A mathematical representation of the reactive scope model

Researchers have long sought to understand and predict an animal's response to stressful stimuli. Since the introduction of the concept of homeostasis, a variety of model frameworks have been proposed to describe what is necessary for an animal to remain within this stable physiological state and the ramifications of leaving it. Romero et al. (Horm Behav 55(3):375-389, 2009) introduced the reactive scope model to provide a novel conceptual framework for the stress response that assumes an animal's ability to tolerate a stressful stimulus may degrade over time in response to the stimulus. We provide a mathematical formulation for the reactive scope model using a system of ordinary differential equations and show that this model is capable of recreating existing experimental data. We also provide an experimental method that may be used to verify the model as well as several potential additions to the model. If future experimentation provides the necessary data to estimate the model's parameters, the model presented here may be used to make quantitative predictions about physiological mediator levels during a stress response and predict the onset of homeostatic overload.