Mathematical modeling of epidemic spread using nonlinear dynamical systems

The spread of an epidemic is a complex nonlinear process that is affected by the process of transmission, the process of recovery, the interaction of the population and the temporal variation in the epidemiological parameters.This study aims to develop mathematical framework for the modelling of the dynamics of epidemics with the help of non-linear dynamics.The population is broken up into epidemiological compartments and the dynamics of the disease spread and recovery are represented by a set of nonlinear differential equations.The framework proposed analyzes the behavior of infection growth, the peak of an epidemic, the recovery pattern, the equilibrium behavior and the stability of the system for varying parameters.The simulation results show that the nonlinear modelling is a powerful tool to capture epidemic dynamics and gain quantitative understanding of transmission dynamics, assessing control strategies, and making epidemic management decisions.