Sustainable Management of Renewable Resources: A Nonlinear Mathematical Model of Awareness Programmes With Implementation Delay

ABSTRACT Sustainable management of renewable resources is essential for ensuring ecological balance and long‐term sustainability in sectors such as forestry, fisheries, and water management. Awareness programmes serve as an important mechanism for emphasizing the need for sustainable management practices and for inducing behavioral changes in the population regarding the utilization of renewable resources. In this study, we formulate and analyze a nonlinear mathematical model to investigate how awareness programmes influence the sustainable use of renewable resources. The analysis includes equilibrium and stability analyses, as well as the impact of time delay in implementing awareness programmes. We also explore the possibility of Hopf bifurcation with time delay as the bifurcation parameter, leading to persistent oscillations in resource density and other state variables. Numerical simulations validate these dynamics, highlighting that timely awareness programmes are crucial for stabilizing resource levels. Our findings emphasize the importance of minimizing funding delays and narrowing the gap between the resource consumption rates by aware and unaware human populations for long‐term sustainability.