Muhammad Shoaib Arif^1,*, Ali Raza^1,2, Kamaleldin Abodayeh³, Muhammad Rafiq⁴, Mairaj Bibi⁵, Amna Nazeer⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 477-491, 2020, DOI:10.32604/cmes.2020.011121

Abstract The essential features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. The aim of our paper, to achieve the comparison analysis of the stochastic susceptible, infected recovered epidemic model. The stochastic modelling is a realistic way to study the dynamics of compartmental modelling as compared to deterministic modelling. The effect of reproduction number has also observed in the stochastic susceptible, infected recovered epidemic model. For comparison analysis, we developed some explicit stochastic techniques, but they are the time-dependent techniques. The implicitly driven… More >

Muhammad Shoaib Arif^1,*, Ali Raza¹, Muhammad Rafiq², Mairaj Bibi³, Rabia Fayyaz³, Mehvish Naz³, Umer Javed⁴

CMC-Computers, Materials & Continua, Vol.59, No.3, pp. 787-804, 2019, DOI:10.32604/cmc.2019.04655

Abstract In this paper, a reliable stochastic numerical analysis for typhoid fever incorporating with protection against infection has been considered. We have compared the solutions of stochastic and deterministic typhoid fever model. It has been shown that the stochastic typhoid fever model is more realistic as compared to the deterministic typhoid fever model. The effect of threshold number T* hold in stochastic typhoid fever model. The proposed framework of the stochastic non-standard finite difference scheme (SNSFD) preserves all dynamical properties like positivity, bounded-ness and dynamical consistency defined by Mickens, R. E. The stochastic numerical simulation of the model showed that increase… More >

Ali Raza¹, Muhammad Shoaib Arif^1,*, Muhammad Rafiq², Mairaj Bibi³, Muhammad Naveed¹, Muhammad Usman Iqbal⁴, Zubair Butt⁴, Hafiza Anum Naseem⁴, Javeria Nawaz Abbasi³

CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.2, pp. 445-465, 2019, DOI:10.32604/cmes.2019.06454

Abstract This writing is an attempt to explain a reliable numerical treatment for stochastic computer virus model. We are comparing the solutions of stochastic and deterministic computer virus models. This paper reveals that a stochastic computer virus paradigm is pragmatic in contrast to the deterministic computer virus model. Outcomes of threshold number C^∗ hold in stochastic computer virus model. If C^∗ < 1 then in such a condition virus controlled in the computer population while C^∗ > 1 shows virus persists in the computer population. Unfortunately, stochastic numerical methods fail to cope with large step sizes of time. The suggested structure… More >

Nagalinga Rajan, Soumyendu Raha¹

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 91-116, 2008, DOI:10.3970/cmes.2008.023.091

Abstract The article describes a numerical method for time domain integration of noisy dynamical systems originating from engineering applications. The models are second order stochastic differential equations (SDE). The stochastic process forcing the dynamics is treated mainly as multiplicative noise involving a Wiener Process in the Itô sense. The developed numerical integration method is a drift implicit strong order 2.0 method. The method has user-selectable numerical dissipation properties that can be useful in dealing with both multiplicative noise and stiffness in a computationally efficient way. A generalized analysis of the method including the multiplicative noise is presented. Strong order convergence, user-selectable… More >