  As per the records of theWorld Health Organization, the first formally
reported incidence of Zika virus occurred in Brazil in May 2015. The disease
then rapidly spread to other countries in Americas and East Asia, affecting
more than 1,000,000 people. Zika virus is primarily transmitted through bites
of infected mosquitoes of the species Aedes (Aedes aegypti and Aedes
albopictus). The abundance of mosquitoes and, as a result, the prevalence of
Zika virus infections are common in areas which have high precipitation, high
temperature, and high population density.Nonlinear spatio-temporal dependency
of such data and lack of historical public health records make prediction of
the virus spread particularly challenging. In this article, we enhance Zika
forecasting by introducing the concepts of topological data analysis and,
specifically, persistent homology of atmospheric variables, into the virus
spread modeling. The topological summaries allow for capturing higher order
dependencies among atmospheric variables that otherwise might be unassessable
via conventional spatio-temporal modeling approaches based on geographical
proximity assessed via Euclidean distance. We introduce a new concept of
cumulative Betti numbers and then integrate the cumulative Betti numbers as
topological descriptors into three predictive machine learning models: random
forest, generalized boosted regression, and deep neural network. Furthermore,
to better quantify for various sources of uncertainties, we combine the
resulting individual model forecasts into an ensemble of the Zika spread
predictions using Bayesian model averaging. The proposed methodology is
illustrated in application to forecasting of the Zika space-time spread in
Brazil in the year 2018.

Populations and Evolution;Applications;Machine Learning