Forest beetle infestation and its impact on ecosystems: Effects of harvesting practices and fire disruptions

Trees play a vital role in the climate by producing oxygen, supporting ecosystems, and benefiting communities and the environment. They are essential for maintaining ecological balance and overall ecosystem health. However, beetle infestations pose a significant threat to forests, causing severe ecological and economic damage, particularly when aggressive species, such as spruce and mountain pine beetles, heavily attack trees. These infestations can lead to widespread tree mortality and long-term environmental consequences. In this study, we highlight the importance of tree plantations and developed a mathematical model to analyze tree-beetle interactions, incorporating the effects of wildfire and harvesting. We examined equilibrium points, their stability, and the basic reproduction number to understand beetle population dynamics. Additionally, we introduced an optimal control strategy to mitigate beetle attacks, incorporating a pesticide variable into the model to reduce beetle populations. The model was numerically solved to generate visual representations, and optimal control strategies were applied to minimize the impact of beetle infestations using pesticides. Sensitivity analysis was conducted to explore factors influencing beetle reproduction, particularly their preference for trees with larger diameters, thicker bark, and extensive phloem, which enhance brood survival and growth. This study underscores the urgency of implementing effective beetle management strategies to protect and restore forest tree populations, ensuring long-term ecosystem sustainability.