A novel fractal fractional mathematical model for HIV/AIDS transmission stability and sensitivity with numerical analysis

Scientific Reports, Journal Year: 2025, Volume and Issue: 15(1)

Published: March 18, 2025

Understanding the complex dynamics of HIV/AIDS transmission requires models that capture real-world progression and intervention impacts. This study introduces an innovative mathematical framework using fractal-fractional calculus to analyze dynamics, emphasizing memory effects nonlocal interactions critical disease spread. By dividing populations into four distinct compartments-susceptible individuals, infected those undergoing treatment, individuals in advanced AIDS stages-the model reflects key phases infection therapeutic interventions. Unlike conventional approaches, proposed nonlinear function, $$\frac{\nabla (\mathscr {I}+\alpha _1\mathscr {T}+\alpha _2\mathscr {A})}{\mathscr {N}}$$ , accounts for varying infectivity levels across stages (where $$\mathscr {N}$$ is total population $$\nabla$$ denotes effective contact rate), offering a nuanced view how treatment efficacy ( $$\alpha _1$$ ) _2$$ shape transmission. The analytical combines rigorous exploration with practical insights. We derive basic reproduction number {R}_0$$ assess outbreak potential employ Lyapunov theory establish global stability conditions. Using Schauder fixed-point theorem, we prove existence uniqueness solutions, while bifurcation analysis via center manifold reveals thresholds persistence or elimination. use computational scheme Adams-Bashforth method interpolation-based correction technique ensure numerical precision confirm theoretical results. Sensitivity highlights medication accessibility delaying spread as vital control strategy by identifying parameters. simulations illustrate predictive ability model, which shows order affects trajectories long-term burden. outperforms integer produces more accurate epidemiological predictions integrating memory-dependent fractional flexibility. These findings demonstrate model's value developing targeted public health initiatives, particularly environments limited resources where monitoring balancing allocation essential. In end, our work provides tool better predict manage evolving challenges bridging gap between mathematics actual control.

Language: Английский

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An optimal control analysis of HIV-Visceral Leishmaniasis co-infection model

Partial Differential Equations in Applied Mathematics, Journal Year: 2025, Volume and Issue: unknown, P. 101216 - 101216

Published: May 1, 2025

Language: Английский

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Impact of Awareness and Protective Measures on the Transmission Dynamics of HIV/AIDS: A Mathematical Analysis

International Journal of Applied and Computational Mathematics, Journal Year: 2025, Volume and Issue: 11(3)

Published: May 13, 2025

Language: Английский

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Dynamic analysis of a Caputo fractional-order SEIR model with a general incidence rate

Scientific Reports, Journal Year: 2025, Volume and Issue: 15(1)

Published: May 21, 2025

Language: Английский

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On the Dynamics of COVID-19 Propagation with Vaccination and Optimal Control Strategies

Brazilian Journal of Physics, Journal Year: 2025, Volume and Issue: 55(3)

Published: April 15, 2025

Language: Английский

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