On mathematical model of infectious disease by using fractals fractional analysis

Abstract

Here, we remarked that fractals or Housdarff derivatives are important tools to investigate various problems. However, fractals when combined with fractional orders of different kernels give birth to a big class of operators. Each operator has its own importance and applicability. One of the fractals-fractional operators is based on the exponential kernel which has also many important uses in modeling of different real-world problems. Reinfection is a worldwide issue nowadays and due to reinfection, people in our society are facing a lot of issues like economical, social, and a high rate of death. A fractal-fractional hybrid model with reinfection was investigated. The mentioned model was considered to deduce the qualitative theory and numerical aspects. Fundamental properties of the mentioned model were deduced including basic reproduction number, equilibrium points, and global and local stability of both equilibrium points. The qualitative analysis was consisted on the existence and stability in sense of Hyers-Ulam of the solutions. Interpolation technique was used to deduce a numerical scheme for the model under our study. Additionally, criteria for uniqueness of solution was proved by the Banach principle. In addition, sensitivity analysis was also included in the paper. Various numerical results were presented using different values of fractals fractional order. Some comparisons of simulated and real data was also given.