Numerical Simulation And Stability Analysis Of A Differential Equation–Based Infectious Disease Transmission Model

Abstract

In order to understand the dynamics of infectious disease transmission and to promote effective public health 
interventions, mathematical modelling is essential. For the purpose of describing the spread of disease within a 
community, this paper develops and analyses an ordinary differential equation based compartmental infectious 
disease model. There are three sections in the population model: vulnerable, infected, and recovered. Stability 
analysis is performed utilizing eigenvalue methods and basic reproduction number principles after analytical 
examination to find the disease-free and endemic equilibrium points. To study the disease's temporal evolution 
under different parameter values, numerical simulations are run using standard numerical techniques. The effects 
of the initial population distribution, recovery rate, and transmission rate on illness dynamics are shown by the 
simulation results. The results demonstrate that numerical simulation is useful for forecasting the actions of 
outbreaks and evaluating methods of disease control. This study lays the groundwork for future work in 
mathematics and computational epidemiology that can handle more complicated cases.