Utilization of Advanced SIR-Based Mathematical Modelsfor Epidemic Analysis with a Focus on COVID-19

چکیده

 Abstract
The entire field of epidemiology, which deals with the dynamics of
diseases over time or across different regions, must be analysed
using mathematical formulas and principles in order to be presented
scientifically. Although this involves dealing with numerous
variables, it offers significant advantages, as the more
comprehensively an epidemic is analysed, the more effective and
accurate the outcomes will be. In this context, we introduce the most
basic model of infectious disease transmission—the SIR model—
and compare it with more advanced and refined models derived
from it. Epidemiological models, particularly the classical SIR
model, are among the most effective tools for analysing the spread
of infectious diseases globally. This paper examines the SIR model
and its extensions, such as the SIRV and SEIR models. Their
applications in epidemic prevention and control—especially during
the global crisis of the COVID-19 pandemic, with which we are well
familiar—are discussed. By employing nonlinear differential
equations and numerical analysis, it is demonstrated how these
models contribute to health policymaking and rational, preventive
decision-making. Since diseases caused by bacteria, viruses, and
fungi are transmitted through direct contact such as sneezing,
coughing, skin contact, and exchange of bodily fluids
complementary health policies are essential to prevent future
outbreaks or the resurgence of second waves of infection as much
as possible.
Keywords: Numerical epidemic analysis, SIR model, SIRV model,
SEIR model, mathematical modelling, transmission rate, recovery
rate.