Mathematical modeling of oak wilt dynamics: the protective role of white oaks in mixed forests.

Abstract

Oak wilt, caused by the fungus Bretziella fagacearum, is a devastating disease that poses a significant threat to oak forests, particularly affecting red oaks with rapid mortality upon infection. In contrast, white oaks exhibit greater resistance, leading to slower disease progression and lower mortality rates. This thesis presents an analysis of oak wilt dynamics in mixed oak forests using a compartmental disease model, emphasizing how species composition influences disease spread and mortality. We use compartmental ordinary differential equation (ODE) model that incorporates the distinct biological characteristics and transmission pathways of red and white oaks. The model accounts for root graft transmission among red oaks, beetle-mediated transmission to both red and white oaks, and differential mortality rates. By formulating species-specific compartments and parameters, we capture the essential mechanisms driving oak wilt epidemics. Through analytical proofs, we show that increasing the proportion of white oaks in a mixed forest leads to a decrease or no increase in both the total mortality and the infection rate due to oak wilt. Specifically, we show that the total mortality Dtotal and the rate of new infections are decreasing functions of the white oak proportion 𝛒𝒘. These results are obtained without relying on specific parameter values, highlighting the robustness of the conclusions. It does for both simple (short term) and extended (long term) models of the disease. It also talks about climate change effects on overall mortality. Our findings are strongly supported by empirical evidence from peer-reviewed literature, confirming the validity of the model and its assumptions. The mathematical analysis aligns with observed patterns in forest ecology, where higher proportions of red oaks compared to white oaks are most affected by disease outbreak. This underscores the critical role of species composition in influencing disease dynamics. This research provides a mathematically rigorous and ecologically meaningful examination of oak wilt dynamics, demonstrating how species composition can serve as risk assessment where red and white oaks coexist. It reinforces the importance of interdisciplinary approaches in addressing complex environmental challenges and offers practical guidance for preserving the health and diversity of oak forests. Most importantly, this finding does not rely on computational tools or highly complex models, highlighting the importance of simple models in shedding light on interesting aspects of complex environments.