Title: SEIR models with heterogeneities in hosts' susceptibility and infectiousness 

Abstract: Population heterogeneity is a key factor in epidemic dynamics, influencing both transmission and final epidemic size. While heterogeneity is often modelled through age structure, spatial location, or contact patterns, differences in host susceptibility have recently gained attention, particularly during the COVID-19 pandemic. 

In this talk, building on the framework proposed by Diekmann and Inaba (2023), I will show how heterogeneities in susceptibility and infectiousness can be integrated into a classical SEIR model, yielding a three-dimensional system of ODEs describing a single epidemic outbreak. The effect of heterogeneity on the attack ratio of an epidemic has been studied by several authors, including Katriel (2012) who proved that, when there is heterogeneity in susceptibility and infectiousness is independent of susceptibility, the attack ratio is always lower than in a homogeneous model with the same value of the basic reproduction number, R0.

The epidemic attack ratio depends on the distribution of susceptibility, and on the function g(x), the mean infectiousness of individuals with relative susceptibility x. When g(x) is a non-decreasing function,  the attack ratio is always lower than in a homogeneous model with the same value of R0; if g(x) is decreasing,  the attack ratio may be greater than in a homogeneous model with the same value of R0.

Assuming a specific family (for instance, the gamma) of distributions for the susceptibility, models with heterogeneity can be easily fit to data..Heterogeneity can help explain the apparent failure of classic SEIR model in fitting the 1978 English boarding school influenza outbreak (Avilov et al, 2024).

In the end, I discuss if and how these methods could be extended to recurrent epidemics.

This is a joint work with Tamas Tekeli and Cinzia Soresina.

References

Avilov, K. K., Li, Q., Lin, L., Demirhan, H., Stone, L., & He, D. (2024). The 1978 English boarding school influenza outbreak: where the classic SEIR model fails. J. Royal Society Interface, 21(220). https://doi.org/10.1098/rsif.2024.0394

Diekmann, O., & Inaba, H. (2023). A systematic procedure for incorporating separable static heterogeneity into compartmental epidemic models. J. Math. Biology, 86, 1–19. https://doi.org/10.1007/s00285-023-01865-0

Katriel, G. (2012). The size of epidemics in populations with heterogeneous susceptibility. J. Math. Biology, 65, 237–262. https://doi.org/10.1007/s00285-011-0460-2

About the speaker: https://andrea-pugliese.maths.unitn.it