Nauman Ahmed^1,2, Umbreen Fatima¹, Shahzaib Iqbal¹, Ali Raza³, Muhammad Rafiq^4,*, Muhammad Aziz-ur-Rehman², Shehla Saeed¹, Ilyas Khan⁵, Kottakkaran Sooppy Nisar⁶

CMC-Computers, Materials & Continua, Vol.68, No.1, pp. 201-212, 2021, DOI:10.32604/cmc.2021.014171

Abstract The present work is related to the numerical investigation of the spatio-temporal susceptible-latent-breaking out-recovered (SLBR) epidemic model. It describes the computer virus dynamics with vertical transmission via the internet. In these types of dynamics models, the absolute values of the state variables are the fundamental requirement that must be fulfilled by the numerical design. By taking into account this key property, the positivity preserving algorithm is designed to solve the underlying SLBR system. Since, the state variables associated with the phenomenon, represent the computer nodes, so they must take in absolute. Moreover, the continuous system (SLBR) acquires two steady states… 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 >

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 >