Dynamic analysis and optimal control of worm propagation model with saturated incidence rate
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(Published version)
Date
2023
Authors
Wang, R.
Xue, Y.
Xue, K.
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Journal article
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Frontiers in Physics, 2023; 10(1098040):1-14
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Abstract
In order to prevent the propagation of computer worms effectively, based on the latent character of worms, the exposed compartments of computer and USB device are introduced respectively, and a series of computer worm propagation models with saturation incidence rate are proposed. The qualitative behavior of the proposed model is studied. Firstly, the threshold R0 of the model is derived by using the next-generation matrix method, which completely characterized the stability of disease free equilibrium and endemic equilibrium. If R0 < 1, the disease free equilibrium is asymptotically stable, implying that the worm dies out eventually and its attack remains under control; if R0 > 1, the asymptotic stability of endemic equilibrium under certain conditions is proved, which means that the worm is always persistent and uncontrollable under such conditions. Secondly, the theoretical results are verified by numerical study, in which the relative importance of each parameter in worm prevalence is evaluated by sensitivity analysis. Finally, so as to minimize the number of computer and USB device carrying computer worms in short span of time, the worm propagation model is extended to incorporate three control strategies. The Pontryagin’s maximum principle is used to characterize the controls’ optimal levels. According to the control effect diagram, the combined strategy is effective in minimizing the transmission dynamics of worm virus in computer and USB devices populations respectively.
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Data source: Data, 10.3389/fphy.2022.1098040
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Copyright 2023 Wang, Xue and Xue. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. (https://creativecommons.org/licenses/by/4.0/)