Logistic model of inflammatory response to coronavirus infection with anti-inflammatory treatment effect.

Massive production of pro-inflammatory cytokine during coronavirus infection causes an inflammation in human blood vessels, i.e. cytokine storm. It can be inhibited by increasing the concentration of anti-inflammatory cytokine in order to reduce the pro-inflammatory cytokine concentration which triggers the cytokine storm. We construct and analyze the mathematical model with logistic term in pro-inflammatory cytokine production and anti-inflammatory treatment effect to characterize the interaction between the two cytokines during coronavirus infection. The model is a three-dimensional system of differential equations which has a treated and an untreated equilibria. The sufficient condition for asymtotic stability of the treated equilibria is pro-inflammatory cytokine concentration must be less than its maximum concentration when the treatment is given for a long time. Fulfillment of this condition can become a parameter to reduce the risk of cytokine storm through the degradation process of pro-inflammatory cytokines. [ABSTRACT FROM AUTHOR]