Dynamics of Botnet Propagation in Software Defined Networks Using Epidemic Models

During COVID-19 the new normal became an increased reliance on remote connectivity, and that fact is far away to change any time soon. The increasing number of networked devices connected to the Internet is causing an exponential growth of botnets. Subsequently, the number of DDoS (Distributed Denial of Service) attacks registered around the world also increased, especially during the pandemic lockdown. Therefore, it is crucial to understand how botnets are formed and how bots propagate within networks. In particular, analytic modelling of the botnets epidemic process is an essential component for understanding DDoS attacks, and thus mitigate their impact. In this paper, we propose two analytic epidemic models; (i) the first one for enterprise Software Define Networks (SDN) based on the SEIRS (Susceptible - Exposed - Infected - Recovered) approach, while (ii) the second model is designed for service providers’ SDN, and it is based on a novel extension of a SEIRS-SEIRS vector-borne approach. Both models illustrate how bots spread in different types of SDN networks. We found that bot infection behaves in a similar way to human epidemics, such as the novel COVID-19 outbreak. We present the calculation of the basic reproduction number $R_{\mathrm {o}}$ for both models and we test the system stability using the next generation matrix approach. We have validated the models using the final value theorem (FVT), with which we can determine the steady-state values that provide a better understanding of the propagation process