What is it about?

In the present work, an adaptation is made of the Bateman linear differential equations describing a system of nuclear levels interconnected by transitions (each with its own rate in general) to the case of epidemiology where only two infection and recovery rates are used. The levels from the Nuclear Physics case are replaced by successive generations of infected people following the human to human to human.... transmission paradigm. Closed mathematical expressions are derived which allow an easy calculation/prediction of the time-dependent properties of these generations and therefore of the whole epidemics, at least at the stage of largest spread before saturation is reached due to decrease of susceptible to the infection people. Using real data as testing ground, reasonable descriptions of the newly registered COVID-19 cases per day is achieved for Europe and the United States till December 2020, including several so-called Pandemic waves. For that description, a normalization of the raw data on the new cases is performed on a day by day basis using the number of tests made per day per 1000 inhabitants. This is the only way to compare in absolute numbers the daily evolution of the COVID-19 or any other pandemic. New data points added for the period January to March 2021 indicate a faster decrease of the COVID-19 spread compared to the predictions of our simple model. This effect is correlated with the begin of vaccinations and may be the decrease of people susceptible to infection due to immunity acquired for some period after recovering. The approach of the present work, by using transmission from one generation of infected people to a new generation allows a much more detailed tracking of the Pandemic spread than the approaches used so far. For example, the most widely used SIR models (and their variants) use instead transitions from one big compartment of susceptible people to another one of infected people followed by recovery leading to a third compartment. Our analysis of the data for Europe and the United States clearly indicates correlations between features of the Pandemic process and the emergence of new SARS-CoV-2 variants, with some of them immediately influencing the spread of the infection disease. Our results may be used by specialists in epidemiology for more detailed studies when the remarks made above about the rates are taken into account. Once again, one has to consider important factors as specifics in every country coexisting with globalization effects, the existence of different social/age groups and different health systems in each country, and so forth. From that point of view, we believe that the mathematical formalism proposed here can help the specialists in epidemiology to solve problems and if necessary, they can introduce modifications in the approach and the software to treat more complex specific situations. In addition, within our formalism the number of epidemics waves can be extended to an arbitrary number just by resetting new values of the infection rate at the corresponding moments in time.

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Why is it important?

Approaching the COVID-19 Pandemic by means of mathematical modeling remains of extreme importance even now, by Spring of 2022. Our new method for description, based on tracking of successive generations of infected people and including the option for considering successive "waves" of the Pandemic, adds an useful complementary investigation tool in the filed due to its simplicity.


The advantages of the simplicity of our method have to be considered with its limitations in describing complex situations in its initial formulation. In small chapter, just before the Summary of the paper, ways for further improvements are indicated and they may have some implementations in the future, hopefully by a larger circle of specialists because of the multidisciplinary character of the problem.

Dr Pavel Petkov

Read the Original

This page is a summary of: New and simple mathematical description of epidemics including consecutive waves, Studies in Applied Mathematics, December 2021, Wiley, DOI: 10.1111/sapm.12477.
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