Modeling time delay, external noise and multiple malware infections in wireless sensor networks

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The essentiality of wireless sensor networks (WSNs) in military and health applications cannot be overemphasized, and this has made these tiny sensors soft targets for malware attacks. However, with the ubiquity of single-group infection models, few researchers have studied the effects of many concurrent infection types on WSNs. Therefore, we proposed the differential Susceptible–Exposed (virus)–Exposed (worm)–Infectious (virus)–Infectious (worm)–Recovered–Susceptible with Vaccination (SE1E2I1I2RV) epidemic model in order to study the dynamics of malicious-code dissemination in WSNs. Using the multi-group model, which represents multiple infections due to worms and viruses, first, delay analyses were performed and, through the Routh-Hurwitz criteria, sufficient conditions for stability were established. Secondly, the SE1E2I1I2RV model was extended to incorporate external noise, thereby changing the deterministic nature of the original model and allowing stochastic analyses for random factors such as temperature, physical obstructions, etc. The role that delay plays in the model is shown when it surpasses the critical value, thus the system loses stability and allows the occurrence of a Hopf bifurcation. Finally, numerical simulations were performed using Matlab in order to account for theoretical analyses.