An almost periodic Ross-Macdonald model with structured vector population in a patchy environment

Area of Science:

• Mathematical epidemiology
• Vector-borne disease dynamics
• Ecological modeling

Background:

• Understanding disease dynamics in heterogeneous environments is crucial for effective control.
• Age structure in vector populations significantly influences disease transmission.
• Patchy environments and host migration add complexity to epidemiological models.

Purpose of the Study:

• To develop and analyze an almost periodic Ross-Macdonald model incorporating vector age structure in a patchy environment.
• To establish a threshold criterion for disease persistence and extinction based on the basic reproduction ratio.
• To investigate the impact of environmental factors and control strategies on disease transmission.

Main Methods:

• Derivation of the basic reproduction ratio (R0) for the proposed model.
• Analysis of the global dynamics using threshold-type results.
• Numerical simulations to explore the effects of biting rate, human migration, and vector maturation period.

Main Results:

• Disease persistence is guaranteed if R0 > 1, while extinction occurs if R0 < 1.
• Biting rate significantly impacts disease transmission; human migration can reduce transmission risk.
• Prolonging the vector maturation period is beneficial for disease control, with a computable threshold for outbreak.

Conclusions:

• The derived threshold dynamics provide a basis for disease management strategies.
• Numerical insights highlight the importance of vector maturation period and migration control.
• Almost periodic models offer a more nuanced understanding of disease transmission compared to simple periodic models.