Prevention and Control of Zika as a Mosquito-Borne and Sexually Transmitted Disease: A Mathematical Modeling Analysis

Abstract

The ongoing Zika virus (ZIKV) epidemic in the Americas poses a major global public health emergency. While ZIKV is transmitted from human to human by bites of Aedes mosquitoes, recent evidence indicates that ZIKV can also be transmitted via sexual contact with cases of sexually transmitted ZIKV reported in Argentina, Canada, Chile, France, Italy, New Zealand, Peru, Portugal, and the USA. Yet, the role of sexual transmission on the spread and control of ZIKV infection is not well-understood. We introduce a mathematical model to investigate the impact of mosquito-borne and sexual transmission on the spread and control of ZIKV and calibrate the model to ZIKV epidemic data from Brazil, Colombia, and El Salvador. Parameter estimates yielded a basic reproduction number 0 = 2.055 (95% CI: 0.523-6.300), in which the percentage contribution of sexual transmission is 3.044% (95% CI: 0.123-45.73). Our sensitivity analyses indicate that 0 is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. Prevention and control efforts against ZIKV should target both the mosquito-borne and sexual transmission routes.

Figure 1. Flow diagram for the spread of ZIKV involving vectorial and sexual transmission.

Green nodes are non-infectious and red nodes are infectious. Blue solid arrows show the progression of infection. Black dashed arrows show direction of human-to-human transmission and red dash-dotted lines show direction of transmission between humans and mosquitoes. An individual may progress from susceptible (S_h) to asymptomatically infected (A_h) to recovered (R_h), or exposed (E_h) to symptomatically infected (I_h1) to convalescent (I_h2) to recovered (R_h), while a mosquito may progress from susceptible (S_v) to exposed (E_v) to infectious (I_v).

Figure 2

(A) ZIKV outbreaks in South and Central Americas. The map indicates the month of first reported cases and the cumulative cases by May 16, 2016, in each country. The map was made with the free software “R: A Language and Environment for Statistical Computing, R Core Team, R Foundation for Statistical Computing, Vienna, Austria (2016) https://www.R-project.org.” accessed on February 1, 2016. (B) Fitting model to data in Brazil, Colombia, and El Salvador up to February 27, 2016. Each panel shows the simulation (red solid curve) versus the observed (black circle), with the best fitting parameters. The red solid curves show median values of 1000 simulations and shaded region show the 95% range. The blue dash curves show the estimated mosquito-human population ratio m(t). The inset panel shows Bayesian Information Criterion (BIC) as a function of the number of nodes (n_m) in m(t) with values m_i at these nodes. Assumed or estimated parameters and initial conditions are given in Table 2.

Figure 3

(A) The box plot of the basic reproduction numbers for one or both transmission routes. The horizontal dashed line is . (B) The partial rank correlation coefficient (PRCC) of the basic reproduction number with respect to model parameters. The circle is the estimated correlation and the bar shows the 95% confidence interval. Parameter ranges are given in Table 1.

Figure 4. The contour plot of the basic reproduction number in terms of two of the three controllable parameters: β (transmission rate of symptomatically infected humans to susceptible humans), m (ratio of mosquitoes to humans), and a (mosquito biting rate).

The blue dashed curve is the contour of . Parameter values are given in Table 1.

Figure 5. The partial rank correlation coefficient (PRCC) of the attack rate with respect to model parameters.

The circle is the estimated correlation and the bar shows the 95% confidence interval. Parameter ranges are given in Table 1.

Figure 6. The contour plot of the attack rate in terms of two of the three controllable parameters: β (transmission rate of symptomatically infected humans to susceptible humans), m (ratio of mosquitoes to humans), and a (mosquito biting rate).

All parameter values are given in Table 1.