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.
Highlights
The mode of transmission consists of two pathways: the primary route, where individuals consumes the pathogen from vibrio contaminated water and seafood; the secondary route being characterised by individuals consuming unhygienic or soiled food that is infested with pathogenic vibrios from an infected person
We begin by doing a sensitivity analysis to the parameters of the model, in order to identify those for which a small perturbation leads to relevant quantitative changes in the dynamics
The resulting graphics show that: (a) the curve of vaccination is the one that most rapidly moves away from zero, meaning that the vaccination program has a big impact for small rates of application; (b) proper hygiene measures are important in the control of cholera, having a bigger impact for greater rates of application of it, being the only control that has precisely the same impact in both communities; (c) the domestic water treatment is useless in the control of cholera transmission, when used simultaneously with the two previous controls
Summary
Fractional calculus is an old subject that raised as a consequence of a pertinent question that L’Hôpital asked Leibniz in a letter about the possible meaning of a derivative of order1/2. Many researchers have focused their attention in modelling real-world phenomena using fractional-order derivatives. The dynamics of those problems have been modelled and studied by using the concept of fractional-order derivatives. The mode of transmission consists of two pathways: the primary route, where individuals consumes the pathogen from vibrio contaminated water and seafood; the secondary route being characterised by individuals consuming unhygienic or soiled food that is infested with pathogenic vibrios from an infected person. This secondary route of transmission is commonly referred to as person-toperson contact [4]. Its devastating force has been more pronounced in impoverished communities [5,6]
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