The Zika Virus (ZIKV) is a virus transmitted by Aedes aegypti mosquitoes (same as the one transmitting dengue and chikungunya fever). The main way of contagion by the ZIKV is caused by the bite of a mosquito that, after feeding from someone contaminated, can transport the virus throughout its life, transmitting the disease to a population that does not have the immunity. It can also be transmitted through a person’s sexual relationship with ZIKV to their partners, even if the infected person does not have the symptoms of the disease. In this work, we present two mathematical models for the Zika epidemic by using (1) ordinary differential equations and, (2) ordinary differential equations with temporal delay (discrete), which is the time it takes mosquitoes to develop the virus. We make a comparison between the two modeling variants. Computational simulations are performed for Su...

Zika virus spreads to people primarily through the bite of an infected Aedes aegypti species mosquito. But it Zika can also be passed through sex from an infected to his or her sex partners and it can be spread from a pregnant woman to her fetus. Zika continues to spreading geographically to areas where competent vectors are present. Although a decline in cases of Zika virus infection has been reported in some countries, or in some parts of countries, vigilance needs to remain high. In this work, we propose a mathematical model that uses diffusion-advection equations to study the impact of the Zika epidemic. We present a numerical scheme linking finite elements (FEM) with finite differences to solve the model. The computer simulations are performed for Paramaribo and Santa Ana that have different demographic characteristics and allow us to extend the study to other regions.

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...

Zika virus spreads to people primarily through the bite of an infected Aedes aegypti species mosquito. But it Zika can also be passed through sex from an infected to his or her sex partners and it can be spread from a pregnant woman to her fetus. Zika continues to spreading geographically to areas where competent vectors are present. Although a decline in cases of Zika virus infection has been reported in some countries, or in some parts of countries, vigilance needs to remain high. In this work, we propose a mathematical model that uses diffusion-advection equations to study the impact of the Zika epidemic. We present a numerical scheme linking finite elements (FEM) with finite differences to solve the model. The computer simulations are performed for Paramaribo and Santa Ana that have different demographic characteristics and allow us to extend the study to other regions.

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 (ZIKV) is a virus transmitted by Aedes aegypti mosquitoes (same as the one transmitting dengue and chikungunya fever). The main way of contagion by the ZIKV is caused by the bite of a mosquito that, after feeding from someone contaminated, can transport the virus throughout its life, transmitting the disease to a population that does not have the immunity. It can also be transmitted through a person’s sexual relationship with ZIKV to their partners, even if the infected person does not have the symptoms of the disease. In this work, we present two mathematical models for the Zika epidemic by using (1) ordinary differential equations and, (2) ordinary differential equations with temporal delay (discrete), which is the time it takes mosquitoes to develop the virus. We make a comparison between the two modeling variants. Computational simulations are performed for Su...