Fractional Model with Social Distancing Parameter for Early Estimation of COVID-19 Spread

Abstract

COVID-19 disease has come up as a life-threatening outbreak at end of 2019. It has impacted almost all countries in the world. The major source of COVID-19 is a novel beta coronavirus. COVID-19 had a great impact on world throughout the year 2020. Now, the situation is becoming normal due to the invention of the vaccine. All major countries started large vaccination drives. Mathematical models are used to study the impact of different measures used to decrease pandemics. Mathematical models such as susceptible-infected-removed model and susceptible-exposed-infected-removed are used to predict the spread of diseases. But these models are not suitable to predict COVID-19 spread due to various preventive measures (social distancing and quarantine) applied to reduce spread. Hence, in the present manuscript, a novel fractional mathematical model with a social distancing parameter has been proposed to provide early COVID-19 spread estimation. Fractional calculus provides flexibility in choosing arbitrary order of derivative which controls data sensitivity. The model has been validated with real data set. It has been observed that the proposed model is highly accurate in spread estimation.

Keywords: COVID-19; Coronavirus; Mathematical modeling; Pandemic modeling.

Fig. 1

Proposed mathematical model with social distancing

Fig. 2

Flowchart for proposed fractional model

Fig. 3

Active COVID-19 cases in India

Fig. 4

COVID-19 spread analysis by different curve fitting tools

Fig. 5

COVID-19 trend in India with different scenarios

Fig. 6

COVID-19 spread before applying social distancing with $\rho =1$

Fig. 7

COVID-19 spread due to breakage in social distancing with $\rho =0.8$

Fig. 8

COVID-19 spread due to breakage in social distancing with $\rho =0.5$

Fig. 9

COVID-19 spread after applying different social distancing with $\rho =1.0$

Fig. 10

COVID-19 spread due to breakage in social distancing with $\rho =0.8$

Fig. 11

COVID-19 spread due to breakage in social distancing with $\rho =0.5$

Fig. 12

COVID-19 spread after applying different social distancing and wearing of facial mask parameter

Fig. 13

COVID-19 spread analysis by SIR model

Fig. 14

COVID-19 spread analysis by SEIR model