Department of Mathematics, Prince Sultan University, Riyadh, Kingdom of Saudi Arabia.
Department of Mathematics, University of Dayton, Dayton, OH, USA.
Infect Dis Poverty. 2016 Jul 13;5(1):72. doi: 10.1186/s40249-016-0161-6.
The 2014 Ebola epidemic is the largest in history, affecting multiple countries in West Africa. Some isolated cases were also observed in other regions of the world.
In this paper, we introduce a deterministic SEIR type model with additional hospitalization, quarantine and vaccination components in order to understand the disease dynamics. Optimal control strategies, both in the case of hospitalization (with and without quarantine) and vaccination are used to predict the possible future outcome in terms of resource utilization for disease control and the effectiveness of vaccination on sick populations. Further, with the help of uncertainty and sensitivity analysis we also have identified the most sensitive parameters which effectively contribute to change the disease dynamics. We have performed mathematical analysis with numerical simulations and optimal control strategies on Ebola virus models.
We used dynamical system tools with numerical simulations and optimal control strategies on our Ebola virus models. The original model, which allowed transmission of Ebola virus via human contact, was extended to include imperfect vaccination and quarantine. After the qualitative analysis of all three forms of Ebola model, numerical techniques, using MATLAB as a platform, were formulated and analyzed in detail. Our simulation results support the claims made in the qualitative section.
Our model incorporates an important component of individuals with high risk level with exposure to disease, such as front line health care workers, family members of EVD patients and Individuals involved in burial of deceased EVD patients, rather than the general population in the affected areas. Our analysis suggests that in order for R 0 (i.e., the basic reproduction number) to be less than one, which is the basic requirement for the disease elimination, the transmission rate of isolated individuals should be less than one-fourth of that for non-isolated ones. Our analysis also predicts, we need high levels of medication and hospitalization at the beginning of an epidemic. Further, optimal control analysis of the model suggests the control strategies that may be adopted by public health authorities in order to reduce the impact of epidemics like Ebola.
2014 年埃博拉疫情是历史上最大的一次，影响了西非的多个国家。世界其他地区也观察到了一些孤立的病例。
在本文中，我们引入了一个确定性的 SEIR 型模型，该模型具有额外的住院、隔离和接种组件，以便了解疾病的动态。我们使用最优控制策略，无论是在住院（有或没有隔离）还是接种的情况下，都可以预测控制疾病所需资源的可能未来结果，以及接种对患病人群的有效性。此外，借助不确定性和敏感性分析，我们还确定了最敏感的参数，这些参数有效地改变了疾病的动态。我们对埃博拉病毒模型进行了数学分析、数值模拟和最优控制策略。
我们使用动力系统工具，对埃博拉病毒模型进行了数值模拟和最优控制策略。允许通过人际接触传播埃博拉病毒的原始模型，扩展到包括不完全接种和隔离。对三种形式的埃博拉病毒模型进行了定性分析后，使用 MATLAB 作为平台，制定并详细分析了数值技术。我们的模拟结果支持定性部分的结论。
我们的模型纳入了一个重要的组成部分，即具有高风险水平的个体与疾病接触，例如一线医护人员、埃博拉病毒患者的家庭成员以及参与死者埋葬的个体，而不是受影响地区的一般人群。我们的分析表明，为了使 R0（即基本繁殖数）小于 1，这是消除疾病的基本要求，孤立个体的传播率应小于非孤立个体的四分之一。我们的分析还预测，在疫情开始时，我们需要大量的药物和住院治疗。此外，对模型的最优控制分析表明，公共卫生当局可能采取的控制策略，以减少埃博拉等传染病的影响。
