Dynamical systems modeling for epidemic spread and control

Epidemic outbreaks are characterized by complex nonlinear dynamics, with the effects of transmission, recovery, population interactions and interventions.This study introduces a framework for the modelling of epidemics and its assessment of disease control mechanisms based on dynamical systems.The susceptible, exposed, infected and recovered populations are modeled using coupled nonlinear differential equations.A time-varying transmission and recovery rates are indicative of changes in the contact patterns, health care response and control measures.To determine the long-term epidemic behavior, disease-free and endemic equilibrium points are determined.Stability analysis offers insight into about conditions necessary for the elimination of a disease or for its persistence.The framework facilitates assessment of transmission reduction, recovery enhancement, and epidemic stability and offers a flexible mathematical basis to learn about outbreaks and to devise effective public health control measures and policies.