Now, it is unarguable that cyber threats arising from malicious codes such as worms possesses the ability to cause losses, damages and disruptions to industries that utilize ICT infrastructure for meaningful daily work. More so for wireless sensor networks (WSN) which thrive on open air communications. As a result epidemic models are used to study propagation patterns of these malicious codes, although they favor horizontal transmissions. Specifically, the literature dealing with the analysis of worms that are both vertically and horizontally (transmitted) is not extensive. Therefore, we propose the Vulnerable–Latent–Breaking Out–Temporarily Immune–Inoculation (VLBTV-I) epidemic model to investigate both horizontal and vertical worm transmission in wireless sensor networks. We derived the solutions of the equilibriums as well as the epidemic threshold for two topological expressions (gleaned from literature). Furthermore, we employed the Runge-Kutta-Fehlberg order 4 and 5 method to solve, simulate and validate our proposed models. Critically, we analyzed the impact of both vertical and horizontal transmissions on the latent and breaking out compartments using several simulations experiments.

This paper revisits malicious object propagation in networks using epidemic theory in such a manner that it proposes the (Pre-quarantining) of nodes in networks. This is a concept that is known by experience to be a standard disease control procedure that involves screening and quarantining of immigrants to a population. As preliminary investigation we propose the Q-SEIRS model and the more advanced Q-SEIRS-V model for malicious objects’ spread in networks. This Pre-quarantine concept addresses and implements the “assume guilty till proven innocent” slogan of the cyber world by providing a mechanism for pre-screening, isolation and treatment for incoming infected nodes. The treated nodes from the pre-quarantine compartment are sent to the recovered compartment while the free nodes join the network population. The paper also derived the reproduction number, equilibria, as well as local stability of the proposed model. Numerical methods are employed to solve the system of equations and MATLAB is used to simulate the system so as to visualize the dynamical behavior of the models. It is seen that pre-screening/pre-quarantining improves the recovery rate in relative terms.