Simulation and application of COVID-19 compartment model using physic-informed neural network

COVID-19 pandemic has had a disruptive and irreversible impact globally, yet traditional epidemiological modeling approaches such as the susceptible-infected-recovered (SIR) model have exhibited limited effectiveness in forecasting of the up-to-date pandemic situation. In this work, susceptible-vaccinated-exposed-infected-dead-recovered (SVEIDR) model and its variants -- aged and vaccination-structured SVEIDR models -- are introduced to encode the effect of social contact for different age groups and vaccination status. Then, we implement the physics-informed neural network (PiNN) on both simulated and real-world data. The PiNN model enables robust analysis of the dynamic spread, prediction, and parameter optimization of the COVID-19 compartmental models. The models exhibit relative root mean square error (RRMSE) of <4\% for all components and provide incubation, death, and recovery rates of $\gamma= 0.0224$, $\lambda=0.0002$, and $\rho=0.0082$, respectively, for the first 310 days of the epidemic in the US. To further improve the model performance, temporally varying parameters can be included, such as vaccination, transmission, and incubation rates. Our implementation highlights PiNN as a reliable candidate approach for forecasting real-world data and can be applied to other compartmental model variants of interest.