Abstract

Mathematical modelling is essential in controlling and understanding the spread of infectious diseases. This study involves mathematical modelling of nonlinear in-contact disease dynamics using nonlinear differential equations and a stability study. The interactions of different groups of people through time are modelled using classical compartmental models, including the Susceptible-Infected-Recovered (SIR) framework. The nonlinear character of the governing equations represents real transmission mechanisms, recovery mechanisms and population dynamics. The model's equilibrium points, such as the disease-free and endemic equilibria, are established and analysed to understand the disease's long-run behaviour better. Stability analysis is a mathematical method that employs linearization and eigenvalue analysis to determine whether a disease will die out or persist in the population. The basic reproduction number R0 is a critical threshold parameter for the dynamics of disease spread. R 0 < 1 Local asymptotic stability of disease-free equilibrium, whereas R 0 appears to be unstable, and an endemic state arises. The analytical conclusions and the effects of model parameters on disease development are demonstrated through numerical simulations. The paper focuses on the utility of nonlinear differential equation models for forecasting outbreak patterns and evaluating control strategies, such as vaccination and treatment. These lessons can be used to make sounder choices regarding the planning of community health and the prevention of illness.