Numerical solutions of a fractional order SEIR epidemic model of measles under Caputo fractional derivative

Measles is a highly contagious illness that can spread throughout a population based on the number of susceptible or infected individuals as well as their social dynamics within the society. The measles epidemic is thought to be controlled for the suffering population using the susceptible-exposed-infectious-recovered (SEIR) epidemic model, which depicts the direct transmission of infectious diseases. To better explain the measles epidemics, we provided a nonlinear time fractional model of the disease. The solution of SEIR is obtained by using the Caputo fractional derivative operator of order μ∈(0,1]. The Homotopy perturbation transform method (HPTM) and Yang transform decomposition methodology (YTDM) have been employed to obtain the numerical solution of the time fractional model. Obtaining numerical findings in the form of a fast-convergent series significantly improves the proposed techniques accuracy. The behaviour of the approximate series solution for several fractional orders is shown graphically which are derived through Maple. A graphic representation of the behaviours of susceptible, exposed, infected, and recovered individuals are shown at different fractional order values. Figures that depict the behaviour of the projected model are used to illustrate the developed results. Finally, the present work may help you predict the behaviour of the real-world models in the wild class with respect to the model parameters. It was found that the majority of patients who receive therapy join the recovered class when various epidemiological classes were simulated at the effect of fractional parameter μ. These approaches shows to be one of the most efficient methods to solve epidemic models and control infectious diseases.