TITLE:
Application of Matrices Modelling for Infectious Diseases of Humans
AUTHORS:
Mohemid Maddallah Al-Jebouri, Mohammed Nokhas Murad Kaki
KEYWORDS:
SEIR Model, Outbreak Prediction, Mathematical Modeling, Epidemic Threshold, Infection Dynamics
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.15 No.9,
September
18,
2025
ABSTRACT: Background: The present study showed a mathematical analysis of the spread of infectious diseases using the classical SEIR (Susceptible-Exposed-Infected-Recovered) model. The model is presented in two forms: the standard nonlinear formulation and a simplified linear version expressed through matrix representation. Methods: By applying the Euler method for numerical approximation, the time evolution of the susceptible, infected, and recovered populations is simulated over a fixed period. The model incorporates key epidemiological parameters, such as the transmission rate (β), exposed rate (σ), and recovery rate (γ), and assumes a closed population. Results: Highlighting how the disease propagates, peaks, and eventually declines, providing insights into the impact of transmission dynamics. Conclusions: This work illustrates the value of mathematical models and matrix-based approaches in analyzing infectious disease dynamics and guiding public health strategies. The SEIR model would serve as a powerful tool for understanding the dynamics of infectious diseases with incubation periods.