In collaboration with a researcher Qureshi from Department of Mathematics, Near East University, a study delves into the intricate dynamics of HIV/AIDS transmission and the impact of antiretroviral therapy (ART) using a novel approach based on the Caputo operator’s fractional framework. Recognized as a dangerous and potentially fatal disease, HIV/AIDS severely weakens the immune system, rendering the body vulnerable to various illnesses. The study employs fractional calculus to characterize the transmission process and assess the efficacy of ART in mitigating HIV/AIDS transmission.
Through the application of fractional calculus, the study unveils the fundamental characteristics of the formulated system and explores the steady states, reproduction parameter, and stability analysis within the fractional framework. Optimal values of the Caputo fractional-order are identified, and system parameters are determined using the least-squares method to ensure alignment with real-world HIV/AIDS data.
Comparisons between classical and Caputo systems reveal the superiority of the Caputo operator in accurately modeling HIV/AIDS transmission dynamics. By employing average and maximum absolute relative percentile errors, the study demonstrates the enhanced performance of the Caputo framework in capturing the complexities of HIV/AIDS transmission.
Furthermore, a sensitivity analysis utilizing the partial rank correlation coefficient (PRCC) technique highlights the critical parameters influencing the formulation of the reproduction parameter, providing valuable insights for refining model accuracy and effectiveness.
The study presents a groundbreaking approach to understanding and modeling HIV/AIDS transmission dynamics, leveraging the innovative Caputo fractional framework. By elucidating the intricate interplay between ART and HIV/AIDS transmission, the research contributes to the advancement of strategies for combating the spread of HIV/AIDS and optimizing treatment outcomes. Through powerful numerical simulations, the study provides a comprehensive visualization of HIV/AIDS time series within the Caputo fractional framework, offering valuable insights for future research and intervention efforts in combating this global health challenge.
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