The impact of two independent gaussian white noises on the behavior of a stochastic epidemic model

• Autorzy: Yavuz Mehmet , Boulaasair Lahcen , Bouzahir Hassane , Diop Mamadou Abdoul , Benaid Brahim

Identyfikatory

DOI

10.17512/jamcm.2024.1.10

• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to investigate a stochastic SIS (Susceptible, Infected, Susceptible) epidemic model in which the disease transmission coefficient and the death rate are subject to random disturbances. Using the convergence theorem for local martingales and solving the Fokker-Planck equation associated with the one-dimensional stochastic differential equation, we demonstrate that the disease will almost surely persist in the mean. In the case of global asymptotic stability of the endemic equilibrium for a SIS deterministic epidemic model, we formulate suitable conditions guaranteeing that the stochastic SIS model has a unique ergodic stationary distribution. Furthermore, we deal with the exponential extinction of the disease. Finally, some numerical simulations are provided to illustrate the obtained analytical results.

Słowa kluczowe

EN

stochastic differential equation; martingale; Fokker-Planck equation; stationary distribution; ergodicity; persistence; extinction

PL

stochastyczne równanie różniczkowe; martyngał; równanie Fokkera-Plancka; ergodyczność; trwałość; wygaśnięcie

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2024
• Tom: Vol. 23, nr 1
• Strony: 121--134
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Yavuz Mehmet

• Necmettin Erbakan University, Department of Mathematics and Computer Sciences, 42090 Meram Konya, Turkey
• Centre for Environmental Mathematics, Faculty of Environment, Science and Economy University of Exeter, Cornwall TR10 9FE, UK

autor

Boulaasair Lahcen

• ISTI Lab, Ibn Zohr University, ENSA, PO Box 1136, Agadir, Morocco

autor

Bouzahir Hassane

• ISTI Lab, Ibn Zohr University, ENSA, PO Box 1136, Agadir, Morocco

autor

Diop Mamadou Abdoul

• UFR Applied Sciences and Technologies, Department of Mathematics Gaston Berger University, PO Box 234, Saint-Louis, Senegal

autor

Benaid Brahim

• ISTI Lab, Ibn Zohr University, ENSA, PO Box 1136, Agadir, Morocco

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).