Abstract

𝑆𝐿𝐼𝐴₁𝐴₂𝑄R ( Susceptible – Latent - Infected – Antidotal -Antivirus – Quarantine – Antidotal - Recovered) is the suggested model in this article, which is an extension of the SEIR model. In this model, we discussed the basic Reproduction number for the MFE ( Malicious object Free Equilibrium) point. We talked about the reproduction number 𝑅0 in MFE and EE point using the Hurwitz criterion. If 𝑅0 is less than 1, the MFE point is stable; if 𝑅0is greater than 1, the VFE point is unstable. Numerous parameter graphs are discussed in two and three dimensions.

Keywords

Antivirus, Endemic Equilibrium, Latent, Malicious Object Free Equilibrium, Threshold Number.

References

[1] Benjamin DoeRr, Mahmoud Fouz, and Tobias Friedrich, “Why Rumors Spread So Quickly in Social Networks,” Communications of the ACM, vol. 55, no. 6, pp. 70-75, 2012.
[CrossRef] [Google Scholar] [Publisher Link]

[2] W.O. Kermack, and A.G. McKendrick, “A Contribution to the Mathematical Theory of Epidemics in Classics of Theoretical Biology (Part Two),” Bulletin of Mathematical Biology, vol. 53, pp. 33-55, 1991.
[CrossRef] [Google Scholar] [Publisher Link]

[3] William Ogilvy Kermack, and A.G. McKendrick, “Contributions to the Mathematical Theory of Epidemics-II,” Proceedings of the Royal Society A, vol. 138, no. 834, pp. 55-83, 1932.
[CrossRef] [Google Scholar] [Publisher Link]

[4] Bimal Kumar Mishra, and Dinesh Kumar Saini, “SEIRS Epidemic Model with Time Delay for Transmission of Malicious Objects in Computer Network,” Applied Mathematics and Computation, vol. 188, pp. 1476-1482, 2007.
[CrossRef] [Google Scholar] [Publisher Link]

[5] M. Karsai et al., “Small But Slow World: How Network Topology and Burstiness Slow Down Spreading,” Physical Review E, vol. 83, no. 2, 2011.
[CrossRef] [Google Scholar] [Publisher Link]

[6] Romualdo Pastor-Satorras, and Alessandro Vespignani, “Epidemic Spreading in Scale-Free Networks,” Physical Review Letters, vol. 86, no. 14, pp. 3200-3203, 2001. 
[CrossRef] [Google Scholar] [Publisher Link]

[7] William Ogilvy Kermack, and A.G. McKendrick, “A Contribution to the Mathematical Theory of Epidemics,” The Royal Society A, vol. 115, no. 772, pp. 700-721, 1927.
[CrossRef] [Google Scholar] [Publisher Link]

[8] Vladimir A. Skormin et al., “BASIS: A Biological Approach to System Information Security,” International Workshop on Mathematical Methods, Models, and Architectures for Network Security, pp. 127-142, 2001.
[CrossRef] [Google Scholar] [Publisher Link]

[9] Kaveri Kanchan Kumari, Aditya Kumar Singh, and Sahdeo Mahto, “Mathematical Models for Stability in Computer Network,” Journal of Computer and Mathematical Sciences, vol.10, no. 1, pp. 92-98, 2019.
[Google Scholar]

[10] Kaveri Kanchan Kumari, Aditya Kumar Singh, and Sahdeo Mahto, “Time Delay Seirs E-Epidemic Model for Computer Network,” International Journal of Mathematical Archive, vol. 9, no. 2, pp. 265-273, 2018.
[Publisher Link]