A hybrid Lagrangian-Eulerian model for vector-borne diseases

Area of Science:

• Mathematical modeling of infectious diseases
• Epidemiology
• Population dynamics

Background:

• Vector-borne diseases pose significant public health challenges.
• Understanding population movement's impact on disease transmission is crucial for control.
• Existing models often simplify host and vector mobility.

Purpose of the Study:

• To develop and analyze a multi-patch, multi-group vector-borne disease model.
• To investigate the influence of host commuting and vector migration on disease dynamics.
• To determine the basic reproduction number and its relationship with population mobility.

Main Methods:

• Formulation of a mathematical model incorporating host commuting (Lagrangian) and vector migration (Eulerian).
• Analysis of global dynamics based on the basic reproduction number (R0).
• Derivation of bounds for R0 independent of mobility matrices.
• Numerical analysis for a two-patch, two-group scenario.

Main Results:

• The basic reproduction number (R0) dictates global disease stability (disease-free or endemic).
• R0 has bounds independent of host residence time and vector migration matrices.
• Non-homogeneous mixing generally increases disease persistence; R0 is minimized with proportional distributions.
• R0 can be estimated from disconnected patch models in homogeneous environments.

Conclusions:

• Population mobility significantly impacts vector-borne disease spread.
• The basic reproduction number provides a robust metric for disease dynamics, with predictable bounds.
• Proportional host and vector distributions minimize R0, suggesting potential control benefits.
• Optimal control strategies can be tailored for homogeneous and heterogeneous environments.