S-I-R Model and COVID-19 Data-Based Numerical Ro Estimation for Pandemic Modeling

A contagious disease transmits from human to human or animal to human. At present world is encountered with such a disease, known as COVID-19. More than half a million people have died due to this pandemic. The pandemic started in China and spread within no time to other parts of the world. Italy and USA are the most unfortunate countries as a large number of deaths occurred in these two countries. No doubt this contagious disease has created social as well as economic problems all over the world, especially in underdeveloped countries. The disease easily transmits to a healthy person during social contact. An epidemic model was developed known as the Kermack-McKendrick model described as SIR (Susceptible Infected and Recovered) model, it deals with the rate of transmission of disease and rate of infection. It gives a trend of infectious disease in a large population. The model helps epidemiologists and health policymakers to understand the probable transmission of disease and to take possible and effective measures to control or reduce the spread of the virus. The factor Ro, known as the reproductive number, can be considered as a threshold value for the disease to be an epidemic. In this study, we used the SIR model to study the effect of COVID-19 in Pakistan. Three coupled differential equations of the SIR model have been solved by numerically using COVID-19 data for Pakistan.
The Ro estimated by the current Pakistan COVID-19 data is found to be 2.656 from which control measures will cause a decrease in Ro. Due to the reduction in Ro, the apex of the infected population curve predicted to be range from 26 % to 3 %, and the time to reach the apex ranges from 161 to 710 days. Also, the current data is compared with the numerical values by solving the SIR model. However, the model has limitations due to which parameters can be approximately calculated that might match the actual values to some extent. The application of the model is simple and students can easily learn about the computational techniques used to solve the coupled differential equations.