Mathematical modelling, analysis and simulation of the spread of gangs in interacting youth and adult populations

Youth that live in public housing communities with high social and financial needs are at risk of getting involved in illegal drug trafficking gangs that are controlled by adults. This social disease spreads like an epidemic in these densely populated sectors and metropolitan area. In this work, a model based on SIR disease dynamics is used to study the spread of gangs in vulnerable youth and adult sub-populations. Three types of mixing patterns govern interaction between the groups: proportionate, preferred and like-with-like. This new model is analysed presenting formulations for the reproduction number, sensitivity analysis, and stability analysis for the like-with-like mixing. Insights gained from simulation results on the sensitivity of the model to parameters show the relevance of the activity parameter over the reproduction number when heterogeneous mixing is present.