Qualitative behaviour of a stochastic hepatitis C epidemic model in cellular level

Dwi Lestari; Noorma Yulia Megawati; Nanang Susyanto; Fajar Adi-Kusumo; Dwi Lestari; Noorma Yulia Megawati; Nanang Susyanto; Fajar Adi-Kusumo

doi:10.3934/mbe.2022070

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 2: 1515-1535. doi: 10.3934/mbe.2022070

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Research article

Qualitative behaviour of a stochastic hepatitis C epidemic model in cellular level

1.
Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia
2.
Department of Mathematics Education, Universitas Negeri Yogyakarta, Yogyakarta, Indonesia

Received: 13 September 2021 Accepted: 28 November 2021 Published: 08 December 2021

In this paper, a mathematical model describing the dynamical of the spread of hepatitis C virus (HCV) at a cellular level with a stochastic noise in the transmission rate is developed from the deterministic model. The unique time-global solution for any positive initial value is served. The Ito's Formula, the suitable Lyapunov function, and other stochastic analysis techniques are used to analyze the model dynamics. The numerical simulations are carried out to describe the analytical results. These results highlight the impact of the noise intensity accelerating the extinction of the disease.
- hepatitis C virus,
- stochastic noise,
- transmission rate,
- extinction,
- persistence in mean,
- numerical simulation
Citation: Dwi Lestari, Noorma Yulia Megawati, Nanang Susyanto, Fajar Adi-Kusumo. Qualitative behaviour of a stochastic hepatitis C epidemic model in cellular level[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 1515-1535. doi: 10.3934/mbe.2022070

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Abstract

In this paper, a mathematical model describing the dynamical of the spread of hepatitis C virus (HCV) at a cellular level with a stochastic noise in the transmission rate is developed from the deterministic model. The unique time-global solution for any positive initial value is served. The Ito's Formula, the suitable Lyapunov function, and other stochastic analysis techniques are used to analyze the model dynamics. The numerical simulations are carried out to describe the analytical results. These results highlight the impact of the noise intensity accelerating the extinction of the disease.

References

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