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Discontinuity, Nonlinearity, and Complexity 9(2) (2020) 187--197 | DOI:10.5890/DNC.2020.06.002

João N.C. Gonçalves$^{1}$,$^{2}$, Helena Sofia Rodrigues$^{3}$,$^{4}$, M. Teresa T. Monteiro$^{1}$,$^{2}$

$^{1}$ Department of Production and Systems, University of Minho, Portugal

$^{2}$ Algoritmi R&D Center, University of Minho, Portugal

$^{3}$ Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Portugal

$^{4}$ School of Business Studies, Viana do Castelo Polytechnic Institute, Portugal

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Abstract

Computer viruses are a serious threat to the general society, due to their implications for private life and corporative systems. This paper begins to briefly illustrate the dynamics of computer viruses within a network system, by taking advantage of the EpiModel R package and using a SIR (Susceptible–Infected–Recovered) epidemic model. However, since devices are not constantly immune to cyberattacks, a SIRS model with an optimal control application is proposed to minimize the levels of infections caused by malicious objects. Additionally, real numerical data related to the number of reported cybercrimes in Japan from 2012 to 2017 are considered. The existence and uniqueness of an optimal control for the proposed control problem are proved. Under proper investment costs, numerical simulations in Matlab show the effectiveness of the proposed control strategy in increasing the rate of immunity and decreasing the chances of re–susceptibility to cyberattacks.

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