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

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

doi:10.3934/mbe.2022070

Cited by 3 publications

(2 citation statements)

References 39 publications

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“…Fig. 2 The plot of the RMSE against the step size ∆ at time T = 4 for Example 6.1 with parameters α 1 = 2, β 1 = 1, κ η = 4 × 6 5 and ε = 0.1.…”

Section: Numerical Resultsmentioning

confidence: 99%

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A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

Haghighi

2024

Preprint

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The main objective of this paper is to develop and analyze a numerical method for the strong approximation of solutions to highly nonlinear stiff It\^{o} stochastic differential equations (SDEs). In this method, we first divide the coefficients of the SDEs into linear and nonlinear parts. Then, in two fully explicit recursive phases, we apply the appropriate truncation transformation only to the nonlinear parts of the coefficients of the SDEs at each step. Theoretical aspects are introduced to establish the $L^q$-convergence theory of the new method in the finite time interval $[0,T]$. The stability and boundedness properties of the solutions generated by the new method are also investigated. An important contribution is that the region of MS-stability of the new method includes the region of MS-stability of the partially truncated method proposed by Yang et al. (2022). Moreover, we show that the proposed method preserves the exponential MS-stability and the asymptotic boundedness of the SDEs. Finally, numerical experiments are performed to compare the efficiency of this method with an existing explicit method developed for nonlinear SDEs. MSC Classification: 65C30 , 65L07 , 65L04

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“…Fig. 2 The plot of the RMSE against the step size ∆ at time T = 4 for Example 6.1 with parameters α 1 = 2, β 1 = 1, κ η = 4 × 6 5 and ε = 0.1.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Stochastic differential equations (SDEs) are used in numerous scientific disciplines, including epidemiology, mechanics, microelectronics and finance [1][2][3][4][5]. Numerical methods, which can be broadly categorized as explicit and implicit, are important tools for approximating solutions to these equations [1,6].…”

Section: Introductionmentioning

confidence: 99%

A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

Haghighi

2024

Preprint

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A minimum principle for stochastic control of hepatitis C epidemic model

et al. 2023

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In this paper, we discussed a stochastic optimal control of hepatitis C that minimizes the side effect and reduces the viral load. The control variables represent the drug therapy used for blocking a new infection and virus production. The solution of control problem is solved using the stochastic minimum principle and a four-step scheme. The numerical simulation is carried out to justify the theoretical analysis. The result shows that using both types of drugs for therapy is much more effective.

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Deterministic and stochastic model for the hepatitis C with different types of virus genome

Alnafisah

El-Shahed

2022

MATH

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<abstract><p>In this paper, a deterministic and stochastic model for hepatitis C with different types of virus genomes is proposed and analyzed. Some sufficient conditions are obtained to ensure the stability of the deterministic equilibrium points. We perform a stochastic extension of the deterministic model to study the fluctuation between environmental factors. Firstly, the existence of a unique global positive solution for the stochastic model is investigated. Secondly, sufficient conditions for the extinction of the hepatitis C virus from the stochastic system are obtained. Theoretical and numerical results show that the smaller white noise can ensure the persistence of susceptible and infected populations while the larger white noise can lead to the extinction of disease. By introducing the basic reproduction number $ R_0 $ and the stochastic basic reproduction number $ R_0^s $, the conditions that cause the disease to die out are indicated. The importance of environmental noise in the propagation of hepatitis C viruses is highlighted by these findings.</p></abstract>

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

Cited by 3 publications

References 39 publications

A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

A minimum principle for stochastic control of hepatitis C epidemic model

Deterministic and stochastic model for the hepatitis C with different types of virus genome

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