This paper presents an optimal control strategy for the Zika virus disease with sexual transmission. A mathematical model for the transmission of the Zika virus is considered with three preventive measures as control, namely: the prevention of the sexual contagion with the use of condoms and the orientation in the transmission of Zika in the homosexual and heterosexual relations, the campaigns against vectors and the protection of the society regarding the contagion by mosquito bites. We examine the implementation of various combinations of the control strategies in order to determine the most cost-effective one. The necessary conditions for the optimal controls are determined using Pontryaguin’s maximum principle and the optimality problem is solved using Runge-Kutta fourth order scheme. Based on the computational results, we conclude that the most efficient control strategy is when i...

This paper presents an optimal control strategy for the Zika virus disease with sexual transmission. A mathematical model for the transmission of the Zika virus is considered with three preventive measures as control, namely: the prevention of the sexual contagion with the use of condoms and the orientation in the transmission of Zika in the homosexual and heterosexual relations, the campaigns against vectors and the protection of the society regarding the contagion by mosquito bites. We examine the implementation of various combinations of the control strategies in order to determine the most cost-effective one. The necessary conditions for the optimal controls are determined using Pontryaguin’s maximum principle and the optimality problem is solved using Runge-Kutta fourth order scheme. Based on the computational results, we conclude that the most efficient control strategy is when i...

The Zika virus has spread rapidly in the Americas since its first identification in Brazil in early 2015. The Zika virus is transmitted by Aedes mosquitoes and by sexual relations. It has been found in humans’ blood, saliva, urine, semen, amniotic fluid. Zika infection lasts only a few days, and signs and symptoms present in only about 20% of people are typically mild. The Zika virus has been considered a teratogen that causes microcephaly and other serious brain anomalies as it may invade fetal nerve cells and disrupt brain development. It has also been related to Guillian-Barré syndrome and to an autoimmune syndrome called acute disseminated encephalomyelitis, or ADEM. A review is done on the Zika virus transmission, perinatal problems and prevention in women of reproductive age, during pregnancy and labor, and fertility treatments, as well as strategic preventive considerations imp...