https://doi.org/10.1140/epjp/s13360-024-05209-9
Regular Article
Numerical modeling of reaction–diffusion e-epidemic dynamics
1
Department of Mathematics, University of Narowal, Narowal, Pakistan
2
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
3
Department of Mathematics, University of Chanab, Gujrat, Pakistan
4
Department of Mathematics, Faculty of Science and Technology, University of Central Punjab, Lahore, Pakistan
5
Department of Mathematics, Art and Science Faculty, Siirt University, 56100, Siirt, Turkey
6
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
7
Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, 99138, Nicosia, Mersin 10, Turkey
c
nauman.ahmd01@gmail.com
f
aliakgul00727@gmail.com
Received:
14
February
2024
Accepted:
23
April
2024
Published online:
21
May
2024
The objective of this paper is to understand the dynamics of virus spread in a computer network by e-epidemic reaction–diffusion model and applying an implicit finite difference (FD) scheme for a numerical solution. The SIR models are used in studies of epidemiology to predict the behavior of the propagation of biological viruses within the population. We divide the population of computer nodes into three parts i.e. susceptible (may catch the virus), infected 1 (infected but not completely), and infected 2 (completely infected). By using Taylor’s series expansion the consistency of the implicit scheme is proved. The unconditional stability of the implicit FD model is proved by using the Von Numan stability analysis. The qualitative analysis of the underlying model is also analyzed such as positivity and boundedness of the model. The numerical stability and bifurcation of is also analyzed. Likewise, identical modeling techniques are adopted to analyze the spread of the virus in digital networks. Because the computer virus behaves in the identical way as the biological virus behaves, this paper emphasizes the significance of diffusion in decreasing the gap between reality and theory, offering a more precise depiction of the spread of the virus within the digital network.
© The Author(s) 2024
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