Modelling the dynamics of online food delivery services on the spread of food-borne diseases

TL;DR

This paper develops a fractional-order mathematical model to analyze how online food delivery and government actions influence the spread of food-borne diseases, emphasizing the importance of effective safety interventions.

Contribution

It introduces a novel fractional-order model incorporating online food delivery dynamics and provides stability and numerical analysis using advanced mathematical techniques.

Findings

Model demonstrates the impact of government interventions on disease spread.

Numerical simulations show convergence and stability across fractional orders.

Highlights the importance of food safety measures in online food delivery.

Abstract

We propose and analyze a deterministic mathematical model for the transmission of food-borne diseases in a population consisting of humans and flies. We employ the Caputo operator to examine the impact of governmental actions and online food delivery services on the transmission of food-borne diseases. The proposed model investigates important aspects such as positivity, boundedness, disease-free equilibrium, basic reproduction number and sensitivity analysis. The existence and uniqueness of a solution for the initial value problem is established using Banach and Schauder type fixed point theorems. Functional techniques are employed to demonstrate the stability of the proposed model under the Hyers-Ulam condition. For an approximate solution, the iterative fractional order Predictor-Corrector scheme is utilized. The simulation of this scheme is conducted using Matlab as the numeric computing environment, with various fractional order values ranging from 0.75 to 1. Over time, all compartments demonstrate convergence and stability. The numerical simulations highlight the necessity for the government to implement the most effective food safety control interventions. These measures could involve food safety awareness and training campaigns targeting restaurant managers, staff members involved in online food delivery, as well as food delivery personnel.