Predicting the Spread of COVID-19 Using SIR Model Augmented to Incorporate Quarantine and Testing

Abstract

India imposed a nationwide lockdown from 25th March 2020 onwards to combat the spread of COVID-19 pandemic. To model the spread of a disease and to predict its future course, epidemiologists make use of compartmental models such as the $\mathrm{SIR}$ model. In order to address some of the assumptions of the standard $\mathrm{SIR}$ model, a new modified version of $\mathrm{SIR}$ model is proposed in this paper that takes into account the percentage of infected individuals who are tested and quarantined. This approach helps overcome the assumption of homogenous mixing of population which is inherent to the conventional $\mathrm{SIR}$ model. Using the available data of the number of COVID-19 positive cases reported in the state of Kerala, and in India till 26th April, 2020 and 12th May 2020, respectively, the parameter estimation problem is converted into an optimization problem with the help of a least squared cost function. The optimization problem is then solved using differential evolution optimizer. The impact of lockdown is quantified by comparing the rising trend in infections before and during the lockdown. Using the estimated set of parameters, the model predicts that in the state of Kerala, by using certain interventions the pandemic can be successfully controlled latest by the first week of July, whereas the $R_0$ value for India is still greater than 1, and hence lifting of lockdown from all regions of the country is not advisable.

Keywords: COVID-19; India; Kerala; Pandemic; Quarantine; SIR Model; Testing.

Fig. 1

Categorization of infected individuals based on factor of testing

Fig. 2

a Growth of active cases with different $\mathit{ft}$ values keeping the rate of spread, $\beta$ and the recovery factor $(\nu )$ constant. $\beta =1.0$, $\nu =0.25$; b growth of active cases with different $\beta$ values keeping the factor of testing $(ft)$ and the recovery factor $(\nu )$ constant.$ft=0.4$, $\nu =0.25$

Fig. 3

Comparison between the actual data and model. a Comparison of the model with total number of confirmed cases; b comparison of the model with number of confirmed cases per day

Fig. 4

Number of new cases per day if the lockdown is opened in Kerala with the existing testing levels

Fig. 5

Number of new cases per day if the lockdown is opened in Kerala with the testing levels increased to 80%

Fig. 6

Number of new cases per day if the lockdown is extended to two months while gradually increasing the testing levels to 60%

Fig. 7

Number of new cases per day in the case of an intermittent or staggered lockdown with existing testing levels

Fig. 8

Number of new cases per day in the case where the lockdown is lifted on 3rd May with adequate social distancing measures

Fig. 9

Comparison of the model with total number of confirmed cases

Fig. 10

Number of active cases in the country if the current scenario continues