Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as dengue fever, Zika, and chikungunya. However, it is difficult to sustain a Wolbachia infection in the mosquito population due to the fitness cost. Field trials indicate that the infection must exceed a critical threshold level to persist. In this talk, I will present a series of differential-equation models of different fidelities to characterize the threshold condition for a sustainable infection in the field.

Our initial ordinary differential equation (ODE) model captures the complex transmission and mosquito life cycle. We identify important reproduction numbers, and the threshold effect is characterized by a backward bifurcation. To simulate the field releases, it is critical to account for the spatial heterogeneity created by mosquito dispersion, but the straightforward spatial extension leads to complex high-dimensional partial differential equations (PDEs). To this end, we first approximate the ODE model using a hierarchy of reduced models, which are more analytically trackable but still preserve the important properties of the original system. We then extend the reduced model to a PDE model and characterize the threshold for a successful spatial invasion as a bubble-shaped distribution. We conduct numerical studies for different scenarios to inform the design of release strategies.

Bio: Zhuolin Qu obtained her Ph.D. in Applied Mathematics in 2016 from Tulane University. She was a postdoctoral fellow at Tulane from 2016 – 2020, and she is currently an Assistant Professor at the University of Texas at San Antonio. She has been working on mathematical biology with particular interests in the mathematical modeling of infectious diseases, computational epidemiology, dynamical systems, and numerical methods for PDEs. She develops both equation-based compartmental models for mosquito-borne diseases and agent-based stochastic models for sexually transmitted diseases.

Personal website: https://zhuolinqu.github.io/

Related publications:

Original ODE model paper - https://epubs.siam.org/doi/abs/10.1137/17M1130800

Reduced model paper - https://epubs.siam.org/doi/abs/10.1137/19M1250054

Spatial model arXiv preprint - https://arxiv.org/abs/2108.10837