COVID-19 disease spread modeling by QSIR method: The parameter optimal control approach

At present, India is in the decreasing phase of the second wave of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). But India as a country is in the second position in a high number of confirmed cases (33,678,786) in the world (after the United States of America) and third position in the number of COVID-19 deaths (after the United States and Brazil) at 465,082 deaths. Almost above numbers are dominantly seen in the second wave only. Thus, future long-term projections are required to mitigate the impact.

The conventional SIR model was modified so that a new compartment Q(quarantine) is added to the conventional SIR model to analyze the COVID-19 impact. The parameter optimal control technique was used to fit the curve by estimating the infection, susceptible, etc.

The model predicts the cumulative number of cases of 2.6928E7 with a confidence interval of 95%, CI[2.6921E7,2.6935E7], and an accuracy of 99.3% on May 25, 2020(480th day from 30 to 01-2020). The estimated R₀ is 1.1475. The model's mean absolute error(E ) is 1.79E4, and the root-mean-square error is (E ) is 3.19E4. The future projection are,3.48E7(Lockdown), 3.80E7(periodic-lockdown), 4.52E7(without lockdown). The whole model accuracy is 99%, and projection accuracy is about 94% up to 01-Nov-2021, The goodness of fit value 0.8954.

The model is over-estimating corona cases initially and then showed a decreased trend. As the number of days increases, the model accuracy decreases; thus, more control points of the cost function are required to fit the model best.