Abstract
In recent decades, many studies have been developed in psychoneuroimmunology that associate stress, arising from multiple different sources and situations, to changes in the immune system, from the medical or immunological point of view as well as from the biochemical one. In this paper, we identify important behaviors of this interplay between the immune system and stress from medical studies and seek to represent them qualitatively in a paradigmatic, yet simple, mathematical model. To that end, we develop an ordinary differential equation model with two equations, for infection level and immune system, respectively, which integrates the effects of stress as an independent parameter. In addition, we perform a geometric analysis of the model for different stress values as well as the corresponding bifurcation analysis. In this context, we are able to reproduce a stable healthy state for little stress, an oscillatory state between healthy and infected states for high stress, and a "burn-out" or stable sick state for extremely high stress. The mechanism between the different dynamical regimes is controlled by two saddle-node in cycle bifurcations. Furthermore, our model is able to capture an induced infection upon dropping from moderate to low stress, and it predicts increasing infection periods upon increasing stress before eventually reaching a burn-out state.
Highlights
It is common knowledge that stress can hurt our health, scientific results regarding this are fairly recent
Many studies have been developed in psychoneuroimmunology that associate stress, arising from multiple different sources and situations, to changes in the immune system, from the medical or immunological point of view as well as from the biochemical one
We develop an ordinary differential equation model with two equations, for infection level and immune system, respectively, which integrates the effects of stress as an independent parameter
Summary
It is common knowledge that stress can hurt our health, scientific results regarding this are fairly recent. Scitation.org/journal/cha stressor in the same way as psychological ones.[9] PNI wants to understand the biochemistry of how behavioral and psychological effects, in particular stress, are reflected in our bodies, i.e., how stress “gets inside the body.”[8,10,11] there is still much to learn, we have a basic understanding of the hormonal reactions of our body to stress and how they affect the immune system, e.g., by specific receptors on cells responsible for the immunity.[6] In addition, there are several studies regarding immunological and medical consequences of stress in animals[12,13] as well as humans,[14,15,16,17] where a key goal is to understand and counteract negative consequences In this context, the difficulties of extensive clinical trials and the lack of a commonly accepted definition, categorization, or measurements of stressors are most evident. The toolbox of nonlinear dynamics for lowdimensional models is extremely powerful[28–30] and has led to a clear identification of new mechanisms in complex systems, e.g., we understand different excitability patterns in neurons much better via low-dimensional dynamics models.[20,31,32] Yet, it is not clear what the elementary nonlinear mechanisms in the context of PNI, and, in particular, of the interplay between stress and the immune system, are
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