Khodakaram Salimifard

Background: Control strategies effectiveness such as decrease in transmission rate (decrease in direct contact and also in the risk of infectious, considering direct contact) and immunization (through vaccinating of susceptible individuals and recovery) are some of important subjects must be decided before any decision making about mass immunization program in order to preventing epidemic crisis. This thesis tries to response to the importance of control strategies for condition that disease-free equilibrium is globally asymptotically stable. Aim: The aim of this research is providing a framework in order to evaluating the long term control strategies effectiveness on epidemic model compartments, epidemics behaviour, and epidemics crisis. Methodology: Methodology of this research is based on rescaled Non-linear ordinary differential equation of Pan’s chaotic model in order to determine equilibrium points, global stability and locally unstable conditions of disease-free and endemic equilibrium points, critical points and bifurcation, basic reproduction number and variation in susceptible unidentified infected identified infected and recovered ratios in time-series. Findings: The effect of transmission rate (from to ) and (from to ) is variable, but via adding and to the model, with the parameters value greater than or equal to critical points, disease-free equilibrium is globally asymptotically stable and endemic equilibrium is locally unstable. Conclusions: Awareness of parameters initial condition, population proportions, and basic reproduction number condition for both disease-free equilibrium and endemic equilibrium in order preventing epidemic crisis reduces costs when and also the level of required activities when epidemic crisis has happened ( and endemic equilibrium is globally asymptotically stable) to turning back the system in disease-free equilibrium point globally asymptotically stable.