The fog and edge computing paradigm provide a distributed architecture of nodes with processing capability for smart healthcare systems driven by Internet of Thing (IoT) applications. It also provides a method to reduce big data transmissions that cause latency and enhance the system's efficiency. Resource provisioning and scheduling in edge and fog systems is a significant problem due to heterogeneity and dispersion of edge/fog/cloud resources. The goal of scheduling is to map tasks to appropriate resources, which belong to NP-hard problems, and it takes much time to find an optimal solution. Meta-heuristic methods achieve near-optimal solutions within a reasonable time. Current edge/fog resource allocation research does not sufficiently address resource allocation problems in mobility-aware microservice-based IoT applications. This paper proposes a meta-heuristic-based micro-service resource provisioning model with mobility management for smart healthcare systems. The proposed approach has been tested on an experimental set-up with a simulation of a critical real-time smart healthcare application with and without considering the mobility of the devices. It applies meta-heuristic methods such as modified genetic and flower pollination algorithms for resource management. The proposed method outperforms the existing solutions in energy consumption, network usage, cost, execution time, and latency by 17%, 20%, 22%, 17%, and 63%, respectively.INDEX TERMS Edge computing, fog computing, Internet of Things, meta-heuristic, microservices, mobility, smart healthcare, time critical applications.