Caputo fractal-fractional mathematical study of SIS epidemic dynamical problem with competitive environment and neural network

The infection of any disease is one of the most highly affected factors for the dynamics of all species population and this may be for the case of human populations throughout the world. The infection of any disease acts like a predator or competitor for the healthy population or species of the environment. In this article, the dynamics of one type of species’ density are investigated by the spreading of infection in the environment along with competition with other species and among themselves. The generalized operator in the sense of Caputo having fractal dimension and non-integer order is operated to consider the problem for testing the complex geometry of the said dynamics. The total density of the species is divided into two agents of healthy class and the infectious class. For the biological validation, the qualitative analysis is carried out in the sense of fixed point theory. The stability analysis for the solution is also treated by using the Ulam-Hyers concept of stability in the sense of the said operator. The numerical scheme has been developed for each quantity along with a graphical representation of different fractional order and fractal dimensions. Using an artificial neural Network (ANN) technique, we have divided the data set into three different categories in this study: training, testing, and validation. This study includes a detailed analysis that we conducted based on this division.