Modeling the Spread of Zika Virus in a Stage-Structured Population: Effect of Sexual Transmission

Abstract

The recent Zika virus outbreak has been spreading rapidly all over the world, expanding its traditionally geographical affected regions, making it a global public health hazard and endangering millions of people. One unique property of the Zika virus compared to most vector-borne diseases is the fact that the virus is transmitted both by mosquitoes and by direct sexual contact. In the present manuscript, we formulate and analyze five mathematical compartmental models of Zika transmission. We model both transmission routes (i.e., vector-borne and sexual transmission). In order to make the model more realistic, heterogeneity in the sexual transmission is modeled in several ways. We fitted the five different models to data, inferred the parameters and selected the most appropriated model, which describes the Zika outbreak in Columbia. For all the models, we estimate the reproduction numbers, namely direct (sexual) transmission, vector transmission and the basic reproduction number (R0). The analysis revealed that the sexual transmission contribution to R0 is highest [15.36% (95% CI 12.83–17.4)] for the model which stratifies each gender to high-risk and low-risk individuals in their sexual behavior. For this model, the estimated R0 is 1.89 (95% CI 1.21–2.13), the direct transmission reproduction number is 0.42 (95% CI 0.29–0.64), and the vector transmission reproduction number is 1.51 (95% CI 1.23–1.87). The sensitivity analysis demonstrated that the value of R0 depends on three controllable parameters: the biting rate, the sexual transmission rate and the average ratio of mosquito to human.