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This article deals with the numerical positivity, boundedness, convergence, and dynamical behaviors for stochastic susceptible-infected-susceptible (SIS) model. To guarantee the biological significance of the split-step backward Euler method applied to the stochastic SIS model, the numerical positivity and boundedness are investigated by the truncated Wiener process. Motivated by the almost sure boundedness of exact and numerical solutions, the convergence is discussed by the fundamental convergence theorem with a local Lipschitz condition. Moreover, the numerical extinction and persistence are initially obtained by an exponential presentation of the stochastic stability function and strong law of the large number for martingales, which reproduces the existing theoretical results. Finally, numerical examples are given to validate our numerical results for the stochastic SIS model. [ABSTRACT FROM AUTHOR]

The paper deals with the numerical positivity, convergence and dynamical behaviors (including extinction and persistence) for stochastic SIS model. Compared with the existing numerical methods, a linearly backward Euler method with truncated Wiener process is introduced with a less computational cost and a better dynamic behavior. We discuss the numerical positivity by the truncated Wiener process, which is the basis for the investigation of convergence and dynamic behavior. The numerical dynamical behaviors (extinction and persistence) are obtained by an exponential representation for the nonlinear stochastic stability function and the large number theorem for martingale, which reproduces the existing theoretical results of exact solution. Finally, numerical examples are given to validate our numerical results for stochastic SIS model. [ABSTRACT FROM AUTHOR]

The paper deals with the asymptotical mean-square stability of the linear θ-methods under variable stepsize and transformation approach for stochastic pantograph differential equations. A limiting equation for the analysis of numerical stability is introduced by Kronecker products. Under the condition which guarantee the stability of exact solutions, the optimal stability region of the linear θ-methods under variable stepsize is given by using the limiting equation, i.e. θ ∈ (1 2 , 1 ] , which is the same to the deterministic problems. Moreover, the linear θ-methods under the transformation approach are also considered and the result of the stability is improved for θ = 1 2 . Finally, numerical examples are given to illustrate the asymptotical mean-square stability under variable stepsize and transformation approach. [ABSTRACT FROM AUTHOR]

A water-fluid mud coupling model is developed based on the unstructured grid finite volume coastal ocean model (FVCOM) to investigate the fluid mud motion. The hydrodynamics and sediment transport of the overlying water column are solved using the original three-dimensional ocean model. A horizontal two-dimensional fluid mud model is integrated into the FVCOM model to simulate the underlying fluid mud flow. The fluid mud interacts with the water column through the sediment flux, current, and shear stress. The friction factor between the fluid mud and the bed, which is traditionally determined empirically, is derived with the assumption that the vertical distribution of shear stress below the yield surface of fluid mud is identical to that of uniform laminar flow of Newtonian fluid in the open channel. The model is validated by experimental data and reasonable agreement is found. Compared with numerical cases with fixed friction factors, the results simulated with the derived friction factor exhibit the best agreement with the experiment, which demonstrates the necessity of the derivation of the friction factor. [ABSTRACT FROM AUTHOR]