A study, conducted by researcher Farman from Department of Mathematics, Near East University and co-authored by experts in the field, introduces a novel approach to modeling the dynamics of HIV/AIDS transmission using fractional calculus. Fractional calculus, a burgeoning field, has increasingly demonstrated its significance in various real-life applications, including control strategies and disease transmission dynamics.
The study proposes a Modified Atangana-Baleanu Caputo (MABC) fractional derivative operator, which extends the capabilities of existing fractional derivatives, particularly in handling equations with integrable singularities at the origin. Unlike traditional methods, the MABC derivative allows for the solution of a broader range of fractional differential equations, including those with nontrivial solutions and without additional imposed conditions. This innovation opens new avenues for understanding complex processes, such as the transmission dynamics of infectious diseases like HIV/AIDS.
By employing the Banach fixed point theory, the researchers establish the stability and existence criteria for steady solutions of the MABC fractional HIV/AIDS model. The study also employs the Laplace Adomian decomposition method to obtain numerical solutions, demonstrating the effectiveness and reliability of the proposed model in capturing the intricate dynamics of infection spread.
One of the key contributions of this research lies in its ability to uncover hidden dynamics of infection through the incorporation of memory aspects in the MABC derivative. This feature enables a more accurate representation of viral disease dynamics compared to traditional integer-order derivatives.
The findings of this study hold significant implications for public health professionals, offering valuable insights and control techniques for combating HIV/AIDS and other communicable diseases. Moreover, the proposed modification expands the applicability of fractional calculus operators, enhancing our understanding of complex processes across various domains.
Through rigorous theoretical analysis and numerical simulations, supported by mathematical software, the study provides a comprehensive framework for studying and addressing the challenges posed by infectious diseases. By shedding light on both singular and nonsingular cases, the research contributes to a deeper understanding of disease dynamics and paves the way for future advancements in modeling complex systems.
More Information:
https://www.sciencedirect.com/science/article/pii/S1110016822007670
