic model with standard incidence and reaction–diffusion

AU - Su, Tan

AU - Kao, Yonggui

AU - Jiang, Daqing

PY - 2025/9

Y1 - 2025/9

N2 - Considering the important effects of population diffusion and vaccine ineffectiveness on disease transmission, a stochastic SVI (Susceptible–Vaccinated–Infected) epidemic model with reaction–diffusion is mainly investigated in this paper. We prove the existence of the unique global positive strong solution by an innovative variable transformation. The sufficient conditions for disease persistence and exponential extinction are also established by suitable Lyapunov functions.

AB - Considering the important effects of population diffusion and vaccine ineffectiveness on disease transmission, a stochastic SVI (Susceptible–Vaccinated–Infected) epidemic model with reaction–diffusion is mainly investigated in this paper. We prove the existence of the unique global positive strong solution by an innovative variable transformation. The sufficient conditions for disease persistence and exponential extinction are also established by suitable Lyapunov functions.

KW - Exponential extinction

KW - Persistence

KW - Reaction–diffusion

KW - Stochastic epidemic model

UR - https://www.scopus.com/pages/publications/105003409733

U2 - 10.1016/j.aml.2025.109579

DO - 10.1016/j.aml.2025.109579

M3 - 文章

AN - SCOPUS:105003409733

SN - 0893-9659

VL - 168

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 109579

ER -

Persistence and extinction of a stochastic SVI epidemic model with standard incidence and reaction–diffusion

Abstract

UN SDGs

Keywords

Access to Document

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