Choose one of the papers below on cybersecurity uploaded on blackboard and first read and understand as much as you can from the paper and write a paragraph (about half a page) describing what the paper is about and give the model and what the variables represent. Then based on which paper you have chosen answer the following question. They are given by the name of the authors (pick one paper and answer its corresponding question not a combination of two). I am asking you to fill in the steps. They just give the answer. I want you to verify and show the work. For the stability of each equilibrium point just find it in the paper and state it. No need to go over their proof since most are using methods we have not discussed. If you need help understanding the paper or you are not getting what they have after trying for some time email me.

Toutonji, Yoo, Park paper:
Write the steps in getting the equilibrium points (worm free and worm epidemic) given in (10) and (11).
Then give the Jacobian matrix and verify the Jacobian matrix for each equilibrium point (so (12) and (19)). Find the characteristic polynomial of the Jacobian matrix for worm-epidemic equilibrium and verify what they have for it in the paper (given after (19)). What is the stability of each equilibrium point?

Roberto, Piqueira, Araujo paper:
Compute the disease-free equilibrium points and show how they get P_1 and P_2. Find the Jacobian matrix and verify their Jacobian matrix for P_1 and P_2 and compute the eigenvalues for P_1 and P_2 and verify what they give for them. For endemic equilibrium point verify their Jacobian matrix. No need to show how they get the endemic equilibrium point. What is the stability for each equilibrium point (disease free and endemic)?

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Stability analysis of VEISV propagation modeling for network worm attack

In this paper, “Stability analysis of VEISV propagation modeling for network worm
attack” having vulnerable – exposed – infectious – secured – vulnerable, combined together and   say VEISV which is a network worm attack model. This model is appropriate for measuring the effects of security countermeasures on worm propagation. In this work author takes into consideration accurate positions for dysfunctional hosts and their replacements in state transition. Authors derive global stability of a worm-free state as well as local stability for a unique worm-epidemic state by using the reproduction rate. Also authors discuss the simulation results to show the positive impact of increasing security countermeasures in the vulnerable state on worm-exposed and infectious propagation waves. At last they find the equilibrium points are confirmed by phase plots....

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