Numerical solution of a fractional SEIR epidemic model using Bernstein series approximation method

Measles is a notable viral disease that presents a grave danger to public health, especially in less developed countries with poor rates of immunization, leading to serious complications and fatalities. The utilization of mathematical modeling, particularly the SEIR (Susceptible-Exposed-Infectious-Recovered) epidemic model, is essential for comprehending the patterns of transmission and assessing the effectiveness of control strategies. Nevertheless, the conventional SEIR model, which relies on integer-order derivatives, does not comprehensively depict the dynamics of disease transmission since it assumes rapid changes in compartments, disregarding the impact of memory effects on epidemics. This paper presents a new fractional-order SEIR model that integrates memory effects in order to provide a more precise representation of measles transmission. The Bernstein series approximation approach is utilized to provide an approximate solution for the nonlinear fractional differential equations of the model. The findings are contrasted with those produced using the Laplace Adomian Decomposition approach for different values of the fractional-order parameter α ∈ (0, 1]. The results indicate that the fractional-order SEIR model offers a more accurate representation of the actual data by including a slighter decrease in infection rates and a more precise tool for modeling the spread of infectious diseases. The absolute error function is employed to assess the accuracy and accuracy of the suggested technique.