Numerical study on fractional order nonlinear SIR-SI model for dengue fever epidemics

Area of Science:

• Mathematical Biology
• Epidemiology
• Fractional Calculus

Background:

• Dengue fever poses a significant global health challenge.
• Existing models often lack the ability to capture long-term dependencies in disease transmission.

Purpose of the Study:

• To develop and analyze a novel fractional-order SIR-SI epidemic model for dengue.
• To investigate the impact of memory effects on dengue transmission dynamics.
• To assess the stability of equilibrium points and derive the basic reproduction number.

Main Methods:

• Formulation of a combined SIR-SI model using nonlinear differential equations.
• Incorporation of fractional-order derivatives (Caputo sense) to model memory effects.
• Analysis of disease-free and endemic equilibrium points for stability.
• Derivation of the basic reproduction number and sensitivity analysis.
• Numerical simulations using the two-step Lagrange polynomial method.

Main Results:

• The fractional-order model provides deeper insights into dengue transmission dynamics.
• Memory effects, captured by fractional derivatives, are shown to be significant.
• Sensitivity analysis identified key parameters influencing disease spread.
• The two-step Lagrange polynomial method effectively simulated the fractional model.

Conclusions:

• Fractional calculus offers a valuable framework for understanding complex epidemic dynamics.
• The study highlights the importance of incorporating memory effects in disease modeling.
• Findings can inform the development of more effective dengue control strategies.