Vector-borne diseases models with residence times - A Lagrangian perspective

Area of Science:

• Mathematical modeling of infectious diseases
• Ecology and population dynamics
• Epidemiology

Background:

• Understanding disease dynamics requires accounting for host-vector interactions and spatial heterogeneity.
• Host movement patterns significantly influence disease transmission and persistence in ecological systems.

Purpose of the Study:

• To formulate a multi-patch, multi-group modeling framework for disease dynamics.
• To analyze the impact of host residence times and group structure on disease spread and stability.
• To investigate the relationship between environmental risk, host-vector interactions, and the basic reproduction number (R0).

Main Methods:

• Development of a nonlinear mathematical model incorporating host dispersal and group structure.
• Computation of the residence times basic reproduction number (R0).
• Analysis of global asymptotic stability for disease-free and endemic equilibria.
• Exploration of patchiness and groupness effects on R0.
• Numerical simulations to assess the impact of residence times on disease prevalence.

Main Results:

• The basic reproduction number (R0) is dependent on the relative environmental risk of infection.
• The model demonstrates robustness: disease-free equilibrium is globally asymptotically stable if R0 ≤ 1.
• A unique endemic equilibrium is globally asymptotically stable when R0 > 1 for irreducible host-vector interactions.
• Patchiness and groupness significantly affect R0.
• Residence times were shown to impact disease prevalence through numerical simulations.

Conclusions:

• Host movement patterns and group structure are critical determinants of disease dynamics and stability.
• The developed model provides a robust framework for analyzing infectious diseases in heterogeneous environments.
• Findings highlight the importance of considering spatial and group structures in epidemiological studies.