HSIRD: A model for characterizing dynamics of malware diffusion in heterogeneous WSNs

Heterogeneous wireless sensor networks (HWSNs), as blocks of the Internet of Things, are vulnerable to malware diffusion breaking the data confidentiality and service availability, owing to their weak defense mechanism and poor resilience. Thus, constructing a malware diffusion model and revealing the rules of malware diffusion in HWSNs are urgently needed. In this context, we propose a Heterogeneous Susceptible-Infectious-Removed-Dead (HSIRD) model based on epidemiology, in order to not only characterize the dead state where a heterogeneous sensor node (HSN) may lose its functionality owing to physical damage or malware attacks but also represent the HSN communication connectivity, which is one of the heterogeneities that exist universally in HWSNs. We then analyze the dynamics of the fractions of HSNs belonging to different degrees in different states and obtain the corresponding differential equations. Using these equations, we prove the existence of equilibrium points of the HSIRD model. Subsequently, we attain the basic reproduction number governing the stability of the equilibrium points. We further prove the stability of the equilibrium points of the model and attain the conditions indicating whether malware in HWSNs will diffuse or die out. Finally, we validate the effectiveness of the model via simulation. The results provide a theoretical foundation for suppressing malware diffusion in malware-infected HWSNs.