each infected node infects each of its susceptible neighbors with probability $q,$ independent of other nodes, i.e., a susceptible node is infected with probability $1-(1-q)^{n}$ if it has $n$ infected neighbors. Each infected node recovers with probability $p$, i.e., its state changes from $I$ to $R$ with probability $p.$ In addition, we assume a recovered node cannot be infected again. Since whether a node gets infected only depends on the states of its neighbors and whether a node becomes a recovered node only depends on its own state in the previous time slot, the infection process can be modeled as a discrete time Markov chain ${\bf X}(t)$ where ${\bf X}(t)=\{X_v(t),v\in{\cal V}\}$ is the states of all the nodes at time slot $t.$ The initial state of this Markov chain is $X_v(0)=S$ for $v\neq v^*$ and $X_{v^*}(0)=I.$

Information Source Detection
----------------------------

We assume ${\bf X}(t)$ is not fully observable since we cannot distinguish susceptible nodes and recovered ones. So at time $t$, we observe ${\bf Y}=\{Y_v, v\in{\cal V}\}$ such that $$Y_v=\left\{
               \begin{array}{ll}
                 1, & \hbox{if $v$ is in state $I$;} \\
                 0, & \hbox{if $v$ is in state $S$ or $R$.}
               \end{array}
             \right.$$ The information source detection problem is to identify 