Posny Drew, Wang Jin, Mukandavire Zindoga, Modnak Chairat
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA.
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA.
Math Biosci. 2015 Jun;264:38-53. doi: 10.1016/j.mbs.2015.03.006. Epub 2015 Mar 28.
Cholera continues to be a serious public health concern in developing countries and the global increase in the number of reported outbreaks suggests that activities to control the diseases and surveillance programs to identify or predict the occurrence of the next outbreaks are not adequate. These outbreaks have increased in frequency, severity, duration and endemicity in recent years. Mathematical models for infectious diseases play a critical role in predicting and understanding disease mechanisms, and have long provided basic insights in the possible ways to control infectious diseases. In this paper, we present a new deterministic cholera epidemiological model with three types of control measures incorporated into a cholera epidemic setting: treatment, vaccination and sanitation. Essential dynamical properties of the model with constant intervention controls which include local and global stabilities for the equilibria are carefully analyzed. Further, using optimal control techniques, we perform a study to investigate cost-effective solutions for time-dependent public health interventions in order to curb disease transmission in epidemic settings. Our results show that the basic reproductive number (R0) remains the model's epidemic threshold despite the inclusion of a package of cholera interventions. For time-dependent controls, the results suggest that these interventions closely interplay with each other, and the costs of controls directly affect the length and strength of each control in an optimal strategy.
霍乱在发展中国家仍然是一个严重的公共卫生问题，全球报告的疫情数量增加表明，控制该疾病的活动以及识别或预测下一次疫情发生的监测计划并不充分。近年来，这些疫情在频率、严重程度、持续时间和地方性方面都有所增加。传染病数学模型在预测和理解疾病机制方面发挥着关键作用，长期以来为控制传染病的可能方式提供了基本见解。在本文中，我们提出了一种新的确定性霍乱流行病学模型，该模型将三种控制措施纳入霍乱流行环境中：治疗、疫苗接种和环境卫生。仔细分析了具有恒定干预控制的模型的基本动力学性质，包括平衡点的局部和全局稳定性。此外，我们使用最优控制技术进行了一项研究，以调查针对随时间变化的公共卫生干预措施的成本效益解决方案，以便在流行环境中遏制疾病传播。我们的结果表明，尽管纳入了一系列霍乱干预措施，但基本再生数（R0）仍然是该模型的疫情阈值。对于随时间变化的控制措施，结果表明这些干预措施相互之间密切相互作用，并且控制成本直接影响最优策略中每种控制措施的持续时间和强度。
