A Mathematical Model for Zika Virus Infection and Microcephaly Risk Considering Sexual and Vertical Transmission

Abstract

We establish a compartmental model for Zika virus disease transmission, with particular attention paid to microcephaly, the main threat of the disease. To this end, we consider separate microcephaly-related compartments for affected infants, as well as the role of asymptomatic carriers, the influence of seasonality and transmission through sexual contact. We determine the basic reproduction number of the corresponding time-dependent model and time-constant model and study the dependence of this value on the mosquito-related parameters. In addition, we demonstrate the global stability of the disease-free periodic solution if R0<1, whereas the disease persists when R0>1. We fit our model to data from Colombia between 2015 and 2017 as a case study. The fitting is used to figure out how sexual transmission affects the number of cases among women as well as the number of microcephaly cases. Our sensitivity analyses conclude that the most effective ways to prevent Zika-related microcephaly cases are preventing mosquito bites and controlling mosquito populations, as well as providing protection during sexual contact.