RUDN mathematician builds COVID-19m spread

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image: Mathematicians at RUDN University built a model of the spread of COVID-19 based on two regression models. Mathematicians divided countries into three groups, based on sprawl rate and climatic conditions, and found an appropriate mathematical approximation for each of them. Based on the model, mathematicians predicted the following waves. The forecast was correct in countries where mass vaccination has not been introduced.
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Credit: RUDN University

Mathematicians at RUDN University built a model of the spread of COVID-19 based on two regression models. Mathematicians divided countries into three groups, based on sprawl rate and climatic conditions, and found an appropriate mathematical approximation for each of them. Based on the model, mathematicians predicted the following waves. The forecast was correct in countries where mass vaccination has not been introduced. The results are published in Mathematics.

The speed of the epidemic’s spread within the country depends, among other things, on climatic conditions: temperature, humidity, winds. For example, during the cold season, the dry air dries up the nasal mucus which acts as a first line of defense against the virus. Therefore, a person gets infected faster. High temperature, on the contrary, prevents the virus from surviving. Based on these considerations, Professor Maria Alessandra Ragusa of RUDN University and her colleagues from Egypt and Italy built models of the spread of COVID-19 separately for three groups of countries with different climatic conditions. It turned out that the model accurately predicts the outcome of the epidemic, but only until the effect of the vaccination begins to be felt.

“The main challenge when studying epidemics is how to predict the behavior of the disease, how many people will be infected in the future, determine the pandemic peak, the second wave of the disease action time and the total number of deaths after the end of the pandemic. We used new state-of-the-art regression models to model daily confirmed cases and predict upcoming coronavirus waves in different countries. “, Maria Alessandra Ragusa, Professor at RUDN University.

Mathematicians have identified three groups of countries. The first category includes countries where the first wave of the pandemic lasted around 180 days. Are these the countries with the lowest application rate, with an annual average temperature of 15-38? (for example, Saudi Arabia, Egypt). In the second group of countries (for example, UK, Germany, Italy) with an average annual temperature of 2-31 ° C, the first wave lasted 90 days. Countries in this group are characterized by an average infection rate and downtime with a low rate of spread of the virus. The third group includes the countries with the highest rate of spread and no downtime, with an average annual temperature of 2 to 18 degrees Celsius – for example, the United States and Russia.

For modeling, scientists used WHO data on the number of cases from March 1 to November 15, 2020. RUDN mathematicians chose the most appropriate regression models – statistical research methods of influence of several variables on a value. The Fourier series and the sum of the sine waves were the most accurate for modeling COVID-19 cases. This means that the curve of new cases of the disease is represented either as a sum of Fourier functions (they can be represented as waves of a certain frequency and of a certain amplitude), or as a sum of sine waves. ordinary.

As a result, Professor Ragusa obtained the calculated values ​​of the peak of the second or third wave in the countries studied. Different models gave close forecasts with a difference of several days. The predictions obtained were compared to the data available at that time. It turned out that the model provides fairly accurate predictions if the country does not introduce widespread vaccination. For example, the calculated value of the peak of new cases in Egypt is 1,481 people on January 11, 2021; the real peak occurred on December 31 with 1,418 cases. In other countries, the model provides an accurate prediction until early 2021. After that, the effect of vaccination takes place and the calculated values ​​differ from reality. For example, for Germany, the predicted and actual values ​​are close until around January 15, 2021, and on February 15, they differ by approximately 2.5 times.

“In our future work, we will develop current predictive models by considering how vaccination affects the rate of spread of the virus”, Maria Alessandra Ragusa, professor at RUDN University.

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