Mathematical Modelling of Epidemic Transmission Dynamics and Numerical Analysis
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Abstract
This research explores the dynamics of epidemic construction employing the traditional Susceptible-Infectious-Recovered (SIR) epidemiological framework within a population. Iterative methods can be performed to address the group of nonlinear ordinary differential equations. To analyze the given model, we employ the Variational Iteration Method (VIM). To prove the efficiency and exactness of the VIM, we perform a comparison assessment with the classical Runge-Kutta method, a broadly used numerical method. We formulate the iterative protocols for each method and implement them in MatLab R2025a to produce numerical observations over a specified period of time. This research offers important awareness of the transmission and oversight of infectious diseases. The numerical representation reinforces that the VIM provides an effective approach for identifying the epidemic patterns and for framing control tactics.
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