Modeling the Dynamics of Forest Guards and Chainsaw Operator Interactions: Stability and Hopf Bifurcation Analysis With Time Delay

This study develops a mathematical model to analyze the dynamic interaction between forest guards and illegal chainsaw operators within Ghana’s forest reserves. Drawing inspiration from predator–prey population models, the system captures the resistance and confrontation patterns between enforcement agents and offenders. The formulated nonlinear differential equations are analyzed for equilibrium points, stability conditions, and coexistence states of the two interacting populations. Sensitivity analysis, based on the least squares method over 12 years, reveals that forest guard mortality rates periodically exceed those of chainsaw operators, suggesting unstable or oscillatory population behavior under certain parameter conditions. Numerical simulations, phase portraits, and surface plots indicate that the trajectories of the system form families of periodic and nonlinear curves, representing cycles of escalation and suppression between both groups. The findings provide quantitative insights into the forest guards and illegal chainsaw operators, offering potential guidance for policy interventions aimed at reducing casualties and promoting sustainable forest governance.