Optimal control applied to Zika virus epidemics in Colombia and Puerto Rico.

Zika virus (ZIKV) is a mostly non-lethal disease in humans transmitted by mosquitoes or humans that can produce severe brain defects such as microcephaly in babies and Guillain-Barré syndrome in elderly adults. The use of optimal control strategies involving information campaigns about insect repellents and condoms alongside an available safe and effective vaccine can prevent the number of infected humans with ZIKV. A system of nonlinear ordinary differential equations is formulated for the transmission dynamics of ZIKV in the presence of three control strategies to evaluate the impact of various scenarios during a ZIKV epidemic. In addition, we estimate parameters using weekly incidence data from previous ZIKV outbreaks in Colombia and Puerto Rico to capture the dynamics of an epidemic in each country when control measures are available. The basic reproduction number, R0, of each country is calculated using estimated parameters (without the controls). The vector-borne transmission threshold (Rv) is dominant in both countries , but the sexual transmission threshold (Rd) in Colombia is considerably higher than in Puerto Rico. Numerical simulations for Colombia show that the most effective strategies are to use three controls since the start of the outbreak. However, for Puerto Rico only information campaigns about mosquito repellents and vaccination are the most effective ways to mitigate the epidemic.