Wireless Sensor Networks has been widely used for monitoring and control applications in our daily life due to its appealing characteristic like low cost, power efficient, easy to implement in many areas such as war zone, medical monitoring optimization and so on. However, Wireless Sensor Networks (WSN) requires a new routing algorithm for health monitoring. In this paper, an efficient routing model called Local Search and Enhanced Betweenness Routing (LS-EBR) in WSN to improve routing efficiency by increasing sensor nodes coverage and minimizing the time for routing is presented. The LS-EBR model in WSN for health monitoring uses enhanced betweenness routing that measures energy consumption of the neighboring nodes in a local search manner. First, a novel Local Search model that does not require global information about the entire network and in turn divert routing from sensor nodes that are more frequently used is used. The aim is to reduce the time for routing. Second, an Enhanced Betweenness Routing model that not only considers routing overhead but also considers the remaining energy of sensor node into account to ensure higher number of sensor nodes to be monitored, thus achieving much higher coverage is designed. Finally, working together with the above Local Search and Enhanced Betweenness Routing by applying Enhanced Betweenness Routing algorithm, reduces the average energy consumed. Simulation results showed that the proposed routing model has advantages over opportunistic routing with respect to coverage and improving routing efficiency by reducing time for routing in wireless sensor networks.