Epidemiological Modeling of Criminal Gangs with Multidelays Persistence and Intervention Instability

Delay differential equation (DDE) model for the study of gang dynamics using insight from mathematical epidemiology. The criminal gang models possess multiple periodic time delays which are informed by the age-structured paradigm. The thresholds for the persistence, equilibria, and stability of the periodic DDE are studied. We consider a crucial scenario identifying the delay before intervention which could be a major factor in how persistent criminal gangs become within a community. We also established that delay in intervention measures (arrest and prosecution rates), can cause the gang endemic equilibrium to lose its asymptotic stability in favor of Hopf bifurcation thereby driving the coexistence between the susceptible and criminal gang populations. Our model reveals that delays in police intervention (in terms of arrest and prosecution) can throw the system into chaos, causing unpredictable surges in gang activity. Additionally, we found that age plays a crucial role, showing how targeting specific age groups can impact gang dynamics. Ultimately, this research highlights the delicate balance between intervention and the unpredictable nature of criminal gangs, reminding us that simple solutions are rarely enough.