A fractional model based on caputo derivative for tuberculosis transmission using real data from Kenya

Area of Science:

• Mathematical modeling
• Epidemiology
• Infectious disease dynamics

Background:

• Tuberculosis (TB) is a leading global infectious killer, disproportionately affecting vulnerable populations.
• Existing TB models often lack the robustness to fully capture complex transmission dynamics.
• There is a critical need for advanced modeling to guide effective TB control policies.

Purpose of the Study:

• To develop and analyze a novel fractional-order mathematical model for tuberculosis transmission in Kenya.
• To rigorously investigate the fundamental mathematical properties of the proposed model.
• To estimate model parameters and identify key drivers of TB spread.

Main Methods:

• Incorporation of the Caputo fractional derivative into a compartmental TB model.
• Analysis of model properties: positivity, boundedness, uniqueness, and existence.
• Parameter estimation, sensitivity analysis using the basic reproduction number, and numerical simulations with the Adams-Bashforth Predictor Corrector scheme.
• Data fitting to validate model performance against real-world TB data.

Main Results:

• An optimal fractional order of approximately 0.85 was identified for best data alignment.
• Sensitivity analysis revealed critical parameters significantly influencing TB transmission dynamics.
• The fractional-order model demonstrated high accuracy in matching real-world TB data.
• Numerical simulations highlighted the impact of memory effects on disease dynamics.

Conclusions:

• The fractional-order TB model provides a more realistic representation of disease transmission, incorporating memory effects.
• The model's findings offer actionable insights for optimizing TB control interventions and policies in Kenya.
• Timely and targeted interventions, informed by advanced modeling, are crucial for strengthening TB control efforts.