Bifurcation analysis of an e-epidemic model in wireless sensor network. Issue 9 (2nd September 2018)

• Record Type: Journal Article
• Authors: Upadhyay, Ranjit Kumar; Kumari, Sangeeta
• Is Part Of: International journal of computer mathematics. Volume 95:Issue 9(2018)
• Page Start: 1775
• Page End: 1805
• Publication Date: 2018-09-02
• Subjects: e-Epidemic model -- wireless sensor network -- computer worms -- cyrtoid type functional response -- stability analysis -- transcritical bifurcation -- Hopf-bifurcation; 92D30 -- 34D08 -- 34D23 -- 34D45 -- 65L07; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1336550
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this paper, we have formulated an e-epidemic energy efficient susceptible-infected–terminally infected-recovered (SITR) model to analyse the attacking behaviour of worms in wireless sensor network (WSN) using cyrtoid type functional response. In this model, once a sensor node has been attacked by the worms, the terminally infected node spreads the worms to its neighbouring nodes using normal communications, which further spread it to their neighbouring nodes and the process continues. To tackle this issue, we proposed an SITR model by considering the sleep mode concept of WSN in which the operational capabilities and power consumption of the motes decreases. Boundedness, existence of equilibrium points, stability and bifurcation analysis are analysed for the proposed model system. Stability and direction of Hopf-bifurcation are also obtained for endemic equilibrium point using center manifold theorem. Finally, numerical simulations are carried out that supports the analytical findings. The impact of the control parameters like transmission rate ( β ), inter-nodes interference coefficient (θ 1 ) and intrinsic growth rate (r 1 ) on the dynamics of the model system are investigated.