The SEIQR–V Model: On a More Accurate Analytical Characterization of Malicious Threat Defense

Abstract

Abstract-Epidemic models have been used in recent times to model the dynamics of malicious codes in wireless sensor network (WSN). This is due to its open nature which provides an easy target for malware attacks aimed at disrupting the activities of the network or at worse, causing total failure of the network. The Susceptible-Exposed-Infectious-Quarantined-RecoveredSusceptible with a Vaccination compartment (SEIQR-V) model by Mishra and Tyagi is one of such models that characterize worm dynamics in WSN. However, a critical analysis of this model and WSN epidemic literature shows that it is absent essential factors such as communication range and distribution density. Therefore, we modify the SEIQR-V model to include these factors and to generate better reproduction ratios for the introduction of an infectious sensor into a susceptible sensor population. The symbolic solutions of the equilibriums were derived for two topological expressions culled from WSN literature. A suitable numerical method was used to solve, simulate and validate the modified model. Simulation results show the effect of our modifications.

A Delayed Epidemic Model for Propagation of Malicious Codes in Wireless Sensor Network

“…As stated in [41], one of the significant features of malicious codes is their latent characteristics, which implies that the nodes are infected at time t − τ and they are surviving in the latent period τ and then become infective at time t. In addition, too large time delay may lead to large number of infected nodes, because of which malicious codes propagation persists in the system. Therefore, compared with the model proposed in [33], the delayed model in our paper is more general. It should be also pointed out that there are some proposed epidemic models for propagation of malicious code in a wireless sensor network such as the models in [5,6,9,42,43], but the authors did not consider the characteristics of networks like communication radius and distributed density of nodes in wireless sensor network.…”

“…Ojha et al [31] proposed a modified SIQRS worm propagation model by introducing quarantined compartment into the model proposed by Feng et al in [27]. Very recently, based on the model proposed in [29,30,32], Nwokoye and Umeh [33] formulated the following modified SEIQRS-V epidemic model for propagation of malicious codes in wireless sensor network:…”

Hopf bifurcation of a delayed worm model with two latent periods

“…where P 31 (ω 10 ) = (p 32m 33 p 33 )ω 6 20 20 , and a family of periodic solutions bifurcate from the worm-induced equilibrium E * ; τ 20 is defined as in Eq. (15).…”

“…Ojha et al [16][17][18] formulated different models with quarantine to depict worm propagation behavior in wireless sensor network. There are also some dynamical models with both vaccination and quarantine [19,20] and other models [21][22][23][24] to model the dynamics of malicious codes in wireless sensor networks. It should be pointed out that most of the models considering the latent state above assume that all the malicious codes in the wireless sensor network have the same latent period.…”

Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence

“…Based on this consideration, the SEIR (Susceptible-Exposed-InfectiousRecovered) model [13,14] and the SEIRS (SusceptibleExposed-Infectious-Recovered-Susceptible) model [11,15] are proposed to describe the dynamics of worm propagation in networks. Considering influence of the quarantine strategy and the vaccination strategy on the propagation of worms, some worm models with quarantine strategy [16][17][18][19] and vaccination strategy [20][21][22][23][24][25] are formulated and analyzed.…”