Fractional-Order Modelling and Optimal Control of Cholera Transmission

TL;DR

This paper develops a fractional-order model for cholera transmission, performs sensitivity and cost-effectiveness analyses, and introduces a variable-order fractional system that improves disease control effectiveness.

Contribution

It introduces a variable-order fractional model ('FractInt') for cholera, enhancing control strategies over traditional fixed-order models.

Findings

Variable-order fractional model outperforms fixed-order models in control effectiveness.

Sensitivity analysis confirms parameter importance for model accuracy.

Cost-effectiveness analysis guides optimal intervention strategies.

Abstract

A Caputo-type fractional-order mathematical model for "metapopulation cholera transmission" was recently proposed in [Chaos Solitons Fractals 117 (2018), 37--49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a 'FractInt' system, shows to be the most effective in the control of the disease.