The vulnerability that exists in the computer network by the infection of virus as soon as the resources are exposed requires the study of the nature of propagation of virus into the network. In this work we have formulated a novel epidemic Susceptible-Infected-Recovered model that deals with the infected nodes in the network in terms of the development of immunity attained after recovery. Positivity and boundedness of the proposed model is examined. Local stability analysis of the proposed model without delay is also analyzed by Routh–Hurwitz criteria apart from the delay sensitivity analysis. The time series analysis regarding the nature of the susceptible, infected and recovered nodes in the network has been performed using real control parameters \(\beta\) (infection rate of the computers), \(\gamma\) (recovered rate of the infected computers). We also analyzed that time delay may play significant role on the stability of the proposed model since whenever delay exceeds the critical value the system loses its stability and a Hopf bifurcation occurs. The numerical simulation results justify that the proposed model is validated against the analytical studies of virus propagation thus verifying the theoretical results.

一旦资源被暴露，由于感染病毒而在计算机网络中存在的漏洞需要研究病毒传播到网络中的性质。在这项工作中，我们制定了一种新的流行病易感感染恢复模型，该模型根据恢复后获得的免疫力发展来处理网络中的感染节点。研究了所提出模型的正性和有界性。除了延迟敏感性分析之外，还通过Routh-Hurwitz标准分析了所提出模型的无延迟局部稳定性分析。已使用实际控制参数\（\ beta \）（计算机的感染率）进行了有关网络中易受感染，受感染和已恢复节点的性质的时间序列分析，\（\ gamma \）（受感染计算机的恢复速率）。我们还分析了时间延迟可能对拟议模型的稳定性起重要作用，因为每当延迟超过临界值时，系统就会失去稳定性并发生Hopf分叉。数值模拟结果证明，所提出的模型可以通过对病毒传播的分析研究得到验证，从而验证了理论结果。