Bushfires and Balance: Proactive <i>versus</i> Reactive Policies in Prescribed Burning

We introduce a new mathematical model to explore the dynamic relationship between prescribed burning and bushfire occurrence, formulated as a system of ordinary differential equations. The model admits a unique steady-state, and its stability is shown to depend critically on the policy framework governing prescribed burning. In particular, reactive policies, where prescribed burning is increased in response to bushfire events, can lead to system instability unless augmented with appropriate feedback control. Conversely, proactive policies that implement moderate, consistent prescribed burning are more effective at stabilizing the system and mitigating the frequency of bushfires. Additionally, higher vegetation regeneration rates contribute positively to equilibrium stability. While this model does not capture the full complexity of fire management, it highlights the potential risks of emotionally driven, reactive responses and underscores the value of preventive, stability-focused strategies. To the best of our knowledge, this is the first mathematical analysis of preventive burning strategies and their long-term impact on bushfire mitigation.