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being N the number of messages being forwarded, T the time required for transmitting the message, P the time needed for each node to process the message before being able to forward it again and finally H stands for the number of hops in or network. Putting it in terms of bacterial conjugation we have that N represents the plasmid size in kilobases, T the time required to move a single kilobase from a cell to another, P may represent the two sources of delay which are referred as recovery and maturation time for donors and recipient cells respectively. Finally H is the actual number of bacterial cells in the linear topology already mentioned.   The aggregated value referred globally as maturation time includes, amongst other factors, (a) the time required for adding the second strand to the plasmid inside the new formed transconjugant cells, (b) the time required to express all genes coding the proteins for the trans-envelope apparatus, and (c) possibly the effect of SOS response triggered by entrance of single stranded DNA into the transconjugant cell\cite{citeulike:8298094}. The Figure ~\ref{fig:interaction-graph} shows the temporal evolution of the linear graph which denotes the bacterial population being infected. In this graph every donor cell, depicted by $B^t_i$ only have a reachable neighbor which can be infected in a conjugative event. In other words the plasmid bearing cell $B^t_i$ can only interact and conjugate with the bacterial agent $B^r_{i+1}$. Thus, in the simplest case where the forwarding delay is fixed, the infection speed can be approximated by a straight line in a form of $y = \alpha + \beta x$ being $\alpha$ the intercept and $\beta$ the slope. The value of slope for the most general case is given by the expression shown in Equation ~\eqref{eq:slope}