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Modeling of Computer Virus Propagation with Fuzzy Parameters

Reemah M. Alhebshi1, Nauman Ahmed2, Dumitru Baleanu3,4,5, Umbreen Fatima6,*, Fazal Dayan7, Muhammad Rafiq8,9, Ali Raza10, Muhammad Ozair Ahmad2, Emad E. Mahmoud11

1 Computer Science Department, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia
2 Department of Mathematics and Statistics, University of Lahore, Lahore, 54590, Pakistan
3 Department of Mathematics, Cankaya University, Balgat, Ankara, 06530, Turkey
4 Department of Medical Research, China Medical University, Taichung, 406040, Taiwan
5 Institute of Space Sciences, Magurele-Bucharest, 077125, Romania
6 Department of Computer Science, University of Lahore, Lahore, 54590, Pakistan
7 Department of Mathematics, School of Science, University of Management and Technology, Lahore, 54000, Pakistan
8 Department of Mathematics, Faculty of Science and Technology, University of Central Punjab, Lahore, 54000, Pakistan
9 Department of Mathematics, Near East University TRNC, Mersin, 10, Turkey
10 Department of Mathematics, Government Maulana Zafar Ali Khan Graduate College Wazirabad, Punjab Higher Education Department (PHED), Lahore, 5400, Pakistan
11 Department of Mathematics and Statistics, College of Science, Taif University, P O Box, 11099, Taif, 21944, Saudi Arabia

* Corresponding Author: Umbreen Fatima. Email:

Computers, Materials & Continua 2023, 74(3), 5663-5678.


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 functions of the computer virus load, are considered fuzzy numbers. Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models. The essential features of the model, like reproduction number and equilibrium analysis, are discussed in fuzzy senses. Moreover, with fuzziness, two numerical methods, the forward Euler technique, and a nonstandard finite difference (NSFD) scheme, respectively, are developed and analyzed. In the evidence of the numerical simulations, the proposed NSFD method preserves the main features of the dynamic system. It can be considered a reliable tool to predict such types of solutions.


Cite This Article

R. M. Alhebshi, N. Ahmed, D. Baleanu, U. Fatima, F. Dayan et al., "Modeling of computer virus propagation with fuzzy parameters," Computers, Materials & Continua, vol. 74, no.3, pp. 5663–5678, 2023.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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