Modeling the Transmission of Wolbachia in Mosquitoes for Controlling Mosquito-Borne Diseases

Explore a comprehensive lecture on modeling Wolbachia transmission in mosquitoes for disease control. Delve into the dynamics of Wolbachia invasion, examining reproductive numbers, critical thresholds, and reduced models. Investigate spatial modeling approaches, including PDE models and critical bubble analysis. Learn about threshold conditions, invasion success, and future work in 2D cylindrical symmetric releases. Gain insights into mathematical approaches for public health applications in vector-borne disease control.

Intro
Aedes aegypti – primary vector for the transmission
Modeling the Wolbachia invasion in mosquitoes
Wolbachia transmission dynamics in mosquitoes
Basic reproductive number Ro
Critical threshold for establishing Wolbachia infection
remove aquatic stage
combine infection groups
removing males
Reduced 2-ODE model mimics the dynamics of 9-ODE
The reduced models preserve the critical threshold
Why we need spatial models?
2.PDE model
Threshold condition for spatial model
Capture the critical bubble (analytically)
Capture the critical bubble (numerically)
Comparison for two approaches
Compare critical bubble with other shapes
Invasion success: above threshold
Summary
Future work: cylindrical symmetric for releases in 2-D
Acknowledgment