Fractional-order delayed Ross-Macdonald model for malaria transmission

Area of Science:

• Mathematical modeling of infectious diseases
• Fractional calculus applications in epidemiology

Background:

• Malaria transmission dynamics are complex and influenced by various factors.
• Understanding the impact of incubation periods and model parameters is crucial for effective control strategies.

Purpose of the Study:

• To propose and analyze a novel fractional-order delayed Ross-Macdonald model for malaria.
• To investigate the influence of Plasmodium incubation periods and fractional order on disease dynamics.
• To determine conditions for model stability and the occurrence of fractional-order Hopf bifurcations.

Main Methods:

• Utilized inequality techniques and contraction mapping theory for existence and uniqueness of solutions.
• Applied fractional linear stability theorem and bifurcation theory to analyze dynamic behavior.
• Investigated system behavior under different time delay scenarios.

Main Results:

• Established sufficient conditions for the existence, uniqueness, and local stability of the positive equilibrium point.
• Demonstrated that time delays can alter system stability, leading to Hopf bifurcations.
• Showed that the fractional order affects the size of the stability interval.

Conclusions:

• Incubation periods and the fractional order significantly influence malaria transmission dynamics.
• Time delays are critical factors that can destabilize the system and induce bifurcations.
• The proposed model provides insights into the complex behavior of malaria transmission.