Stochastic modeling using Adomian method and fractionnal differential equations

TL;DR

This paper models toxin accumulation in humans with immune deficiencies using fractional differential equations of order one-half, employing the Adomian Decomposition Method and Riemann-Liouville fractional integration.

Contribution

It introduces a novel fractional differential equation model for toxin dynamics in vulnerable populations, combining Adomian decomposition and fractional calculus techniques.

Findings

Model effectively captures toxin accumulation over time.

Demonstrates the applicability of fractional calculus in biological systems.

Provides a framework for assessing food-borne disease risks.

Abstract

In this paper, we propose a fractional differential equation of order one-half, to model the evolution through time of the dynamics of accumulation and elimination of the contaminant in human organism with a deficient immune system, during consecutive intakes of contaminated food. This process quantifies the exposure to toxins of subjects living with comorbidity (children not breast-fed, the elderly, pregnant women) to food-born diseases. The Adomian Decomposition Method and the fractional integration of Riemann Liouville are used in the modeling processes.