Nowadays, big data are everywhere. Examples of big data include weather data, web-search data, disease reports, as well as epidemic data and statistics. These big data can be easily generated and collected from a wide variety of data sources. A data science frameworksuch as predictive analytics framework-helps mining data from various big data sources to find useful information and discover knowledge, which can then be transformed into wisdom for appropriate actions. In this paper, we present an innovative big data predictive analytics framework over hybrid big data sources. To demonstrate the effectiveness and practicality of our framework, we conduct several case studies, including one on applying the framework to disease analytics. More specifically, we integrate, incorporate and analyze weather data and web-search data to predict and forecast dengue cases based on a hybrid of three kernels in support vector machine (SVM) ensemble. Results show how our predictive analytics framework benefits health agencies in disease control and prevention.