Estimating transmission parameters and the reproduction number: COVID-19 in Sri Lanka as a case study

The study of the dynamics of an infectious disease is fundamental to understanding its community spread. These include obtaining estimates for transmission rates, recovery rates and the average number of secondary cases per infectious case (reproduction number). Social behaviors, control measures, environmental conditions and long recovery times result in time varying parameters. Further, imperfect data and many uncertainties lead to inaccurate estimations. This is particularly true in third-world countries, where a greater proportion of people with mild infections may not seek medical treatment. Data on the prevalence of COVID-19 provides an excellent source for case studies to analyse time-dependent parameters. Using Sri Lankan COVID-19 data, we demonstrate how one could utilize Itô stochastic differential equations with a gamma distribution correction to estimate disease transmission parameters as a function of time. As we illustrated here, the model is well-suited for forecasting the dates of peak prevalence and the number of new cases using the estimated parameters.