Mathematical Modelling of the Spread of the Coronavirus under Social Restrictions

Al-arydah, M.; Dib, K.; Berhe, H. W.; Madhu, K.

COVID-19 has affected most countries and declared as pandemic. Most countries have implemented some social restrictions to control it. In this work we will use mathematical modelling to assess the current social restrictions in controlling the spread of the disease. We formulate a simple susceptible-infectious-recovery (SIR) model to describe the spread of the coronavirus under social restrictions. The transmission rate in this model is considered variable to catch social restrictions impact. We analyze this model, then fit the model to 160 days induced death data in Italy, Iran, USA, Germany, France, India, Spain and China. we estimate some factors that help in understanding not only the spread of the disease but also assess the current social restriction in controlling this disease. Results: We find a formula for the basic reproduction function (R(t)) and the maximum number of daily infected people. Then estimate the model's parameters with 95% confidence intervals in these countries. We notice that the model has excellent fit to the disease death data in all considered countries except Iran. The percentage of disease death estimated by the model in Germany and France are 3.8% and 1.2% respectively, which are close to reported percentages values. Finally, we estimate the time, after first reported death, spent under social restrictions to reduce the basic reproduction function (R(t)) to one unit. The times to do that in Italy, USA, Germany, France, Spain and China are 40, 50, 34,58, 31, and 15 days respectively. However, the Indian social restrictions in the 160 days were not enough to reach $R(t)=1$. The transmission rate is between 0.1035- 1.6076 and recovery rate is between 0-0.2456. The disease death rates calculated for Germany and France are more realistic than others with average value 0.0023. Extending the same social restrictions for enough time could control the disease in Italy, USA, Germany, France, India, Spain and China. While, more social restrictions are needed to control the disease in India.