DOI: https://doi.org/10.36719/2663-4619/126/169-175
Yusif Yagublu
Azerbaijan State Oil and Industry University
Master's student
https://orcid.org/0009-0004-8109-0294
yagubluyusiff@gmail.com
Investigation and Application of Nonlocal Multipoint Boundary
Value Problem for a System of Ordinary Differential Equations
Abstract
This paper investigates a nonlocal multipoint boundary value problem for a first-order system of ordinary differential equations. The fundamental matrix and Green's function method are used to solve the problem. Sufficient conditions for the existence and uniqueness of the solution are proved based on the Banach contraction principle. The theoretical results are applied to an epidemiological SIR model. In this model, the dynamics between susceptible, infected, and recovered groups of the population are studied. Multipoint boundary conditions correspond to measurements taken at different time points, which allows real epidemiological data to be incorporated into the model. Numerical calculations are performed, and results are presented in tabular form. The results show that multipoint boundary conditions provide more accurate predictions in epidemiological forecasting compared to classical initial conditions.
Keywords: system of differential equations, multipoint boundary value problem, Green's function, Banach contraction principle, SIR model, epidemiological modeling