A fractional-order simplified cytokine dynamics model formulation
Abstract
In this work, we present a fractional-order formulation of the interaction dynamics between two cytokine groups. We consider an example of application of a drug that modifies the inhibitory interaction between these two groups. This simplified formulation qualitatively models the complex process observed during the so-called cytokine storm, in which a disbalance between the cytokine production can produce a hyperexcited state. In the integer-order model, we establish qualitative results showing a transition from a low-level production state to a high-level production state as the drug dose is increased. On the other hand, under the fractional-order formulation we establish results showing that the system resists such transition as the fractional order is decreased, staying for a longer time in the low concentration state. Considering the memory index interpretation of the fractional-order derivative, our results show that as the memory index is increased, the system is more resistant to the drug, and this, in turn, produces that a higher dose is necessary to transition from a low concentration state to hyperexcited concentration state.
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References
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