Champredon, D. | Search bioRxiv

bioRxiv2018

Equivalence of the Erlang SEIR epidemic model and the renewal equation

Most compartmental epidemic models can be represented using the Euler-Lotka renewal equation (RE). The value of the RE is not widely appreciated in the epidemiological modelling community, perhaps because its equivalence to standard models has not been presented rigorously in non-trivial cases. Here, we provide analytical expressions for the intrinsic generation interval distribution that must be used in the RE in order to yield epidemic dynamics that are identical to those of the susceptible-exposed-infectious-recovered (SEIR) compartmental model with Erlang-distributed latent and infectious periods. This class of models includes the standard (exponentially-distributed) SIR and SEIR models as special cases.

epidemiology↗

bioRxiv2018

Exploring how generation intervals link strength and speed of epidemics

Infectious-disease outbreaks are often characterized by the reproductive number and exponential rate of growth r. provides information about out-break control and predicted final size. Directly estimating is difficult, while r can often be estimated from incidence data. These quantities are linked by the generation interval - the time between when an individual is infected by an infector, and when that infector was infected. It is often infeasible to ob-tain the exact shape of a generation-interval distribution, and to understand how this shape affects estimates of . We show that estimating generation interval mean and variance provides insight into the relationship between and r. We use examples based on Ebola, rabies and measles to explore approximations based on gamma-distributed generation intervals, and find that use of these simple approximations are often sufficient to capture the r- relationship and provide robust estimates of .

epidemiology↗