Treatment of methanol toxicity through ethanol and folinic acid: a mathematical study

Methanol poisoning is an infrequent but immensely dangerous intoxication, causing severe metabolic disturbances, neurological dysfunction, and even death, if not treated timely and properly. In this article, we formulate a mathematical model based on the chemical kinetics reaction, to analyse the effect of co-administration of the antidote ethanol and folinic acid for the treatment of methanol toxicity. The maximum concentration level of formic acid has been identified, and through a one-dimensional impulsive system, we determined the maximum dosing interval of folinic acid. Under appropriate assumptions we have demonstrated the existence and stability of the equilibrium-like periodic orbit of our system with impulsive administration of folinic acid and ethanol. The dynamical changes of toxic metabolites are illustrated numerically for different doses and dosing intervals. We performed a sensitivity analysis to identify the key parameters affecting formic acid concentration during treatment. Model results were validated by comparing them with clinical and experimental data on methanol half-life during ethanol therapy and formic acid clearance under folinic acid treatment. Based on our detailed analytical and numerical analysis, we recommend an effective dosing regimen of folinic acid and ethanol to detoxify the human body and clearly identify the conditions beyond which hemodialysis becomes essential. We verified all of our analytical outcomes through numerical simulation.