A minimal model for household effects in epidemics

Abstract

Shelter-in-place and other confinement strategies implemented in the current COVID-19 pandemic have created stratified patterns of contacts between people: close contacts within households and more distant contacts between the households. The epidemic transmission dynamics is significantly modified as a consequence. We introduce a minimal model that incorporates these household effects in the framework of mean-field theory and numerical simulations. We show that the reproduction number R 0 depends on the household size in a surprising way: linearly for relatively small households, and as a square root of size for larger households. We discuss the implications of the findings for the lockdown, test, tracing, and isolation policies.

Epidemic dynamics in inhomogeneous populations and the role of superspreaders

“…We choose this factor to ensure that E[σ] = E[s]. In the numerical calculations in this section we used the following parameters roughly following [30][31][32]…”

“…An interesting feature is that a wide correlated distribution of s and σ leads to an earlier start of the epidemics instead of the S-like curve of the standard SIR model. Figure 1 with parameters in equation (31). A classical SIR solution for the same susceptibility and infectivity is also shown.…”

“…For another comparison we take the empirical number of contacts between the individuals (Appendix G) as a proxy for both s and σ. We renormalize the number of contacts to obtain the average infectivity E[s] in equation (31). This leads to variance ζ 2 = 17.27 day −1 (ζ = 4.16 day −1/2 ).…”

A minimal model for household-based testing and tracing in epidemics

“…A household state can therefore be described by a four-dimensional vector of integers, ( s, i, q, r ). We make the same assumption as in [1]: the intra-household rate of infection is fast. Then the simplified state diagram for a household is shown in Figure 2.…”

“… Abstract In a previous work [1], we discussed virus transmission dynamics modified by a uniform clustering of contacts in the population: close contacts within households and more distant contacts between households. In this paper, we discuss testing and tracing in such a stratified population.…”