Bimal K. Mishra

Work place: Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi-835215, India



Research Interests: Mathematical Analysis, Mathematical Software


Bimal Kumar Mishra is presently serving as a Professor in the Department of Mathematics at the Birla Institute of Technology, Mesra in Ranchi (India). After completing his doctoral degree in Mathematics in the year 1997, he subsequently obtained a post-doctorate in the same subject in 2007. He has been actively involved in both teaching and research for almost two decades. His area of interest for research includes mathematical modelling of cyber attacks and defence, non-linear dynamical systems and their stability, and also the study of infectious diseases. He has presented his work through more than hundred research publications in various journals of international repute and conferences.

Author Articles
A Mathematical Model on Selfishness and Malicious Behavior in Trust based Cooperative Wireless Networks

By Kaushik Haldar Nitesh Narayan Bimal K. Mishra

DOI:, 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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