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Equivalence of the Erlang-distributed SEIR epidemic model and the renewal equation. (English) Zbl 1404.92173

Summary: Most compartmental epidemic models can be represented using the renewal equation. The value of the renewal equation is not widely appreciated in the epidemiological modelling community, perhaps because its equivalence to standard models has not been presented rigorously in nontrivial cases. Here, we provide analytical expressions for the intrinsic generation-interval distribution that must be used in the renewal equation 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.

MSC:

92D30 Epidemiology
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62P10 Applications of statistics to biology and medical sciences; meta analysis
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