A spatial model of COVID-19 transmission in England and Wales: early spread, peak timing and the impact of seasonality

Abstract

An outbreak of a novel coronavirus was first reported in China on 31 December 2019. As of 9 February 2020, cases have been reported in 25 countries, including probable human-to-human transmission in England. We adapted an existing national-scale metapopulation model to capture the spread of COVID-19 in England and Wales. We used 2011 census data to inform population sizes and movements, together with parameter estimates from the outbreak in China. We predict that the epidemic will peak 126 to 147 days (approx. 4 months) after the start of person-to-person transmission in the absence of controls. Assuming biological parameters remain unchanged and transmission persists from February, we expect the peak to occur in June. Starting location and model stochasticity have a minimal impact on peak timing. However, realistic parameter uncertainty leads to peak time estimates ranging from 78 to 241 days following sustained transmission. Seasonal changes in transmission rate can substantially impact the timing and size of the epidemic. We provide initial estimates of the epidemic potential of COVID-19. These results can be refined with more precise parameters. Seasonal changes in transmission could shift the timing of the peak into winter, with important implications for healthcare capacity planning. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK.

Keywords: human movement; modelling; seasonality; spatial.

Figure 1.

Model structure within each ward, together with associated parameters estimated from the literature. (Online version in colour.)

Figure 2.

The number of cases of COVID-19 in England and Wales in the absence of any control measures, 100 realizations of the spatial model, seeded in Brighton, using best-guess parameters from Li et al. [2] (a) Daily infection dynamics. (b) The distribution of predicted time to peak incidence. (c) The distribution of predicted attack rate. (Online version in colour.)

Figure 3.

The variability in predicted epidemic curves for a COVID-19 outbreak in England and Wales, seeded in Brighton, in the absence of any control measures. Unlike in figure 2, here we incorporate measured parameter uncertainty. (a) Daily infection dynamics. (b) The distribution of predicted time to peak incidence. (c) The distribution of predicted attack rate.

Figure 4.

Predicted epidemic curves for a COVID-19 outbreak broken down by region for England and Wales. (Online version in colour.)

Figure 5.

(a) Peak time in major cities from various starting locations. Each panel is a starting location and the box plots show the distribution in peak times in each destination city from 10 runs. (b) Average peak time in each city shown as a matrix from the start location. (Online version in colour.)

Figure 6.

Peak timing in major cities for a generalized epidemic with multiple initial seed locations. Box plots represent the variability between 10 parameter sets with the same R₀ (1.95, 2.4) and mean doubling time (6.6, 4.7 days).

Figure 7.

Effect of seasonal changes in transmission rate, assuming a reduction in transmission over the summer. (Main panel) Incidence over time, for different values of seasonal scaling. (Inset) Variation of scaling term for the course of one year, with transmission being at its lowest in July. A strong suppression in the initial growth phase may generate a perverse outcome of a second peak in the winter. (Online version in colour.)