Work place: Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi-835215, India
E-mail: narayan.nitesh26@gmail.com
Website:
Research Interests: Solid Modeling, Mathematical Analysis, Mathematical Software
Biography
Nitesh Narayan is an active researcher with interest in the domain of network epidemics and mathematical modeling. He holds a master's degree in technology in Scientific Computing from the Birla Institute of Technology, Mesra (India).
By Kaushik Haldar Nitesh Narayan Bimal K. Mishra
DOI: https://doi.org/10.5815/ijcnis.2015.10.02, Pub. Date: 8 Sep. 2015
Developing mathematical models for reliable approximation of epidemic spread on a network is a challenging task, which becomes even more difficult when a wireless network is considered, because there are a number of inherent physical properties and processes which are apparently invisible. The aim of this paper is to explore the impact of several abstract features including trust, selfishness and collaborative behavior on the course of a network epidemic, especially when considered in the context of a wireless network. A five-component differential epidemic model has been proposed in this work. The model also includes a latency period, with a possibility of switching epidemic behavior. Bilinear incidence has been considered for the epidemic contacts. An analysis of the long term behavior of the system reveals the possibility of an endemic equilibrium point, in addition to an infection-free equilibrium. The paper characterizes the endemic equilibrium in terms of its existence conditions. The system is also seen to have an epidemic threshold which marks a well-defined boundary between the two long-term epidemic states. An expression for this threshold is derived and stability conditions for the equilibrium points are also established in terms of this threshold. Numerical simulations have further been used to show the behavior of the system using four different experimental set-ups. The paper concludes with some interesting results which can help in establishing an interface between epidemic spread and collaborative behavior in wireless networks.
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