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Although mobile health monitoring where mobile sensors continuously gather, process, and update sensor readings (e.g. vital signals) from patient's sensors is emerging, little effort has been investigated in an energy-efficient management of sensor information gathering and processing. Mobile health monitoring with the focus of energy consumption may instead be holistically analyzed and systematically designed as a global solution to optimization subproblems. This paper presents an attempt to decompose the very complex mobile health monitoring system whose layer in the system corresponds to decomposed subproblems, and interfaces between them are quantified as functions of the optimization variables in order to orchestrate the subproblems. We propose a distributed and energy-saving mobile health platform, called mHealthMon where mobile users publish/access sensor data via a cloud computing-based distributed P2P overlay network. The key objective is to satisfy the mobile health monitoring application's quality of service requirements by modeling each subsystem: mobile clients with medical sensors, wireless network medium, and distributed cloud services. By simulations based on experimental data, we present the proposed system can achieve up to 10.1 times more energy-efficient and 20.2 times faster compared to a standalone mobile health monitoring application, in various mobile health monitoring scenarios applying a realistic mobility model.