Investigating the Estimation of the infection rate and the fraction of infections leading to death in epidemiological simulation

Sammanfattning: The main goal of this project is to investigate the behaviors of parameters used when modeling an epidemic. A stochastic SIHDRe model is used to simulate how an epidemic evolves over time. The SIHDRe model has nine parameters, and this project focuses on the infection rate (β) and the fraction of infections leading to deaths (FID), with all other parameters being considered known. Both parameters are time dependent. To estimate the two chosen parameters, this project uses synthetic data so that comparisons between estimations with true parameters are possible. A dynamic optimization procedure inspired by Model Predictive Control is utilized for the predictions. Using synthesized data from hospitalizations and deaths, a cost function is minimized to obtain estimations of the parameters. Only a subset of the time span, called a window, is considered for every parameter optimization. The parameters within the window are optimized and the window then moves forward in time defined by a time step until the parameters are optimized over the whole time span. To obtain error estimations of the parameters, synthetic bootstrapping is used, using optimized parameters to simulate new epidemics of which the parameters are optimized. The square difference between the new estimations compared to the original estimations can be used to obtain the standard deviation of the estimated parameters. This project also discusses how regularization parameters within the cost functions are chosen so that the estimated parameters will be most similar to the real parameter values, and end-of-data effects, i.e. increased uncertainty towards the end of a window, is also discussed.