ON FRACTAL-FRACTIONAL WATERBORNE DISEASE MODEL: A STUDY ON THEORETICAL AND NUMERICAL ASPECTS OF SOLUTIONS VIA SIMULATIONS

Waterborne diseases are illnesses caused by pathogenic bacteria that spread through water and have a negative influence on human health. Due to the involvement of most countries in this vital issue, accurate analysis of mathematical models of such diseases is one of the first priorities of researchers. In this regard, in this paper, we turn to a waterborne disease model for solution's existence, HU-stability, and computational analysis. We transform the model to an analogous fractal-fractional integral form and study its qualitative analysis using an iterative convergent sequence and fixed-point technique to see whether there is a solution. We use Lagrange's interpolation to construct numerical algorithms for the fractal-fractional waterborne disease model in terms of computations. The approach is then put to the test in a case study, yielding some interesting outcomes.

Automated summary

Waterborne diseases caused by pathogenic bacteria in water pose a threat to human health. Mathematical modeling and analysis of these diseases are essential for researchers worldwide. In this paper, a waterborne disease model is transformed into a fractal-fractional integral form for qualitative analysis, with the use of an iterative convergent sequence and fixed-point technique to determine the existence of solutions. Numerical algorithms based on Lagrange's interpolation are developed for computational purposes. The effectiveness of this approach is demonstrated through a case study, providing interesting outcomes.