Schematic of sampling processes leading to different epidemic models described.

A) The classic SIR model arises from sampling 2 individuals from a population of susceptible (black), infectious (red), and recovered (blue) individuals. B) Sampling n individuals yields a generalization of the SIR model, the group-SIR. Infections occur independently between each S-I pair present in a congregation. C) Denoting individuals by the maximum congregation size they are willing to attending yields the risk-SIR model. Societies can be defined by a distribution of congregation sizes which determine the epidemiological dynamics (Boyer et al., 2022).

Generalized SIR dynamics.

A) Group-SIR dynamics, where transmission occurs within groups with sizes here denoted by the subscript. B) Risk-SIR dynamics, where transmission occurs within groups according to a distribution here set with sizes n=2,3, and 4 at equal frequency. Subpopulations are denoted by their risk level shown, which specifies the maximum gathering size they are willing to attend. C) The sequential peaks of infection cause the overall infection fatality ratio (IFR) to be dynamic when it varies between subpopulations. Here we compare IFR dynamics when the IFR is positively correlated with risk level (IFR high risk) and when the IFR is negatively correlated with risk level (IFR low risk). Note, we assume that mortality dynamics are the same as recovery dynamics to demonstrate this qualitative point.

Variant frequency dynamics depend on which risk subpopulation it emerges within.

A) Risk distribution of an epidemic (red) and a neutral variant (blue) that emerges within the highest risk subpopulation. B) The associated frequency dynamics of the emerging neutral variant. C) Frequency dynamics of a variant with 50% greater transmissibility relative to the background epidemic emerging in different risk subpopulations

Selection bias of fast growing clades.

a) An example of a fast growing clade that continues to grow beyond the point it was identified (blue vertical line) and its risk distribution among infectious individuals as compared to all others infectious at the moment of censusing (inset). b) Median difference between the median of the fastest growing risk distribution and the risk distribution of the rest of the epidemic for given censusing frequency within a 100% bandwidth for epidemics with subpopulations [5000, 0, 5000, 0, 5000] for risk numbers 2-6. c) Relative frequency dynamics of the fastest growing lineages following censusing across different censusing parameters for epidemics with subpopulations [5000, 0, 5000, 0, 5000] for risk numbers 2-6. Red lines denote median and interquartile ranges across 250 simulations shown in transparent black lines.

Homophily biases risk distributions.

a) Smoothed probability distributions of the risk distribution of epidemics initiated with 20 individuals at the respective equilibrium distribution after 500 population changes (total recovery or transmission events). Vertical dashed lines specify respective equilibrium risk distributions. B) Relative probability of a more social risk distribution than a less social risk distribution for epidemics initiated with 20 infectious individuals distributed according to the equilibrium risk distribution denoted as homophily. C) Relative probability of a more social risk distribution than a less social risk distribution for epidemics initiated with 1 infectious individuals either in the more social subpopulation (dashed lines) or the less social subpopulation (solid lines).

Dynamics of a variant with increased transmissibility relative to wildtype emerging in different risk subpopulations.

Equilibrium risk distribution for exponentially growing epidemics in societies with transmission heterogeneity as the amount of cross transmission between two subpopulation varies.

Dynamics of the variance of the probability density function over risk distributions for a growing epidemic with two subpopulations.

It initially increases because we initialize the population at a specific risk distribution (delta distribution) and it eventually decreases as the risk distribution drifts less for larger populations.

Growth rate bias, ρ, for epidemics initialized with different population sizes, N0, of infected distributed by the equilibrium risk distribution (here fH = .6.

Epidemics were run for 75 populations changes and the vertical line delineates epidemics that stochastic extinction can affect (smaller initial populations). (inset) Focusing on epidemics where not enough population changes have occurred for stochastic extinction to occur.