Conceptual Analysis of a Fractional Order Epidemic model of Measles Capturing Logistic growth using Laplace Adomian Decomposition Method

Abstract

Measles is a highly contagious, dangerous virus-borne disease. Prior to the advent of the measles vaccine and widespread immunization in 1963, severe outbreaks occurred every 2-3 years. Mathematical model of measles with logistic growth and enlightenment to go for vaccination was proposed and presented, the disease-free and endemic equilibria were obtained and their stabilities were investigated, basic reproduction number was generated using next generation matrix. Laplace-Adomian decomposition was utilized to carry out the numerical simulation in order to investigate the impact of the parameters of the model. The results were presented graphically and it was established that both enlightenments to go for vaccination and vaccination itself are effective methods are the measure to eradicate transmission of the disease measles in the population

Keywords

• vaccination
• disease free equilibrium
• endemic equilibrium
• laplace adomian decomposition method