Fractal-fractional modelling of thrombocytopenia influence on pregnant women in the context of dengue infection with Mittag-Leffler decay analysis - Vijayalakshmi, G. M.; Ariyanatchi, M.; Govindan, Vediyappan; İnç, Mustafa (Springer Heidelberg, 2025)
The consequences of thrombocytopenia on pregnant women and its subsequent impacts on new born are explored in this research using a fractional-order mathematical framework, which is a novel method. We establish the theoretical foundation for our investigation by focussing on mathematical analysis, namely fractional calculus, and its applications in computer science and infectious disease modelling. We formulate the problem by utilizing a framework that combines the fractal-fractional operator with a general Mittag-Leffler kernel through system dynamics equations, and this allows us to deduce solutions for the proposed approach. Theoretical analysis is carried out to justify the basis of the model and to confirm its uniqueness based on the Atangana-Baleanu fractal-fractional operator, by fixed-point theory. We also carry out qualitative analysis to ensure that solutions are nonnegative and exhaustively analyze Ulam-Hyers stability to understand the behavior and stability of the system. Numerical simulations are then executed to explore the diverse fractional-order dynamics within the proposed model, yielding valuable insights into preventive measures and control strategies for epidemics in society. Additionally, our simulations include an exploration of the Lorenz chaos attractor in 3D, adding complexity and depth to the dynamics elucidated in the paper. In conclusion, our study offers a comprehensive understanding of thrombocytopenia's effects on pregnant women and new-borns, providing a basis for informed decision-making and further research in this critical area.
Keywords: Dengue mathematical model; Fractal fractional operator; Uniqueness solution; Lipchitz function; Ulam-Hyers stability