Dynamics of Transmission and Control of COVID-19: A Real-time Estimation Using the Kalman Filter

Abstract

We develop a new method for estimating the effective reproduction number of an infectious disease (R) and apply it to track the dynamics of COVID-19. The method is based on the fact that in the SIR model, R is linearly related to the growth rate of the number of infected individuals. This time-varying growth rate is estimated using the Kalman filter from data on new cases. The method is very easy to apply in practice, and it performs well even when the number of infected individuals is imperfectly measured, or the infection does not follow the SIR model.Our estimates of R for COVID-19 for 124 countries across the world are provided in an interactive online dashboard, and they are used to assess the effectiveness of non-pharmaceutical interventions in a sample of 14 European countries.

Mediation by human mobility of the association between temperature and COVID-19 transmission rate

“…It measures the average number of people infected by a single infected person during the period of infection. We collected the data for the estimates of R from February 22, 2020 to June 22, 2020 (time span varies by country and the starting point is the date when the number of confirmed cases in a country reaches 100) from a previous work by Arroyo-Marioli et al (2020) . To construct this proxy, they used data on new cases, recoveries, and deaths and estimated the growth rate by Kalman-filtering techniques.…”

“…To construct this proxy, they used data on new cases, recoveries, and deaths and estimated the growth rate by Kalman-filtering techniques. Arroyo-Marioli et al (2020) believed that “the method is robust in the sense that the estimates of R remain fairly accurate even when new cases are imperfectly measured, or the true dynamics of the disease do not follow the SIR model”. Readers are referred to Arroyo-Marioli et al (2020) for the details of estimating the reproductive number.…”

A Convex Optimization Solution for the Effective Reproduction NumberRt

“…Using these predictions, they estimate R t , based on a SIR model. Arroyo-Marioli et al 16 introduce a method to estimate R t employing the growth rate of the number of infected individuals derived from the SIR model. However, the model seems to work well with the SEIR (SIR extended with a compartment for exposed) model.…”

Monitoring and Tracking the Evolution of a Viral Epidemic Through Nonlinear Kalman Filtering: Application to the Covid-19 Case

“…This filter, which constitutes a generalization of the technique known as "recursive least squares", estimates the maximum likelihood evolution (that is, the most statistically probable, according to the assumed uncertainties and the observed samples) of the state of a dynamic system, and can be generalized to the non-linear case, including situations where the model parameters are also to be estimated. References [8] and [9] are among the very few applications of KF in epidemiology, dealing respectively with the estimation of the Covid-19 reproductive number, and the evolution of AIDS.…”

“…For instance, it is stated in [12] that "using : as a threshold parameter for a population-level model could produce misleading estimates of the infectiousness of the pathogen, the severity of an outbreak, and the strength of the medical and/or behavioral interventions necessary for control". Moreover, if : is estimated from time series of reported data, as in [8], then there is no way, at least for a new virus such as Covid-19, to subsequently check or contrast the accuracy of the estimates. This probably explains the wide confidence intervals so far reported for : values [13].…”