Accurately predicting the lifespan of a network is crucial for effectively managing network resources and ensuring efficient and reliable network operation. This is particularly important in application-specific wireless sensor networks (WSNs) such as environmental monitoring, industrial automation, and smart cities. In this paper, we present an analytical model that aims to estimate the network lifetime of WSNs utilizing multipath routing protocols. Our proposed model takes into account various routing parameters, including the deployment area, remaining node energy, link quality, and location of the sensor nodes, which all play significant roles in determining network lifetime. Through simulation outcomes and mathematical analysis, we demonstrate the validity and effectiveness of our proposed analytical model.