An epidemic model for cholera with optimal control treatment
An epidemic model for cholera with optimal control treatment
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DOI：
10.1016/j.cam.2016.11.002
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发表时间：
2017-07-01
影响因子：
2.4
通讯作者：
Torres, Delfim F. M.
中科院分区：
文献类型：
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作者：
Lemos-Paiao, Ana P.;Silva, Cristiana J.;Torres, Delfim F. M.
我们提出了一个通过隔离治疗霍乱的数学模型。该模型在流行病学和数学上都被证明是正确的。特别是，我们证明模型的所有解都是正的且有界的；并且初始条件在某个有意义的集合中的每个解决方案始终保留在该集合中。证明了唯一的无病平衡点和地方病平衡点的存在，并计算了基本再生数。然后，我们研究这些平衡点的局部渐近稳定性。提出并分析了最优控制问题，其目标是通过隔离获得成功的治疗。我们提供最佳的检疫策略，以尽量减少感染个体的数量和细菌浓度，以及与检疫相关的成本。最后，对2010年阿蒂博尼特省（海地）霍乱疫情进行了数值模拟，说明了模型及其分析的实用性。 (C) 2016 Elsevier B.V. 保留所有权利。
We propose a mathematical model for cholera with treatment through quarantine. The model is shown to be both epidemiologically and mathematically well posed. In particular, we prove that all solutions of the model are positive and bounded; and that every solution with initial conditions in a certain meaningful set remains in that set for all time. The existence of unique disease-free and endemic equilibrium points is proved and the basic reproduction number is computed. Then, we study the local asymptotic stability of these equilibrium points. An optimal control problem is proposed and analyzed, whose goal is to obtain a successful treatment through quarantine. We provide the optimal quarantine strategy for the minimization of the number of infectious individuals and bacteria concentration, as well as the costs associated with the quarantine. Finally, a numerical simulation of the cholera outbreak in the Department of Artibonite (Haiti), in 2010, is carried out, illustrating the usefulness of the model and its analysis. (C) 2016 Elsevier B.V. All rights reserved.