Effects of multiple transmission pathways on Zika dynamics

Abstract

Although the Zika virus is transmitted to humans primarily through the bite of infected female Aedes aegypti mosquitoes, it can also be sexually and vertically transmitted within both populations. In this study, we develop a new mathematical model of the Zika virus which incorporates sexual transmission in humans and mosquitos, vertical transmission in mosquitos, and mosquito to human transmission through bites. Analysis of this deterministic model shows that the secondary transmission routes of Zika increase the basic reproductive number ( $R_0$ ) of the virus by 5%, shift the peak time of an outbreak to occur 10% sooner, increase the initial growth of an epidemic, and have important consequences for control strategies and estimates of $R_0$ . Furthermore, sensitivity analysis show that the basic reproductive number is most sensitive to the mosquito biting rate and transmission probability parameters and reveal that the dynamics of juvenile mosquito stages greatly impact the peak time of an outbreak. These discoveries deepen our understanding of the complex transmission routes of ZIKV and the consequences that they may hold for public health officials.

Keywords: Basic reproductive number estimate; Control strategies; Epidemic growth rate; Secondary transmission pathways; Zika virus.

Fig. 1

ZIKV Transmission Model Schematic: The solid lines in this flow chart represent movement between different state variables. Thin dashed lines represent disease transmission between different classes of the same population, thick dashed lines represent disease transmission across different populations, and dotted lines represent birth in the mosquito population.

Fig. 2

ZIKV Dynamics: Full Model vs. Vector-Only Model.

Fig. 3

The Ratio of Human Infections Over Time. The figures show the ratio of Zika cases in models including secondary transmission pathways a, b, c, or d to Zika cases in the vector-only model over the time course of an outbreak.

Fig. 4

Sensitivity Analysis for$R_{0f}$: Sensitivity Indices are listed in order of decreasing magnitude. Parameters not shown (i.e. ${\gamma }_e,r,q,s,{\beta }_{mf},K,\alpha ,{\mu }_e,\delta ,\gamma$) have indices $<0.003$.

Fig. 5

Sensitivity Analysis for Peak Time: Sensitivity Indices are listed in order of decreasing magnitude.

Fig. 6

Cumulative Infections Under Continuous Application of Larvicides, Adulticides, & Repellents. Early control refers to initiation of the combined control measures at day 108 while delayed control refers to initiation at day 123.

Fig. 7

Fitting Vector-Only Model to Zika Incidence Data. Vector-only model is fit to ZIKV incidence data produced by full model (dots).