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