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A hybrid Lagrangian-Eulerian model for vector-borne diseases.

Daozhou Gao1, Xiaoyan Yuan2

  • 1Department of Mathematics and Statistics, Cleveland State University, Cleveland, OH, 44115, USA. d.gao51@csuohio.edu.

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|June 18, 2024
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Summary

This study introduces a vector-borne disease model considering host commuting and vector migration. Disease spread is influenced by population movements, with the basic reproduction number determining outcomes and offering bounds for control strategies.

Keywords:
Basic reproduction numberEulerian approachLagrangian approachOptimal vector controlPopulation movementVector–borne disease

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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.