We formulate a new mathematical model for the Zika infection with mutations and optimal controls. The Zika virus with mutations that cause defects in the newly birth for infected pregnant woman and may lead to further infections in society. Therefore, in the present paper, we utilize this concept into our model and presented a new mathematical model for the characterization of Zika infection with possible controls. Initially, we present the model and provide the mathematical results. The stability of the model at the disease free case is presented. Utilizing the data of Colombia for the year 2016, and estimated and fitted the parameters to model. The results of the model for the data set present that the model is best suitable for this data set. The estimated and fitted parameters for Zika virus give ${\mathcal{R}}_0\approx 0.5477$. We show the stability of the model graphically when ${\mathcal{R}}_0$ greater or less than one. Further, we use the controls, preventions through bednets for humans and pregnant women who may have safety upon restrict their travel to epidemic areas of Zika virus, the possible treatments for the infected compartments and the use of insecticide spraying on mosquitoes. Keeping in mind these controls, we formulate an optimal control problem. We show the existence of the optimal control problem and obtain the mathematical results for the control characterizations. We provide the solution of the model numerically keeping in mind the real data and propose a set of controls for the elimination of the Zika virus from a community.

我们为Zika感染建立了具有突变和最佳控制的新数学模型。带有寨卡病毒的突变会导致受感染孕妇的新生婴儿出现缺陷，并可能导致社会进一步感染。因此，在本文中，我们将这一概念应用到模型中，并提出了一种新的数学模型，用于通过可能的控制来表征寨卡病毒感染。最初，我们介绍模型并提供数学结果。提出了模型在无病情况下的稳定性。利用哥伦比亚2016年的数据，对参数进行估算和拟合。数据集的模型结果表明，该模型最适合此数据集。寨卡病毒的估计参数和拟合参数给出${\mathcal{[R}}_0\approx 0.5477$。我们在以下情况下以图形方式显示模型的稳定性${\mathcal{[R}}_0$大于或小于一个。此外，我们使用控制和预防措施，通过蚊帐为人类和孕妇提供安全性，以限制他们前往寨卡病毒流行区的旅行，对感染车厢的可能治疗以及在蚊子上喷洒杀虫剂。牢记这些控件，我们制定了一个最优控件问题。我们展示了最优控制问题的存在，并获得了用于控制特性的数学结果。我们在数值上牢记真实数据，提供了模型的解决方案，并提出了一套从社区消除寨卡病毒的控制措施。