## Abstract

We formulate a simple susceptible-infectious-recovery (SIR) model to describe the spread of the coronavirus under strict social restrictions. The transmission rate in this model is exponentially decreasing with time. We find a formula for basic reproduction function and estimate the maximum number of daily infected individuals. We fit the model to induced death data in Italy, United States, Germany, France, India, Spain, and China over the period from the first reported death to August 7, 2020. We notice that the model has excellent fit to the disease death data in these countries. We estimate the model's parameters in each of these countries with 95% confidence intervals. We order the strength of social restrictions in these countries using the exponential rate. We estimate the time needed to reduce the basic reproduction function to one unit and use it to order the quality of social restrictions in these countries. The social restriction in China was the strictest and the most effective and in India was the weakest and the least effective. Policy-makers may apply the Chinese successful social restriction experiment and avoid the Indian unsuccessful one.

Original language | British English |
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Journal | Mathematical Methods in the Applied Sciences |

DOIs | |

State | Accepted/In press - 2021 |

## Keywords

- coronavirus
- COVID-19
- mathematical model
- parameter estimations
- social distancing
- variable transmission rate