Modeling the Spread of COVID-19 Using Nonautonomous Dynamical System with Simplex Algorithm-Based Optimization for Time-Varying Parameters

The S I R D V (Susceptible, Infected, Recovered, Death, Vaccinated) compartmental model along with time-varying parameters is used to model the spread of COVID-19 in the United States. Time-varying parameters account for changes in transmission rates, people’s behaviors, safety precautions, government regulations, the rate of vaccinations, and also the probabilities of recovery and death. By using a parameter estimation based on the simplex algorithm, the system of differential equations is able to match real COVID-19 data for infections, deaths, and vaccinations in the United States of America with relatively high precision. Autoregression is used to forecast parameters in order to forecast solutions. Van den Driessche’s next-generation approach for basic reproduction number agrees well across the entire time period. Analyses on sensitivity and elasticity are performed on the reproduction number with respect to transmission, exit, and natural death rates in order to observe the changes from a small change in parameter values. Model validation through the Akaike Information Criterion ensures that the model is suitable and optimal for modeling the spread of COVID-19.