a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler. Of course we always have conservation of individuals: The change in each class in a small time interval is: Since we know , and sum up to , we can reduce one equation from the above, which leads to a set of differential equations using relative variable and as follows which we can write Compared with the ordinary SIR model, we see that the only difference to the ordinary SIR model is that we have a factor in the first equation instead of just . We immediately see that the ignorants can only decrease since and . Also, if which means the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters. Epidemic models in social network We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define to be the state of node i at time t. Then is a stochastic process on . At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function so that for in , is when the state of network is , node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any , we try to find . If node i is in state I and node j is in state S, then ; if node i is in state I and node j is in state I, then ; if node i is in state I and node j is in state R, then . For all other , . The procedure on a network is as follows: We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong local clustering around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the