Optimal Control of Aquatic Diseases: A Case Study of Yemen’s Cholera Outbreak

Ana P. Lemos-Paião (), Cristiana J. Silva (), Delfim F. M. Torres () and Ezio Venturino ()
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Ana P. Lemos-Paião: University of Aveiro
Cristiana J. Silva: University of Aveiro
Delfim F. M. Torres: University of Aveiro
Ezio Venturino: Università di Torino

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 3, No 17, 1008-1030

Abstract: Abstract We propose a mathematical model for the transmission dynamics of some strains of the bacterium Vibrio cholerae, responsible for the cholera disease in humans. We prove that, when the basic reproduction number is equal to one, a transcritical bifurcation occurs for which the endemic equilibrium emanates from the disease-free point. A control function is introduced into the model, representing the distribution of chlorine water tablets for water purification. An optimal control problem is then proposed and analyzed, where the goal is to determine the fraction of susceptible individuals who should have access to chlorine water tablets in order to minimize the total number of new infections plus the total cost associated with the distribution of chlorine water tablets, over the considered period of time. Finally, we consider real data of the cholera outbreak in Yemen, from April 27, 2017 to April 15, 2018, choosing the values of the parameters of the uncontrolled model that fit the real data. Using our optimal control results, we show, numerically, that the distribution of chlorine water tablets could have stopped, in a fast way, the worst cholera outbreak that ever occurred in human history. Due to the critical situation of Yemen, we also simulate the case where only a small percentage of susceptible individuals has access to chlorine water tablets and obtain an optimal control solution that decreases, substantially, the maximum number of infective individuals affected by the outbreak.

Keywords: SIQRB cholera model; Equilibrium points; Feasibility and local stability; Optimal control; 2018 cholera outbreak in Yemen; 34C60; 49K15; 92D30 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01668-z

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