Construction of positivity preserving numerical method for stochastic age-dependent population equations

Tan, Jianguo; Men, Weiwei; Pei, Yongzhen; Guo, Yongfeng

doi:10.1016/j.amc.2016.08.010

Cited by 14 publications

(11 citation statements)

References 15 publications

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“…e initial values in our numerical experiment are S(0) � 2, I(0) � 1.5, R(0) � 0.4. e control C k , D k , E k is measurable and for any t ∈ [0, T]. We use BIM [14] to prove the simulation of stochastic model (13). Figure 1 shows the solution curves that we used by the EM method; it represents the variation of population for susceptible S(t), infected I(t) and recovered S(t), respectively.…”

Section: Numerical Simulationmentioning

confidence: 99%

The Positivity of Numerical Method for Susceptible-Infected-Recovered-Susceptible Epidemic Model

Feng

Zong

2020

Mathematical Problems in Engineering

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Sudden environmental perturbations may affect the positivity of the solution of the susceptible-infected-recovered-susceptible (SIRS) model. Most of the SIRS epidemic models have no analytical solution. Thus, in order to find the appropriate solution, the numerical technique becomes more essential for us to solve the dynamic behavior of epidemics. In this paper, we are concerned with the positivity of the numerical solution of a stochastic SIRS epidemic model. A new numerical method that is the balanced implicit method (BIM) is set, which preserves the positivity under given conditions. The BIM method can maintain positive numerical solution. An illustrative numerical instance is presented for the numerical BIM of the stochastic SIRS model.

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Section: Numerical Simulationmentioning

confidence: 99%

The Positivity of Numerical Method for Susceptible-Infected-Recovered-Susceptible Epidemic Model

Feng

Zong

2020

Mathematical Problems in Engineering

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“…Similarly, we have 18) we then compute 19) where g 1 = (18β 2 T + 24σ 2 )K 2 , g 2 = [(1e) 2 (18β 2 T + 24σ 2 )]K 2 , g 3 = (18β 2 T + 24σ 2 )K 2 + 18(1e) 2 β 2 TK 2 + 24(1e) 2 σ 2 K 2 + 9(μ + α) 2 T. Moreover, we have…”

Section: Theorem 31 Let S(t) I(t) V (T) Be the True Solution And Smentioning

confidence: 99%

“…Hence, the main purpose of this present paper is to structure a new method to maintain the nonnegative path of the solution for a stochastic epidemic SIVS model, which is the balanced implicit method. The main technique we developed is based on Tan's principle [19].…”

Section: Introductionmentioning

confidence: 99%

Construction of positivity-preserving numerical method for stochastic SIVS epidemic model

Zhang

2019

Adv Differ Equ

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In this paper we propose the balanced implicit numerical techniques for maintaining the nonnegative path of the solution in stochastic susceptible-infected-vaccinated-susceptible (SIVS) epidemic model. We can hardly acquire the explicit solution for the SIVS model, so we often use the numerical scheme to produce approximate solutions. The Euler-Maruyama (EM) method is a useful and effective means in producing numerical solutions of SIVS model. The EM method to simulate the stochastic SIVS model often results in the problem that the numerical solution is not positive. In order to eliminate the negative path of the solution in a stochastic SIVS epidemic model, we construct a numerical method preserving positivity for the SIVS model. It is proved that the balanced implicit method (BIM) can preserve positivity and we show the convergence of the BIM numerical approximate solution to the exact solution. Finally, a numerical example is offered to support the theoretical results and verify the availability of the approach.

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“…Recently, the SSθ method has attracted many scholars' attention because of its advantages in dealing with the flexibility and the stability for the SDEs [11][12][13][14][15][16][17][18]. Researchers find that SSθ method or its improved forms have pretty stable properties, convergence rates, and structure-preserving properties [14,15,[18][19][20], and the SSθ method includes Euler method and split-step backward Euler (SSBE) method by fixing θ = 0 and θ = 1, respectively. However, as far as we know, few results on the convergence of SSθ method for stochastic age-dependent capital models with Poisson jumps and fBm have been reported.…”

Section: ∂K(at) ∂Tmentioning

confidence: 99%

Strong convergence of the split-step θ-method for stochastic age-dependent capital system with Poisson jumps and fractional Brownian motion

Kang

Zhang

2018

Adv Differ Equ

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Most stochastic age-dependent capital systems cannot be solved explicitly, so it is necessary to develop numerical methods and study the properties of numerical solutions. In this paper, we consider a class of stochastic age-dependent capital systems with Poisson jumps and fractional Brownian motion (fBm) and investigate the convergence of the split-step θ-method (SSθ) for this system. It is proved that the numerical approximation solutions converge to the analytic solutions for the equations, and the order of approximation is also provided. Finally, a numerical experiment is simulated to illustrate that the SSθ method has better accuracy than the Euler method.

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Construction of positivity preserving numerical method for stochastic age-dependent population equations

Cited by 14 publications

References 15 publications

The Positivity of Numerical Method for Susceptible-Infected-Recovered-Susceptible Epidemic Model

The Positivity of Numerical Method for Susceptible-Infected-Recovered-Susceptible Epidemic Model

Construction of positivity-preserving numerical method for stochastic SIVS epidemic model

Strong convergence of the split-step θ-method for stochastic age-dependent capital system with Poisson jumps and fractional Brownian motion

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