Does Unemployment Induce Crime in Society? A Mathematical Study

Shyam Sundar^1, , Agraj Tripathi² and Ram Naresh³

¹Department of Mathematics, Pranveer Singh Institute of Technology, Kanpur, India

²Department of Mathematics, AITH, Kanpur, India

³Department of Mathematics, School of Basic and Applied Sciences, Harcourt Butler Technical University, Kanpur-208002, India

Cite this paper:
Shyam Sundar, Agraj Tripathi and Ram Naresh. Does Unemployment Induce Crime in Society? A Mathematical Study. American Journal of Applied Mathematics and Statistics. 2018; 6(2):44-53. doi: 10.12691/ajams-6-2-2

Abstract

Today unemployment has become a global phenomenon which may be instrumental in forcing unemployed persons to earn their livelihood in an illegal manner resulting in a crime. It is possible that unemployed individuals may become more prone to develop a tendency of committing a crime when they come in contact with persons involved in criminal activities but are still unexposed. Further, when unemployed individuals are exposed to have committed a crime, they are captivated and finally awarded imprisonment if the offence charged on them is proved under the existing criminal laws. In this paper, a nonlinear mathematical model is developed to study the role of unemployment in inducing crime by taking into account four dependent variables representing the unemployment class, the employment class, the criminal class and the jail class. The model analysis, using stability theory of ordinary differential equations, provides some local and nonlinear stability conditions regarding stability of equilibrium of the model system. It is inferred that the endemic equilibrium is locally asymptotically stable as well as nonlinearly stable. Numerical simulations of the model system have also been carried to support the analytical findings and showing the effect of certain key parameters on different variables. It is observed that the increase in unemployment rate induces crime in the community leading to increase the burden on jail class.

Keywords:
unemployment criminals jail equilibrium analysis stability

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