Total Variation Regularization for Compartmental Epidemic Models with Time-varying Dynamics

Traditional methods to infer compartmental epidemic models with time-varying dynamics can only capture continuous changes in the dynamic. However, many changes are discontinuous due to sudden interventions, such as city lockdown and opening of field hospitals. To model the discontinuities, this study introduces the tool of total variation regularization, which regulates the temporal changes of the dynamic parameters, such as the transmission rate. To recover the ground truth dynamic, this study designs a novel yet straightforward optimization algorithm, dubbed iterative Nelder-Mead, which repeatedly applies the Nelder-Mead algorithm. Experiments on the simulated data show that the proposed approach can qualitatively reproduce the discontinuities of the underlying dynamics. To extend this research to real data as well as to help researchers worldwide to fight against COVID-19, the author releases his research platform as an open-source package.