Population dynamics

The modeling of dynamical systems has evolved in the mathematical sciences. This is how the ordinary derivatives in differential equations evolved in other forms of operators. Indeed, the development of physical systems over time has imposed the use of fractional derivative operators. Since these derivatives are of fractional order, they can approximate real data with more flexibility than conventional derivatives. In addition, they also take into consideration non-locality, which classical derivatives cannot do. In this work, the model is applied to a real phenomenon: tetanus vaccination. The choice of this model comes from several reasons. Moreover, vaccination is the preferred remedy of several governments because it allows not only to cure but also to prevent disease.Thus, this immune-strengthening character consolidates large-scale treatment. On the other hand, the second originality of the work concerns the culmination of the numerical results. Indeed, unlike the classical numerical scheme, the results obtained make it possible to considerably improve the system of mathematical equations.