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Vector-borne disease models with Lagrangian approach.

Daozhou Gao1,2, Linlin Cao3

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

Journal of Mathematical Biology
|January 31, 2024
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Summary
This summary is machine-generated.

Population dispersal significantly impacts vector-borne disease spread. Our model shows heterogeneous mixing and host subdivision can increase disease transmission, influencing control strategies.

Keywords:
Basic reproduction numberGlobal dynamicsInfectious disease networkLagrangian approachPopulation movementVector-borne disease

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Ecology

Background:

  • Vector-borne diseases pose significant public health challenges.
  • Understanding spatial spread dynamics is crucial for effective control.
  • Population dispersal influences disease transmission patterns in heterogeneous environments.

Purpose of the Study:

  • To develop a multi-group, multi-patch model analyzing population dispersal effects on vector-borne disease spread.
  • To define and utilize the basic reproduction number (R0) and network connectivity for disease dynamics.
  • To investigate bounds on R0 and compare modeling approaches.

Main Methods:

  • Lagrangian approach to model host and vector movement, preserving individual identity.
  • Characterization of host-vector network connectivity using residence times matrices.
  • Analysis of global stability of the disease-free equilibrium based on R0.

Main Results:

  • The basic reproduction number (R0) determines the global dynamics of the disease.
  • Heterogeneous mixing in a homogeneous environment increases R0.
  • Lagrangian and Eulerian models show substantial differences in R0 upper bounds.
  • Increased host subdivision can lead to a larger R0.

Conclusions:

  • Population dispersal and environmental heterogeneity are key factors in vector-borne disease spread.
  • The model provides biologically meaningful bounds for R0, aiding in disease management.
  • Numerical simulations highlight the impact of host movement and control strategies on disease transmission.