The interplay of network structure and correlated infectious traits in epidemic models
Abhay Gupta, Nicholas W. Landry
TLDR
This paper models epidemics by considering how network structure and correlated individual disease traits affect spread, deriving R0 and informing interventions.
Key contributions
- Introduces a new mathematical framework for epidemic modeling with correlated susceptibility and transmissibility.
- Applies framework to SIR model, incorporating population subgroups and joint trait distributions.
- Derives analytical expressions for the basic reproduction number (R0) considering network structure.
- Validates findings with simulations and explores implications for effective social interventions.
Why it matters
This paper addresses a critical gap in epidemic modeling by integrating the often-overlooked covariance between individual susceptibility and transmissibility with network structure. Its novel framework and analytical R0 derivations offer a more realistic understanding of disease spread. This work is crucial for designing more effective and targeted public health interventions.
Original Abstract
Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and infection rates is well-understood, less studied is the impact of population-level covariance between susceptibility and transmissibility, despite empirical evidence showing that both susceptibility and transmission vary across individuals. We introduce a mathematical modeling framework incorporating population subgroups, each with its own joint distribution of susceptibility and transmissibility. We apply this framework to the susceptible-infected-recovered (SIR) model to examine the effect of community structure and degree heterogeneity. We derive analytical expressions for the basic reproduction number, which, when reduced, corroborates prior results and validate these results with numerical simulations. We pair these estimates with simulations exploring first, the temporal dynamics of this model with the homogeneous SIR model, and second, implications for effective social intervention. This analysis provides a foundation for future studies exploring the interplay between structural and dynamical heterogeneity in infectious disease transmission.
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