Modified SEIQHRDP and machine learning prediction for the epidemics

This paper is dedicated to investigating the transmission and prediction of viruses within human society. In the first phase, we augment the classical Susceptible-Exposed-Infectious-Recovered (SEIR) model by incorporating four novel states: protected status ($P$), quarantine status ($Q$), self-home status ($H$), and death status ($D$). The numerical solution of this extended model is obtained using the well-established fourth-order Runge-Kutta algorithm. Subsequently, we employ the next matrix method to calculate the basic reproduction number ($R_0$) of the infectious disease model. We substantiate the stability of the basic reproductive number through an analysis grounded in Routh-Hurwitz theory. Lastly, we turn to the application and comparison of statistical models, specifically the Autoregressive Integrated Moving Average (ARIMA) and Bidirectional Long Short-Term Memory (Bi-LSTM) models, for time series prediction.