STABILITY ANALYSIS OF GANG HIERARCHY MODEL: A GRAPHICAL APPROACH
Crime is a purposeful action or exclusion infringing upon regulation. A non linear mathematical model has been proposed and investigated where concentration is on reducing crime in the society. In modelling process, total population is divided into four compartments based on gang hierarchy namely, potential, fringe, core member and jailed. The basic reproductive number 〖(R〗_0) is calculated using next generation matrix and found to be greater than 1 which is an ideal situation. Both local and global stability analysis is derived to understand the rate of criminals committing crime in society. Graph-theory method based on Kirchhoff’s matrix theorem is used to prove the global stability of the endemic equilibrium which is globally asymptotically stable. The model is validated by numerical simulation to authenticate theoretical results.
Mathematical model, gang hierarchy, Lyapunov function, global stability, equilibria, simulation.