On the early epidemic dynamics for pairwise models

Abstract

The relationship between the basic reproduction number R 0 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 intrinsic growth rate and R 0 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 R 0 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.

A Network Epidemic Model with Preventive Rewiring: Comparative Analysis of the Initial Phase

“…This extended model will allow for a better understanding of the impact of rewiring on R 0 derived under this approach, here denoted by R P A 0 . ) with µ = 2L/N being the average degree (see [21] for details). Note that, since we focus our analysis on the early epidemic stage with a very small number of initially infectious nodes, we approximate the expected degree of the susceptible central node of a triple by E(D), the mean degree of a node reached by following a randomly chosen link in a wholly susceptible population at t = 0, i.e., when the degree distribution is the initial one.…”

“…Note that, when there is no rewiring (ω SI = ω SE = ω EI = 0), it follows that E(D P A I ) = E(D), as expected. Moreover, when ω EI = 0, ξ * is given by (21) and E(D P A I ) can be explicitly expressed in terms of the model parameters.…”

Oscillations in epidemic models with spread of awareness

“…For the proof of (a3), consider again the function f (i) defined in (24) and rearrange its terms in the following way: Note that under the assumptions of (a3), the sum of the terms that enter this expression with a positive sign is strictly increasing in i, and the sum of the terms −β a i − δ a (i) is nondecreasing. Thus, f (i) is strictly increasing in i and we can rule out the existence of two interior equilibria.…”

“…Responses arising from risk perception of the disease are, for instance, avoidance behavior implying breaking off connections with infectious acquaintances (social distancing), and preventive behaviors, like handwashing or wearing face masks [22,23]. In epidemic network models, which take into account the contact network in a population, social avoidance has been modeled by means of several mechanisms of dynamic rewiring [16,20,24,30,34]. Other approaches cast preventive actions into classic epidemic models by dividing each of the susceptible/infectious/removed classes between responsive and non-responsive individuals [13,21], or by explicitly considering a new class of individuals who are both susceptible and aware, with a lowered susceptibility to infection relative to unaware hosts.…”

The 2017 plague outbreak in Madagascar: data descriptions and epidemic modelling

“…Implementations and calculations using current methods raised also an issue that has been discussed elsewhere [31], that is estimating the reproduction number using serial interval could yield very high value during the first days of the epidemic growing phase as the denominator of the estimator is 180 extremely small during this period. Overestimate of R0 has also been observed in populations with heterogeneous contact pattern population [42].…”