A computational framework for modelling infectious disease policy based on age and household structure with applications to the COVID-19 pandemic

Abstract

The widespread, and in many countries unprecedented, use of non-pharmaceutical interventions (NPIs) during the COVID-19 pandemic has highlighted the need for mathematical models which can estimate the impact of these measures while accounting for the highly heterogeneous risk profile of COVID-19. Models accounting either for age structure or the household structure necessary to explicitly model many NPIs are commonly used in infectious disease modelling, but models incorporating both levels of structure present substantial computational and mathematical challenges due to their high dimensionality. Here we present a modelling framework for the spread of an epidemic that includes explicit representation of age structure and household structure. Our model is formulated in terms of tractable systems of ordinary differential equations for which we provide an open-source Python implementation. Such tractability leads to significant benefits for model calibration, exhaustive evaluation of possible parameter values, and interpretability of results. We demonstrate the flexibility of our model through four policy case studies, where we quantify the likely benefits of the following measures which were either considered or implemented in the UK during the current COVID-19 pandemic: control of within- and between-household mixing through NPIs; formation of support bubbles during lockdown periods; out-of-household isolation (OOHI); and temporary relaxation of NPIs during holiday periods. Our ordinary differential equation formulation and associated analysis demonstrate that multiple dimensions of risk stratification and social structure can be incorporated into infectious disease models without sacrificing mathematical tractability. This model and its software implementation expand the range of tools available to infectious disease policy analysts.

Modelling the epidemiological implications for SARS-CoV-2 of Christmas household bubbles in England

“…Our findings have since been corroborated by subsequent additions to the literature on the topic of quantifying the effect of household bubbles on the transmission of SARS-CoV-2, with a variety of modelling approaches represented [28, 29]. In detail, Danon et al .…”

“…They found that whilst the creation of support bubbles between a single-person household and another household of any size had a small impact on transmission, scenarios where all households form a bubble would be highly likely to cause extensive transmission. Later work from Hilton et al [29] provided an infectious disease modelling framework formulated in terms of tractable systems of ordinary differential equations that includes explicit representation of age/risk structure and household structure. Our results are in agreement with their findings on the usage of short-term social bubbles, which suggested that shortterm relaxation in mixing restrictions would have a small but non-negligible impact on the epidemic dynamics, with larger temporary bubbles and longer mixing periods associated with higher prevalence.…”

“…The model framework described here is reasonably parsimonious compared to fine-detailed household models [29][30][31][32]. With regards to informing policy in response to a global public health emergency such as a pandemic, parsimonious models that can be promptly set up and that are able to generate results in extremely short time-scales can be helpful tools for providing high-level insights, on the basis that a reasonable but imperfect answer is better than none [33].…”

Generating synthetic population for simulating the spatiotemporal dynamics of epidemics

“…Several studies have revealed that the household structure has a profound impact on the transmission of infectious diseases [12][13][14]. Although previous research has attempted to associate both household-and individual-level attributes in a unified manner, they most simply fit the marginal distribution of household-level attributes (e.g., household size), and thus fail to capture and reproduce the interdependencies among agents within the same household [15].…”

Estimation of introduction and transmission rates of SARS-CoV-2 in a prospective household study

“…Household studies are considered the gold standard for the study of infectious disease transmission, as they provide a setting in which transmission events can be pinned down to one or a small number of potential infectors [7][8][9][10][11][12][13][14][15][16][17][18]. Classical analyses of household data use statistical regression techniques to estimate the fraction of persons that are infected over the course of a household outbreak (the secondary attack rate or SAR), stratified by person-type and household characteristics [19].…”