Estimating Time-Dependent Transmission Rates of Sars-Cov-2 in a Stratified Population: A Systematic Comparison of Three Methods

Abstract

Background & aims of study: Retrospectively estimating time-dependent transmission rates from SIR-type models that describe transmission events and the development of immunity across subpopulations is central for assessing the impact of non-pharmaceutical interventions, behavioral changes, and seasonal effects on the spread of SARS-CoV-2. In this study, we compared and validated different methods for estimating time-dependent transmission rates within a Bayesian inference framework.

Method & results: We implemented three methods (Brownian motion, b-splines, and Gaussian processes) to model time-dependent transmission rates for SARS-CoV-2 in a Bayesian SIR-type model implemented in Stan. First, we compared their performance on a set of unstratified simulated data. We showed that all methods can accurately recover time-dependent transmission rates, but that the spline-based method performs best in terms of time per effective sample size. Second, we applied the spline-based method to age-stratified simulated data to confirm its functionality. Lastly, we applied this method to 2020 laboratory-confirmed SARS-CoV-2 cases and three rounds of seroprevalence surveys from Geneva, Switzerland, which allowed us to obtain detailed estimates of the effective reproduction number Re. Additionally, we estimated that the ascertainment of 0-19 year olds (38.8%, 90% credibility interval, CrI: 21.5-56.0%) was almost half the ascertainment compared to adults that were 60 years and older (74.7%, 90% CrI: 64.5-86.1%), at the end of 2020. 

Implications: Our study illustrates the potential of combining Bayesian inference with stratified, time-dependent SIR-type models. We propose an efficient and validated implementation of this framework, available in the R package HETTMO. We show that the multilevel structure allows the estimation of parameters for which we did not directly observe data (such as the youngest age group). Our methods can be easily adapted and applied to other stratified SIR-type models with time-dependent transmission rates. Such models will advance our understanding of respiratory virus transmission across different sub-populations.

Note: This conference abstract was presented at the 9th International Conference on Infectious Disease Dynamics organized by the journal Epidemics. This abstract has not been screened by SSRN for potential for public harm and should not be used to inform any clinical decision making. No competing interests or funding statements have been declared.