On fractional impulsive system for methanol detoxification in human body

Abstract

Methanol toxicity causes many deaths every year especially in low-income classes of society. An impulsive differential equation system is presented, which is useful in examining the effectiveness of activated charcoal in detoxifying the body with methanol poisoning. We provide a theoretical study of the model. The considered model is analyzed for the qualitative theory and uniqueness of the solution is discussed by using the Banach contraction principle and Schauder fixed point theory. We derive the basic stability analysis using Ulam-Hyres (UH) criteria and its generalized version and showed that model is asymptotically stable. Moreover, the stability check for recursive methodology is also given. The fractional dynamics of the problem can give a better understanding of the use of activated charcoal for simple and cheap first aid. We have studied the adsorption capacity of activated charcoal with impulsive differential equations. The results from Caputo fractional operator provides a more accurate idea of first aid in public and primary health centres, which can reduce the deaths by methanol poisoning. Finally, using generalized Adams-Bashforth-Moulton Method (GABMM), we generated the numerical scheme for the system.