A crime is an act which is destructive not exclusively to the individual yet to the local area, society or state. Spread of crime can happen through interaction between non-criminal and criminals. Using an epidemiological approach, a nonlinear mathematical model for the spread of crime in a society has been proposed and analysed in this paper. The threshold parameter R0 is computed by employing the next generation matrix (NGM) technique. Two equilibrium points are obtained by analysis conducted: crime-free equilibrium and crime-persistent equilibrium. Stability of equilibria is obtained using the Jacobian matrix. The equilibrium analysis of the model shows that crime-free equilibrium is locally asymptotically stable if R0 < 1, crime is temporary and will disappear over time. On the contrary, if R0 > 1, the criminals number increases and the crime-persistent equilibrium is locally asymptotically stable. Numerical simulation is performed to check the influence of key parameters on the spread of crime in the society.

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Mathematical Modelling and Analysis of Spread of Crime in a Society

  • Priya Satish,
  • Anita Chaturvedi,
  • Kokila Ramesh

摘要

A crime is an act which is destructive not exclusively to the individual yet to the local area, society or state. Spread of crime can happen through interaction between non-criminal and criminals. Using an epidemiological approach, a nonlinear mathematical model for the spread of crime in a society has been proposed and analysed in this paper. The threshold parameter R0 is computed by employing the next generation matrix (NGM) technique. Two equilibrium points are obtained by analysis conducted: crime-free equilibrium and crime-persistent equilibrium. Stability of equilibria is obtained using the Jacobian matrix. The equilibrium analysis of the model shows that crime-free equilibrium is locally asymptotically stable if R0 < 1, crime is temporary and will disappear over time. On the contrary, if R0 > 1, the criminals number increases and the crime-persistent equilibrium is locally asymptotically stable. Numerical simulation is performed to check the influence of key parameters on the spread of crime in the society.