Mathematical modeling and analysis of the influence of family background on the spread of crime

Crimes are social ills that make a society unsafe to live in. Since a child is born into a family and a society is made up of different families, we develop a model to study the influence of family background on the spread of crime in the society. Five compartments are considered including: those who can commit crime (S), those who are resistant to committing crime (R),  those who are committing crime alone (I),  those who are committing crime in group (G) and the criminals who are under rehabilitation (J). The validity of the model was established. Crime reproductive ratio \({\mathcal{C}}_{R}\) ${\mathcal{C}}_R$ was computed and used to derive the necessary and sufficient conditions for crime eradication and persistence. Simulation was conducted using the computer-in-built Runge–Kutta scheme implemented in software maple and the results showed that the effectiveness of crime education together with strict security and legal system up to 70% were sufficient to eradicate criminal activities in a community.