A mathematical study of the influence of media on the asymptotic dynamics of diseases

This study explores the asymptotic behavior of a stochastic epidemic model that accounts for the impact of media coverage. The initial focus lies on determining the conditions leading to the exponential extinction of the disease. Additionally, we investigate the weak convergence of the probability d...

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Main Authors: Lahcen Boulaasair, Hassane Bouzahir, N. Seshagiri Rao, Salma Haque, Nabil Mlaiki
Format: Article
Language:English
Published: Elsevier 2024-12-01
Series:Partial Differential Equations in Applied Mathematics
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S2666818124003681
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author Lahcen Boulaasair
Hassane Bouzahir
N. Seshagiri Rao
Salma Haque
Nabil Mlaiki
author_facet Lahcen Boulaasair
Hassane Bouzahir
N. Seshagiri Rao
Salma Haque
Nabil Mlaiki
author_sort Lahcen Boulaasair
collection DOAJ
description This study explores the asymptotic behavior of a stochastic epidemic model that accounts for the impact of media coverage. The initial focus lies on determining the conditions leading to the exponential extinction of the disease. Additionally, we investigate the weak convergence of the probability distribution of the stochastic process N(t), representing the total population, to a one-dimensional stochastic process with density calculated through the Fokker–Planck equation. Subsequently, we demonstrate the persistent nature of the disease and utilize Has’minskii theory to establish the presence of a unique ergodic stationary distribution for our stochastic epidemic model. Finally, numerical simulations are conducted to validate the theoretical findings.
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publishDate 2024-12-01
publisher Elsevier
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series Partial Differential Equations in Applied Mathematics
spelling doaj-art-e1ab7f42469c45868d1cac5b3fc4ef632025-08-20T02:50:09ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210098210.1016/j.padiff.2024.100982A mathematical study of the influence of media on the asymptotic dynamics of diseasesLahcen Boulaasair0Hassane Bouzahir1N. Seshagiri Rao2Salma Haque3Nabil Mlaiki4ISTI Lab, ENSA, Ibn Zohr University, Agadir, MoroccoISTI Lab, ENSA, Ibn Zohr University, Agadir, MoroccoDepartment of Mathematics & Statistics, School of Applied Science & Humanities, Vignan’s Foundation for Science, Technology & Research, Vadlamudi 522213, Andhra Pradesh, IndiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia; Corresponding author.This study explores the asymptotic behavior of a stochastic epidemic model that accounts for the impact of media coverage. The initial focus lies on determining the conditions leading to the exponential extinction of the disease. Additionally, we investigate the weak convergence of the probability distribution of the stochastic process N(t), representing the total population, to a one-dimensional stochastic process with density calculated through the Fokker–Planck equation. Subsequently, we demonstrate the persistent nature of the disease and utilize Has’minskii theory to establish the presence of a unique ergodic stationary distribution for our stochastic epidemic model. Finally, numerical simulations are conducted to validate the theoretical findings.http://www.sciencedirect.com/science/article/pii/S2666818124003681Disease dynamicsMedia coverageExponential extinctionPersistence in meanFokker–Planck equationStationary distribution
spellingShingle Lahcen Boulaasair
Hassane Bouzahir
N. Seshagiri Rao
Salma Haque
Nabil Mlaiki
A mathematical study of the influence of media on the asymptotic dynamics of diseases
Partial Differential Equations in Applied Mathematics
Disease dynamics
Media coverage
Exponential extinction
Persistence in mean
Fokker–Planck equation
Stationary distribution
title A mathematical study of the influence of media on the asymptotic dynamics of diseases
title_full A mathematical study of the influence of media on the asymptotic dynamics of diseases
title_fullStr A mathematical study of the influence of media on the asymptotic dynamics of diseases
title_full_unstemmed A mathematical study of the influence of media on the asymptotic dynamics of diseases
title_short A mathematical study of the influence of media on the asymptotic dynamics of diseases
title_sort mathematical study of the influence of media on the asymptotic dynamics of diseases
topic Disease dynamics
Media coverage
Exponential extinction
Persistence in mean
Fokker–Planck equation
Stationary distribution
url http://www.sciencedirect.com/science/article/pii/S2666818124003681
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