Fractional-Order Modelling and Optimal Control of Cholera Transmission
Rosa, S.
; Torres, D. F. M. T.
Fractal and Fractional Vol. 5, Nº 4, pp. 261 - 261, December, 2021.
ISSN (print):
ISSN (online): 2504-3110
Scimago Journal Ranking: 0,64 (in 2021)
Digital Object Identifier: 10.3390/fractalfract5040261
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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.
