A mathematical model for Zika virus disease: Intervention methods and control of affected pregnancies

Zika virus is spread to human populations primarily by Aedes aegypti mosquitoes, and Zika virus disease has been linked to a number of developmental abnormalities and miscarriages, generally coinciding with infection during early pregnancy. In this paper, we propose a new mathematical model for the transmission of Zika and study a range of control strategies to reduce the incidence of affected pregnancies in an outbreak. While most infectious disease models primarily focus on measures of the spread of the disease, our model is formulated to estimate the number of affected pregnancies throughout the simulated outbreak. Thus the effectiveness of control measures and parameter sensitivity analysis is done with respect to this metric. In addition to traditional intervention strategies, we consider the introduction of Wolbachia-infected mosquitoes into the native population. Our results suggest a threshold parameter for Wolbachia as an effective control measure, and show the natural time scale needed for Wolbachia-infected mosquitoes to effectively replace the native population. Additionally, we consider the possibility of a Zika vaccine, both to avoid an outbreak through herd immunity and as a control measure administered during an active outbreak. With emerging data on persistence of Zika virus in semen, the proposed compartmental model also includes a component of post-infectious males, which introduces a longer time scale for sexual transmission than the primary route. While the overall role of sexual transmission of Zika in an outbreak scenario is small compared with the dominant human-vector route, this model predicts conditions under which subpopulations may make this secondary route more significant.