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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Stability Analysis of E-epidemic SIT Model with Beddington-DeAngelis Functional Response for Wireless Sensor Network

Discontinuity, Nonlinearity, and Complexity 12(4) (2023) 737--756 | DOI:10.5890/DNC.2023.12.003

Kalyan Das$^1$, V. Madhusudanan$^2$, M. Humayun Kabir$^{3,4}$, M. Osman Gani$^{3,4}$

$^1$ Department of Basic and Applied Sciences, National Institute of Food Technology Entrepreneurship and

Management, HSIIDC Industrial Estate, Kundli-131028, Haryana, India

$^2$ Department of Mathematics, S. A. Engineering College, Chennai 600077, Tamil Nadu, India

$^3$ Mathematical and Computational Biology (MCB) Research Group, Department of Mathematics,

Jahangirnagar University, Dhaka 1342, Bangladesh

$^4$ Center for Mathematical Modeling and Applications (CMMA), Meiji University, Tokyo 164-8525, Japan

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Abstract

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 $\omega_2$ 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.

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