Mathematical model for inflammatory response to coronavirus infection with anti-inflammatory treatment intervention.

Increasing the concentration of anti-inflammatory cytokine inhibits inflammation in human blood vessels due to the excessive production of the pro-inflammatory cytokine, i.e., cytokine storm during Coronavirus infection. This research aims to construct and analyze a mathematical model of the interaction between pro-inflammatory cytokine and anti-inflammatory cytokine with the addition of treatment factor on anti-inflammatory cytokine to identify the effect and the appropriate level of the treatment in reducing the possibility of the cytokine storm. The method used in this research is constructing a three-dimensional differential equation system as the mathematical model of inflammatory response system including the treatment factor, then analyzing the model by calculating the equilibrium points and their local stability and giving numerical simulation, as well as medical interpretation of the results as the conclusion. There are two equilibrium points in the model related to the treatment effect. The infection equilibrium point represents the static condition of the concentrations for a long time without treatment while the disease-free equilibrium point represents the static condition for a long time with treatment. The infection equilibrium point is a saddle, so that the cytokine storm has a possibility to be triggered. The disease-free equilibrium point is asymptotically stable, therefore the production of pro-inflammatory cytokine is reduced to a specific value due to the effect of the treatment on anti-inflammatory cytokine. The maximum rate of treatment should be in the range of values which is a condition for the existence and asymptotic stability of the disease-free equilibrium point, so that the concentration of pro-inflammatory cytokine can be reduced. Furthermore, the possibility of cytokine storms can be decreased. [ABSTRACT FROM AUTHOR]