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 >

Kamaleldin Abodayeh¹, Ali Raza^{2, *}, Muhammad Shoaib Arif², Muhammad Rafiq³, Mairaj Bibi⁴, Muhammad Mohsin⁵

CMC-Computers, Materials & Continua, Vol.62, No.3, pp. 1125-1142, 2020, DOI:10.32604/cmc.2020.08885

Abstract This paper aims to perform a comparison of deterministic and stochastic models. The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model. Also, the deterministic solution is itself mean of the stochastic solution of the model. For numerical analysis, first, we developed some explicit stochastic methods, but unfortunately, they do not remain consistent in certain situations. Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model. The proposed method is independent of the choice of parameters and behaves well in all scenarios. So, some… More >

Muhammad Shoaib Arif^{1, *}, Ali Raza¹, Muhammad Rafiq², Mairaj Bibi³, Javeria Nawaz Abbasi³, Amna Nazeer³, Umer Javed⁴

CMC-Computers, Materials & Continua, Vol.62, No.1, pp. 61-77, 2020, DOI:10.32604/cmc.2020.08595

Abstract We are presenting the numerical simulations for the stochastic computer virus propagation model in this manuscript. We are comparing the solutions of stochastic and deterministic computer virus models. Outcomes of a threshold number R₀ hold in stochastic computer virus model. If R₀ < 1 then in such a condition virus controlled in the computer population while R₀ > 1 shows virus rapidly spread in the computer population. Unfortunately, stochastic numerical techniques fail to cope with large step sizes of time. The suggested structure of the stochastic non-standard finite difference technique can never violate the dynamical properties. On this basis, we… More >

Muhammad Shoaib Arif¹, Ali Raza¹, Wasfi Shatanawi^{2, 3, *}, Muhammad Rafiq⁴, Mairaj Bibi⁵

CMC-Computers, Materials & Continua, Vol.61, No.3, pp. 1025-1043, 2019, DOI:10.32604/cmc.2019.08405

Abstract We are presenting the numerical analysis for stochastic SLBR model of computer virus over the internet in this manuscript. We are going to present the results of stochastic and deterministic computer virus model. Outcomes of the 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 spread in the computer population. Unfortunately, stochastic numerical techniques fail to cope with large step sizes of time. The suggested structure of the stochastic non-standard finite difference scheme (SNSFD) maintains all diverse characteristics such as dynamical consistency, bounded-ness… More >