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Optimal Control of Aquatic Diseases: A Case Study of Yemen’s Cholera Outbreak
Journal of Optimization Theory and Applications ( IF 1.6 ) Pub Date : 2020-05-23 , DOI: 10.1007/s10957-020-01668-z
Ana P. Lemos-Paião , Cristiana J. Silva , Delfim F. M. Torres , Ezio Venturino

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.

中文翻译:

水生疾病的最佳控制:也门霍乱爆发的案例研究

我们为霍乱弧菌的某些菌株的传播动力学提出了一个数学模型,霍乱弧菌是人类霍乱病的罪魁祸首。我们证明,当基本再生数等于 1 时,会发生跨临界分叉,其中地方性平衡从无病点发出。模型中引入了一个控制函数,表示用于净水的氯水片的分布。然后提出并分析了一个最佳控制问题,其目标是确定应该获得氯水片的易感个体的比例,以最大限度地减少新感染的总数以及与分配氯水相关的总成本片剂,在考虑的时间段内。最后,我们考虑了也门霍乱爆发的真实数据,从 2017 年 4 月 27 日到 2018 年 4 月 15 日,选择适合真实数据的非受控模型的参数值。使用我们的最佳控制结果,我们从数字上表明,氯水片的分布可以迅速阻止人类历史上发生过的最严重的霍乱爆发。由于也门的危急情况,我们还模拟了只有一小部分易感人群可以获得氯水片的情况,并获得了一个最佳控制解决方案,从而大大减少了受疫情影响的最大感染人数。使用我们的最佳控制结果,我们从数字上表明,氯水片的分布可以迅速阻止人类历史上发生过的最严重的霍乱爆发。由于也门的危急情况,我们还模拟了只有一小部分易感人群可以获得氯水片的情况,并获得了一个最佳控制解决方案,从而大大减少了受疫情影响的最大感染人数。使用我们的最佳控制结果,我们从数字上表明,氯水片的分布可以迅速阻止人类历史上发生过的最严重的霍乱爆发。由于也门的危急情况,我们还模拟了只有一小部分易感人群可以获得氯水片的情况,并获得了一个最佳控制解决方案,从而大大减少了受疫情影响的最大感染人数。
更新日期:2020-05-23
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