Modeling the non-integer dynamics of a vector-borne infection with nonlocal and nonsingular kernel

Area of Science:

• Epidemiology
• Mathematical Biology
• Fractional Calculus

Background:

• Vector-borne infections present a significant global health and economic challenge.
• Effective prevention, control, and treatment strategies are crucial.

Purpose of the Study:

• To develop and analyze a mathematical model for vector-borne disease transmission incorporating vaccination.
• To utilize fractional calculus (Atangana-Baleanu derivative) for modeling disease dynamics.
• To investigate the impact of vaccination on disease spread.

Main Methods:

• Formulation of a mathematical model using the Atangana-Baleanu fractional derivative.
• Determination of the basic reproduction number (R0) using the next-generation matrix method.
• Analysis of local asymptotic stability at the disease-free equilibrium.
• Application of fixed-point theory to establish the existence of solutions.
• Development of a numerical scheme for simulating model dynamics.

Main Results:

• The model solutions are proven to be positive and bounded for positive initial conditions.
• The threshold parameter (R0) was determined, indicating disease transmissibility.
• Stability analysis confirmed the behavior at the disease-free equilibrium.
• Numerical simulations visualized the impact of various parameters on disease dynamics.

Conclusions:

• Fractional calculus provides a robust framework for modeling vector-borne disease dynamics.
• The study offers insights into critical factors influencing disease transmission and control.
• Findings can inform public health strategies for vector-borne disease prevention and mitigation.