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

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.

Spatially resolved simulations of the spread of COVID-19 in European countries (preprint)

We explore the spatial and temporal spread of the novel SARS-CoV-2 virus under containment measures in three European countries based on fits to data of the early outbreak. Using data from Spain and Italy, we estimate an age dependent infection fatality ratio for SARS-CoV-2, as well as risks of hospitalization and intensive care admission. We use them in a model that simulates the dynamics of the virus using an age structured, spatially detailed agent based approach, that explicitly incorporates governamental interventions, changes in mobility and contact patterns occurred during the COVID-19 outbreak in each country.Our simulations reproduce several of the features of its spatio-temporal spread in the three countries studied. They show that containment measures combined with high density are responsible for the containment of cases within densely populated areas, and that spread to less densely populated areas occurred during the late stages of the first wave. The capability to reproduce observed features of the spatio-temporal dynamics of SARS-CoV-2 makes this model a potential candidate for forecasting the dynamics of SARS-CoV-2 in other settings, and we recommend its application in low and lower-middle countries which remain understudied.

The effectiveness of social bubbles as part of a Covid-19 lockdown exit strategy, a modelling study (preprint)

BackgroundDuring the Covid-19 lockdown, contact clustering in social bubbles may allow extending contacts beyond the household at minimal additional risk and hence has been considered as part of modified lockdown policy or a gradual lockdown exit strategy. We estimated the impact of such strategies on epidemic and mortality risk using the UK as a case study. MethodsWe used an individual based model for a synthetic population similar to the UK, that is stratified into transmission risks from the community, within the household and from other households in the same social bubble. The base case considers a situation where non-essential shops and schools are closed, the secondary household attack rate is 20% and the initial reproduction number is 0.8. We simulate a number of strategies including variations of social bubbles, i.e. the forming of exclusive pairs of households, for particular subsets of households (households including children and single occupancy households), as well as for all households. We test the sensitivity of the results to a range of alternative model assumptions and parameters. ResultsClustering contacts outside the household into exclusive social bubbles is an effective strategy of increasing contacts while limiting some of the associated increase in epidemic risk. In the base case scenario social bubbles reduced cases and fatalities by 17% compared to an unclustered increase of contacts. We find that if all households were to form social bubbles the reproduction number would likely increase to 1.1 and therefore beyond the epidemic threshold of one. However, strategies that allow households with young children or single occupancy households to form social bubbles only increased the reproduction number by less than 10%. The corresponding increase in morbidity and mortality is proportional to the increase in the epidemic risk but is largely focussed in older adults independently of whether these are included in the social bubbles. ConclusionsSocial bubbles can be an effective way of extending contacts beyond the household limiting the increase in epidemic risk, if managed appropriately.

Forecasting the scale of the COVID-19 epidemic in Kenya (preprint)

Background The first COVID-19 case in Kenya was confirmed on March 13th, 2020. Here, we provide forecasts for the potential incidence rate, and magnitude, of a COVID-19 epidemic in Kenya based on the observed growth rate and age distribution of confirmed COVID-19 cases observed in China, whilst accounting for the demographic and geographic dissimilarities between China and Kenya. Methods We developed a modelling framework to simulate SARS-CoV-2 transmission in Kenya, KenyaCoV. KenyaCoV was used to simulate SARS-CoV-2 transmission both within, and between, different Kenyan regions and age groups. KenyaCoV was parameterized using a combination of human mobility data between the defined regions, the recent 2019 Kenyan census, and estimates of age group social interaction rates specific to Kenya. Key epidemiological characteristics such as the basic reproductive number and the age-specific rate of developing COVID-19 symptoms after infection with SARS-CoV-2, were adapted for the Kenyan setting from a combination of published estimates and analysis of the age distribution of cases observed in the Chinese outbreak. Results We find that if person-to-person transmission becomes established within Kenya, identifying the role of subclinical, and therefore largely undetected, infected individuals is critical to predicting and containing a very significant epidemic. Depending on the transmission scenario our reproductive number estimates for Kenya range from 1.78 (95% CI 1.44 - 2.14) to 3.46 (95% CI 2.81-4.17). In scenarios where asymptomatic infected individuals are transmitting significantly, we expect a rapidly growing epidemic which cannot be contained only by case isolation. In these scenarios, there is potential for a very high percentage of the population becoming infected (median estimates: >80% over six months), and a significant epidemic of symptomatic COVID-19 cases. Exceptional social distancing measures can slow transmission, flattening the epidemic curve, but the risk of epidemic rebound after lifting restrictions is predicted to be high.

Estimation of country-level basic reproductive ratios for novel Coronavirus (COVID-19) using synthetic contact matrices (preprint)

The outbreak of novel coronavirus (COVID-19) has the potential for global spread, infecting large numbers in all countries. In this case, estimating the country-specific basic reproductive ratio is a vital first step in public-health planning. The basic reproductive ratio (R0) is determined by both the nature of pathogen and the network of contacts through which the disease can spread - with this network determined by socio-demographics including age-structure and household composition. Here we focus on the age-structured transmission within the population, using data from China to inform age-dependent susceptibility and synthetic age-mixing matrices to inform the contact network. This allows us to determine the country-specific basic reproductive ratio as a multiplicative scaling of the value from China. We predict that R0 will be highest across Eastern Europe and Japan, and lowest across Africa, Central America and South-Western Asia. This pattern is largely driven by the ratio of children to older adults in each country and the observed propensity of clinical cases in the elderly.