Study of the spread of viral diseases based on modifications of the SIR model

The spread of infectious diseases is a complex phenomenon with many interacting factors. The key role of mathematical epidemiology is to create pathogen spread patterns. These models serve as the mathematical basis for understanding the complex dynamics of the spread of the disease. There are various mathematical models of epidemics, but depending on the type of epidemic, there is a need for their careful analysis and improvement. In 1927, Kermak W. and Mackendrick A. published their theory, on the basis of which the SIR-model (Susceptible-Infected-Removed) was built. This theory was a hypothesis about the spread of an infectious disease among the population. This model has still not lost its relevance and is well suited for predicting the spread of infectious diseases. The aim of the work was to develop and study a mathematical model of the spread of the epidemic based on existing models of epidynamics.
The work investigated the processes of epidemics using the classical SIR model and its modifications: SEIRD models (Susceptible-Exposed-Infected-Removed-Dead) and SEIHFRmodels (Susceptible-Exposed-Infected-Hospitalized-Funeral-Removed). A numerical simulation of the dynamics of the spread of viral disease in various scenarios of its course has been carried out. The modern methods and means of mathematical modeling of the spread of viral diseases have been investigated; analyzed their effectiveness depending on the type of epidemic. New modifications of well-known models based on systems of differential equations that take into account the characteristics of the acquisition of immunity, as well as the effect of delay in detecting infected people, are pro-posed. The sensitivity of the parameters included in the model is investigated.
The results can be used to study the processes of modern epidemics, including the coronavirus pandemic, as well as to effectively predict the dynamics of the disease, to develop effective mechanisms to contain and control epidemics of a local and global nature.

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