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**Optimal control strategies of Zika virus model with mutant.**
*(English)*
Zbl 1453.92285

Summary: 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.

### MSC:

92D30 | Epidemiology |

92C60 | Medical epidemiology |

49J15 | Existence theories for optimal control problems involving ordinary differential equations |

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