Mathematical modeling of natural resource and human interaction: Applications to the harvesting of Pacific Yew for cancer treatment

Natural resources such as terrestrial plants and marine sponges have played a dominant role in deriving anticancer compounds for cancer treatments including chemotherapy. Unfortunately, without proper regulation of society's resource needs, we risk depleting natural resources due to overexploitation, which could lead to the collapse of ecosystems. To address this issue, we present a modeling framework employing ordinary differential equations to study the dynamics of the interaction between human needs and natural resource motivated by the native species of North America: the Pacific Yew tree. Our analytical results demonstrate how human behavior such as the harvesting rate of the resource may lead to different dynamical scenarios such as cancer-free, resource depletion, and/or multiple attractors; and the mechanisms of generating backward bifurcations. Our bifurcation analysis results and the application to the data suggests that the resource can sustain cancer patient populations with low harvesting rates, or endure higher rates to support a smaller portion of cancer patients. Our framework sheds light on the sustainable coexistence of natural resources and drug production and indicate the future work of incorporating optimal control strategies is needed. By exploring the dynamics of population interactions, we identify key factors influencing the preservation of natural resources while meeting the demand for cancer treatment. These insights contribute to understanding ecological impacts and offer strategies for the sustainable utilization of natural resources in addressing critical public health challenges.