On the early epidemic dynamics for pairwise models

The relationship between the basic reproduction number R0 and the exponential growth rate, specific to pair approximation models, is derived for the SIS, SIR and SEIR deterministic models without demography. These models are extended by including a random rewiring of susceptible individuals from infectious (and exposed) neighbours. The derived relationship between the exponential growth rate and R0 appears as formally consistent with those derived from homogeneous mixing models, enabling us to measure the transmission potential using the early growth rate of cases. On the other hand, the algebraic expression of R0 for the SEIR pairwise model shows that its value is affected by the average duration of the latent period, in contrast to what happens for the homogeneous mixing SEIR model. Numerical simulations on complex contact networks are performed to check the analytical assumptions and predictions.