Wafa F. Alfwzan¹, Dumitru Baleanu^2,3,4, Fazal Dayan^5,*, Sami Ullah⁵, Nauman Ahmed^4,6, Muhammad Rafiq^7,8, Ali Raza^4,9

Intelligent Automation & Soft Computing, Vol.37, No.2, pp. 1909-1924, 2023, DOI:10.32604/iasc.2023.039249

Abstract A susceptible, exposed, infectious, quarantined and recovered (SEIQR) model with fuzzy parameters is studied in this work. Fuzziness in the model arises due to the different degrees of susceptibility, exposure, infectivity, quarantine and recovery among the computers under consideration due to the different sizes, models, spare parts, the surrounding environments of these PCs and many other factors like the resistance capacity of the individual PC against the virus, etc. Each individual PC has a different degree of infectivity and resistance against infection. In this scenario, the fuzzy model has richer dynamics than its classical counterpart in epidemiology. The reproduction number… More >

Reemah M. Alhebshi¹, Nauman Ahmed², Dumitru Baleanu^3,4,5, Umbreen Fatima^6,*, Fazal Dayan⁷, Muhammad Rafiq^8,9, Ali Raza¹⁰, Muhammad Ozair Ahmad², Emad E. Mahmoud¹¹

CMC-Computers, Materials & Continua, Vol.74, No.3, pp. 5663-5678, 2023, DOI:10.32604/cmc.2023.033319

Abstract Typically, a computer has infectivity as soon as it is infected. It is a reality that no antivirus programming can identify and eliminate all kinds of viruses, suggesting that infections would persevere on the Internet. To understand the dynamics of the virus propagation in a better way, a computer virus spread model with fuzzy parameters is presented in this work. It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity, which depends on the quantity of virus. Considering this, the parameters and being… More >

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 >

Umbreen Fatima¹, Dumitru Baleanu^2,3,4, Nauman Ahmed^5,8, Shumaila Azam⁵, Ali Raza^6,*, Muhammad Rafiq⁷, Muhammad Aziz-ur Rehman⁸

CMC-Computers, Materials & Continua, Vol.66, No.3, pp. 3183-3194, 2021, DOI:10.32604/cmc.2021.012666

Abstract Reaction–diffusion systems are mathematical models which link to several physical phenomena. The most common is the change in space and time of the meditation of one or more materials. Reaction–diffusion modeling is a substantial role in the modeling of computer propagation like infectious diseases. We investigated the transmission dynamics of the computer virus in which connected to each other through network globally. The current study devoted to the structure-preserving analysis of the computer propagation model. This manuscript is devoted to finding the numerical investigation of the reaction–diffusion computer virus epidemic model with the help of a reliable technique. The designed… 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 >

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 >