In the absence of valid medicine or vaccine for treating the pandemic Coronavirus (COVID-19) infection, other control strategies like; quarantine, social distancing, self- isolation, sanitation and use of personal protective equipment are effective tool used to prevent and curtail the spread of the disease. In this paper, we present a mathematical model to study the dynamics of COVID-19. We then formulate an optimal control problem with the aim to study the most effective control strategies to prevent the proliferation of the disease. The existence of an optimal control function is established and the Pontryagin maximum principle is applied for the characterization of the controller. The equilibrium solutions (DFE & endemic) are found to be locally asymptotically stable and subsequently the basic reproduction number is obtained. Numerical simulations are carried out to support the analytic results and to explicitly show the significance of the control. It is shown that Quarantine/isolating those infected with the disease is the best control measure at the moment.

在没有有效的药物或疫苗来治疗大流行性冠状病毒（COVID-19）感染的情况下，其他控制策略应包括：隔离，社会隔离，自我隔离，环境卫生和个人防护设备的使用是预防和减少疾病传播的有效工具。在本文中，我们提出了一个数学模型来研究COVID-19的动力学。然后，我们制定了一个最佳的控制问题，旨在研究预防疾病扩散的最有效控制策略。建立了最优控制函数的存在，并将庞特里亚金极大值原理应用于控制器的表征。发现平衡解（DFE和地方性）是局部渐近稳定的，随后获得了基本的繁殖数。进行数值模拟以支持分析结果并明确显示控制的重要性。结果表明，隔离/隔离感染该病的人是目前最好的控制措施。