Stochastic epidemic models featuring contact tracing with delays

TL;DR

This paper develops a stochastic SEIR epidemic model incorporating contact tracing delays, analyzing its behavior through a birth-death process and deriving key reproduction numbers and extinction probabilities.

Contribution

It introduces a novel stochastic model with contact tracing delays and provides explicit analytical results, including the reproduction number and extinction probability.

Findings

Contact rate influences the reproduction number and epidemic potential.

Distribution of delays affects epidemic spread but delay correlation has minimal impact.

Explicit formulas for extinction probability under certain assumptions.

Abstract

This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious contacts, who are then removed if they have not been already after some tracing delay. The epidemic is analysed via an approximating, modified birth-death process, for which a type-reproduction number is derived in terms of unnamed individuals, that is shown to be infinite when the contact rate is sufficiently large. We obtain explicit results under the assumption of either constant or exponentially distributed infectious periods, including the epidemic extinction probability in the former case. Numerical illustrations show that, while the distributions of latent periods and delays have an effect on the spread of the epidemic, the assumption of whether the delays experienced by individuals infected by the same individual are of the same or independent length makes little difference.