Stability Analysis of E-epidemic SIT Model with Beddington-DeAngelis Functional Response for Wireless Sensor Network - Das, Kalyan; Madhusudanan, V.; Kabir, M. Humayun; Gani, M. Osman (Discontinuity, Nonlinearity, and Complexity, 2026)
Nowadays, a wireless sensor network (WSN) is an emerging and robust technology that can facilitate our everyday life. To investigate the assaulting conduct of worms in wireless sensor networks, we propose a Susceptible-Infected-Terminally-infected (SIT) model utilizing Holling type-II and Beddington-DeAngelis functional responses. The Positivity and boundedness of solutions of the model are analyzed to assure the feasibility of solutions. We determine the existence of possible equilibrium points under feasible conditions. With the aid of a characteristic equation, local stability analysis of all feasible equilibrium points is investigated. Global stability analysis of the steady states is also investigated under Lassalle's invariance principle and Bendixson-Dulac criteria. The global stability of the endemic equilibrium point is performed under a suitable Lyapunov function. Numerical simulations are performed to validate the analytical findings under suitable initial data. It is revealed that a Hopf bifurcation occurs where the endemic steady state of the system becomes unstable when the parameter $ω_2$ is globally varied. Furthermore, a periodic time series and a period-doubling behavior are exposed in the system due to the instability of the endemic steady state in a parameter regime. Finally, the results are significantly beneficial to predict and control the spread of worms in a WSN.