Fractional nonlinear dynamics and forward bifurcation in a memory-based cholera model

Area of Science:

• Epidemiology
• Mathematical Biology
• Dynamical Systems

Background:

• Cholera transmission exhibits complex memory-dependent and nonlinear dynamics.
• Traditional integer-order models may not fully capture these intricate behaviors.
• Understanding these dynamics is crucial for effective disease control.

Purpose of the Study:

• To explore fractional-order epidemic models for cholera transmission.
• To integrate preventive behaviors and environmental feedback into a fractional model.
• To analyze the impact of memory effects on epidemic dynamics and control.

Main Methods:

• Developed a fractional-order susceptible-infected-recovered-individuals adopting preventive measures-bacteria (SIR-IPM-B) model using the Caputo derivative.
• Analyzed the existence, uniqueness, and boundedness of the model's solutions.
• Derived the basic reproduction number (R0) and performed stability and bifurcation analyses.
• Designed a fractional optimal control strategy for cholera intervention.

Main Results:

• Fractional dynamics, influenced by memory, were shown to transition the system from a disease-free to an endemic state via forward bifurcation.
• Numerical simulations demonstrated that fractional dynamics suppress infection peaks by extending transient memory effects.
• The model indicated enhanced epidemic resilience and reduced environmental contamination due to fractional dynamics.
• The study highlighted the significant impact of fractional-order memory and nonlinear coupling on epidemic thresholds and control effectiveness.

Conclusions:

• Fractional-order models provide a more comprehensive framework for understanding cholera dynamics due to memory effects.
• The integration of preventive behaviors and environmental factors in fractional models is effective for disease control.
• Fractional dynamics offer a promising approach to enhance epidemic resilience and mitigate waterborne disease outbreaks.