Forecasting Covid-19 in the United Kingdom: A dynamic SIRD model

Making use of a state space framework, we present a stochastic generalization of the SIRD model, where the mortality, infection, and underreporting rates change over time. A new format to the errors in the Susceptible-Infected-Recovered-Dead compartments is also presented, that permits reinfection. The estimated trajectories and (out-of-sample) forecasts of all these variables are presented with their confidence intervals. The model only uses as inputs the number of reported cases and deaths, and was applied for the UK from April, 2020 to Sep, 2021 (daily data). The estimated infection rate has shown a trajectory in waves very compatible with the emergence of new variants and adopted social measures. The estimated mortality rate has shown a significant descendant behaviour in 2021, which we attribute to the vaccination program, and the estimated underreporting rate has been considerably volatile, with a downward tendency, implying that, on average, more people are testing than in the beginning of the pandemic. The evolution of the proportions of the population divided into susceptible, infected, recovered and dead groups are also shown with their confidence intervals and forecast, along with an estimation of the amount of reinfection that, according to our model, has become quite significant in 2021. Finally, the estimated trajectory of the effective reproduction rate has proven to be very compatible with the real number of cases and deaths. Its forecasts with confident intervals are also presented.

Automated summary

In this study, a stochastic generalization of the SIRD model is presented using a state space framework, where the mortality, infection, and underreporting rates are allowed to vary over time. The model is applied to the UK COVID-19 data from April 2020 to September 2021, and the estimated trajectories and forecasts of various variables are provided. The estimated infection rate shows a trajectory in waves that aligns with the emergence of new variants and the implementation of social measures. The mortality rate exhibits a significant decrease in 2021, which is attributed to the vaccination program. The estimated underreporting rate is volatile but generally decreasing, suggesting increased testing compared to the early stages of the pandemic. The proportions of the population in susceptible, infected, recovered, and dead groups, as well as the estimated amount of reinfection, are also presented. The estimated trajectory of the effective reproduction rate closely matches the real number of cases and deaths.