An optimized SIR Modeling for Analyzing the Spreading Rate of Covid-19 Pandemic

Abstract

Today, an important social problem for mankind is the proliferation of corona virus (COVID-19) spreading in various countries. This virus outbreaks like an epidemic, transmitted quickly among population due to social interaction with the infected individual. This research focuses on examining virus spreading rate among the individuals accurately. In the proposed work, to analyze the behavior of the virus spreading rate, a probabilistic mathematical model is designed. It consists of three stages namely Susceptible-Infected-Recovered (SIR) and formulated using mean field approximation method. Initially, to limit the virus spreading rate, a threshold value is obtained using reproductive ratio which is derived by performing stability analysis. In addition, to control the virus spreading rate of the individuals, optimization control technique is introduced on both states of the susceptible and infected individual population. It is demonstrated through simulation studies that the optimal control of the susceptible population by the proposed model is achieved in 7 to 11 days whereas the existing models have taken 20 to 45 days. Likewise, for infected population, the optimal control is achieved in 12 to 15 days by the proposed model whereas the existing models take 35 to 50 days. In order to prove the accuracy of the model, a real time Covid-19 data from France country is also demonstrated.