A total of more than 27 million confirmed cases of the novel coronavirus outbreak, also known as COVID-19, have been reported as of September 7, 2020. To reduce its transmission, a number of strategies have been proposed. In this study, mathematical models with nonpharmaceutical and pharmaceutical interventions were formulated and analyzed. The first model was formulated without the inclusion of community awareness. The analysis focused on investigating the mathematical behavior of the model, which can explain how medical masks, medical treatment, and rapid testing can be used to suppress the spread of COVID-19. In the second model, community awareness was taken into account, and all the interventions considered were represented as time-dependent parameters. Using the center-manifold theorem, we showed that both models exhibit forward bifurcation. The infection parameters were obtained by fitting the model to COVID-19 incidence data from three provinces in Indonesia, namely, Jakarta, West Java, and East Java. Furthermore, a global sensitivity analysis was performed to identify the most influential parameters on the number of new infections and the basic reproduction number. We found that the use of medical masks has the greatest effect in determining the number of new infections. The optimal control problem from the second model was characterized using the well-known Pontryagin’s maximum principle and solved numerically. The results of a cost-effectiveness analysis showed that community awareness plays a crucial role in determining the success of COVID-19 eradication programs.

中文翻译：

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在社区意识的影响下，印度尼西亚对COVID-19根除计划的最佳控制

截至2020年9月7日，总共报告了超过2700万例确诊的新型冠状病毒爆发病例，也称为COVID-19。为减少其传播，已提出了许多策略。在这项研究中，建立并分析了具有非药物和药物干预作用的数学模型。在没有社区意识的情况下制定了第一个模型。该分析着重于研究模型的数学行为，这可以解释如何使用医用口罩，药物治疗和快速测试来抑制COVID-19的扩散。在第二个模型中，考虑了社区意识，所有考虑的干预措施均表示为时间依赖性参数。使用中心流形定理，我们表明两个模型都表现出正向分支。通过将模型与印度尼西亚三个省（雅加达，西爪哇和东爪哇）的COVID-19发病率数据拟合，可以得到感染参数。此外，进行了全球敏感性分析，以确定对新感染数量和基本繁殖数量影响最大的参数。我们发现，使用医用口罩在确定新感染数量方面效果最大。使用著名的庞特里亚金的最大原理对第二个模型的最优控制问题进行了表征，并进行了数值求解。成本效益分析的结果表明，社区意识在确定COVID-19根除计划的成功中起着至关重要的作用。