Determining the network topology is typically a challenging problem due to the number of nodes and connection between them. Complexity is added whenever this identification problem relies solely on a subset of the outputs of some dynamical system or distributed algorithm running on those nodes. In this paper, we focus on both the source identification and network topology discovery problems in the context of infection networks where a subset of the nodes are elected as observers. The solution consists in writing the binary constraints associated with the problem. Convex relaxations are also proposed and investigated through simulations where a pattern emerges that placing observers in high-degree nodes increases the accuracy of the method.