The use of Internet connectivity for remote patient monitoring is often unsuitable for rural communities where Internet infrastructure is lacking, and power outages are frequent. This paper explores the rural connectivity problem in the context of remote patient monitoring and analyzes the feasibility of utilizing a delay tolerant network (DTN) architecture that leverages the social behaviors of rural community members to enable out-of-range monitoring of patients in rural communities without local transportation systems. The feasibility is characterized using delivery latency and delivery rate with the number of participants and the number of sources as variables. The architecture is evaluated for Owingsville, KY using U.S. Census Bureau, the National Cancer Institute's, and IPUMS ATUS sample data. The findings show that within a 24 hour window, there is an exponential relationship between the number of participants in the network and the delivery rate with a minimal delivery of 38.7%, a maximal delivery rate of a 100% and an overall average delivery rate of 89.8%.