Development of a smart and connected community (SCC) health framework is an indispensable part in the development of smart cities. Smartphones with increased processing capability, integrated sensors, storage capacity, and cloud connectivity have a key role to play in developing this SCC Health framework. In this paper, we report a novel smartphone-based framework for continuous monitoring of arrhythmia, obstructive sleep apnea (OSA), chronic obstructive pulmonary disease (COPD), and flu. In addition to personalized monitoring, community-wide temporal and spatial monitoring are also possible in this approach. A custom smartphone app is developed that has the ability for collection of body sensor data via Bluetooth, loading machine learning algorithms dynamically from the webserver, computing disease severity in real-time, sharing of anonymous data, and visualization of community health status via the webserver. The framework has been tested for online monitoring of OSA, COPD, and flu severity. An accuracy of +/- 1 degrees F has been achieved for flu measurement and a mean absolute error (MAE) of 8.27 AHI has been achieved for OSA severity estimation using heart rate variability and SpO(2). The app has a power consumption of 218 mW when active, uses a memory of 7 MB, and requires a total storage space of 9.36 MB. This framework aims to improve community health, reduce waste in healthcare spending, and facilitate early treatment in case of disease exacerbation.