Zhuolin Qu

Chlamydia is the most commonly reported sexually transmitted disease in the United States.  Untreated asymptomatic infections may cause permanent damage to the women’s reproductive system.  Routine screening is recommended for women with risk factors to identify these "silent" infections.

In close collaboration with the Tulane School of Public Health team, we develop and analyze a stochastic and individual-based model to simulate the chlamydia epidemic on dynamic sexual networks, and we evaluate the efficacy of screening high-risk men to control chlamydia prevalence in women. Read more about the "Check It" Program.

The proposed model presents a robust framework for modeling other sexually transmitted diseases spreading in a population with assortative mixing.

Left: Chlamydia epidemic spread over a static sexual network. Larger nodes (person) have more neighbors (sexual partners). The infection status of each person is tracked using the Susceptible (Green) - Infectious (Red) - Susceptible (SIS) framework.  Right: Model prediction for the impact of male screening on the prevalence in women under different intervention coverage. Darker region gives a higher Chlamydia prevalence in women.

Collaborators

James Mac Hyman (Tulane University) Patricia Kissinger (Epidemiology, Tulane) Asma Azizi (Kennesaw State University)  Charles Stoecker (Global Health Management and Policy, Tulane)

While most of my recent research is on modeling infectious diseases, I have extensive experience in developing numerical methods for nonlinear PDEs.

Fast operator splitting methods for nonlinear PDEs

The operator splitting methods are divide-and-conquer strategies to solve the PDEs with operators of different natures. The main idea is to decompose a complex equation into simpler sub-equations, which provides great flexibility in choosing different numerical methods for each sub-problem.

Phase Field Models

Phase-field models are mathematical models for interfacial phenomena. They were originally derived for the microstructure evolution and phase transition, and they have been extended to many other physical phenomena, such as the growth of cancerous tumors, phase separation of block copolymers, and dewetting and rupture of thin liquid films.

The molecular beam epitaxy (MBE) equation with slop selection $$ u_{t}=-\delta \Delta^{2} u+\nabla \cdot\left(|\nabla u|^{2} \nabla u-\nabla u\right), \quad \delta>0.$$ The Cahn-Hilliard equation $$ u_{t}=-\delta \Delta^{2} u+\Delta\left(u^{3}-u\right),  \quad \delta>0.$$

Left and middle: Solution of 2-D MBE equation subject to a random initial data (uniformly distribution). The pyramid edges form a random network over the surface. The cells of the network grow in time via a coarsening process. Right: The mean height remains practically zero at all times, which verifies the mass conservation of the numerical method.

Left four plots: Solution of 2-D Cahn-Hilliard equation in time, subject to a non-mean-zero initial condition. Right: Adaptive time-stepping is used to speed up the computation while still accurately captures different stages of phase separation.

Buckley-Leverett Equations

In fluid dynamics, the Buckley-Leverett (BL) equation is a model for two-phase flow in porous medium. The modified Buckley-Leverett (MBL) has considered the dynamic capillary pressure that results from difference in the pressures of the two phases. One application for MBL is on secondary recovery by water-drive in oil reservoir simulation.

Rotational Modified BL (MBL) equation in 2-D
$$u_t + \nabla\cdot\left(\vec{V}{\displaystyle \frac{u^2}{u^2+M(1-u)^2}}\right) = \varepsilon\,\Delta\,u + \varepsilon^2\tau \Delta u_t,\quad \vec{V}=[y,-x] , \quad \varepsilon>0, \quad \tau>0.$$

Comparison of numerical solutions for BL (top row) and MBL (bottom row) equations. Initial condition is a smooth 2-D Gaussian function cut off by a plateau. Left: View from the top. Right: 3-D view. The numerical solution for the MBL equation reproduces the non-monotone profile observed in experiments.

Collaborators

Alexander Kurganov (Southern University of Science and Technology, China) Tao Tang (Southern University of Science and Technology, China) Chiu-Yen Kao (Claremont McKenna College) Ying Wang (University of Oklahoma) Yuanzheng Cheng (Goldman Sachs)