Diffusive phenomena are ubiquitous in nature and society, and have been extensively studied in various fields, such as natural sciences and engineering. Recently, however, the more challenging inverse problem of diffusion source detection in a network has started to receive a significant amount of attention. A lot of research has concentrated on finding origins in tree-like networks, however these approaches cannot be easily extended to generic networks. Furthermore, only some methods consider realistic temporal diffusion dynamics. We introduce a novel method to localise the source of multiple rumours in an arbitrary network of known topology, using partial observations of the network nodes. We first present two mathematical models of the discrete-time, susceptible infected propagation dynamics, which accurately capture the diffusion process and have low computational complexity. The first one is a simplified likelihood of infection at a node, at a certain time after the rumour is initiated. The second is a formulation of the infection likelihood of a node, as a function of its shortest distance to the source. We then design an efficient single source detection algorithm, which leverages these mathematical models of diffusion, and the assumption that the start time of the propagation is known. Finally, we show how these methods can be extended to the case when the start time of the rumour is unknown, by taking advantage of the dissimilarity in dynamics of infection, of different nodes in the network. Simulation results show that a high source estimation probability is achieved using a small number of observations.