This paper intends to investigate the impact of external computers and removable devices on virus spread in a network with heterogeneous immunity. For that purpose, a new dynamical model is presented and discussed. Theoretical analysis reveals the existence of a unique viral equilibrium that is locally and globally asymptotically stable with no criteria. This result implies that efforts to eliminate viruses are not possible. Therefore, sensitivity analysis is performed to have more insight into parameters’ impact on virus prevalence. As a result, strategies are suggested to contain virus spread to an acceptable level. Finally, to rationalize the analytical results, we execute some numerical simulations.
In this paper, we build a mathematical model to study the impact of external removable devices on a network with weakly- and strongly-protected computers. The model describes the dynamics between weak, strong, infected computers and susceptible, infected removable media. Analytical investigations of the model produce two equilibrium points: virus-free and endemic. Moreover, we investigate the local and global stability of both equilibria. The existence and stability conditions of the equilibrium points depend primarily on the basic reproduction number ($R_{0}$R0) of the model. Furthermore, we perform numerical simulations to substantiate the analytical results. Also, a sensitivity analysis is carried out to examine the critical parameters that lead to strategies to control the dissipation of viruses.
In this paper, we investigate the influence of two types of isolation on malware propagation within a computer network. Model 1 proposes the network quarantine strategy, where infected computers are fully disconnected from the network. As for model 2, the control strategy is the anti-virus software quarantine, where infected files in a computer are contained in an isolation folder. Both models consider the aspect of heterogeneous immunity, that is, weak and strong immunization of computers in a network. Analytical examinations produced a virus-free equilibrium and an endemic equilibrium for each model. It has been observed that the quarantine reproduction number Rq plays an essential role in the existence and stability of the equilibrium points. Furthermore, numerical simulations are accomplished to substantiate the qualitative results. Finally, a sensitivity analysis is executed to specify the dominant parameters on Rq. It is found that the performance of network quarantine is better than anti-virus software quarantine in controlling malware propagation.
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