Methanol Toxicology and Treatment: A Mathematical Study to Explore Alcohol Dynamics

Methanol poisoning is common in low income countries and such harmful intoxication causes severe metabolic disturbances. It may cause death under serious cases of methanol toxicity. Although methanol itself may be harmless, but it is oxidized to formaldehyde, further it breakdowns to formic acid which is lethal in humans with high concentration. The breakdown is assisted by two major enzymes alcohol dehydrogenase and formaldehyde dehydrogenase. High accumulation of formic acid within humans imposes larger threats causing casualties in extreme cases if remains untreated. During methanol poisoning the primary therapeutic application of ethanol is administered to slowdown the formation of toxic metabolites by competitive substitution of the methanol due to its intrinsic binding affinity. Moreover, supportive role of administering sodium bicarbonate in the patient assist the neutralization of the metabolic acidosis in human. In this research article, we formulate a mathematical model to study the effect of co-administration of ethanol and sodium bicarbonate to treat methanol toxicity among humans. We studied the system analytically and numerically and observed the dynamics of the therapy in an impulsive fashion. We have obtained a parameter dependent maximum dosing time interval to perform complete competitive inhibition of the methanol below the safe threshold level for recovery of the intoxicated human patients. Our analytical and numerical results are in accordance with the published experimental findings.