Including human behavior in infectious disease models The COVID-19 pandemic has revealed the good and the bad of infectious disease models. While a well-developed model provides invaluable insights needed to understand and combat the pandemic, many models suffer from imperfect or simplistic assumptions that result in inaccurate or even completely wrong predictions. In this talk, …
A multi-scale approach for modeling cell dynamics The characterization of biological phenomena related to cell evolution and their interactions with the microenvironment often involves processes occurring across a range of spatial and temporal scales. As a result, mathematical models designed to describe cell dynamics must capture this inherent multi-scale complexity. In this seminar, we introduce …
How cells stay together; a mechanism for maintenance of a robust cluster explored by local and nonlocal continuum models Formation of organs and specialized tissues in embryonic development requires migration of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here explore a recent local approximation of nonlocal continuum …
Reconstruction of stochastic differential equations characterizing noisy single-cell molecular dynamics In the talk, I shall introduce our recent work on developing machine-learning-based methods for reconstructing noisy single-cell molecular dynamics as stochastic differential equations, which aims to quantify intrinsic fluctuations in the stochastic process characterizing cellular dynamics. I will then discuss how to apply my methods …
Parabolic System of Aggregation Formation in Bacterial Colonies The goal of this talk is to study a fourth-order nonlinear parabolic system with dispersion for describing bacterial aggregation. Analytical solution of traveling wave is found by taking into account the dispersion coefficient. Numerically, we demonstrate that the initial concentration of bacteria in the form of a …
Cancer Detection via Electrical Impedance Tomography and Optimal Control of Elliptic PDEs A new mathematical framework utilizing the theory of Partial Differential Equations(PDE), inverse problems and optimal control of systems with distributed parameters for the detection of the cancerous tumor growth in the human body is developed. The Inverse Electrical Impedance Tomography (EIT) problem on …
Continuous culture models of microbial kinetics In this talk, I will start with a bit of history of mathematical models of microbial kinetics in both batch and continuous cultures, briefly discuss the principle of competitive exclusion, and then concentrate on the models that incorporate the bacterial aggregation in various forms such as the flocculation and …
Mathematical modeling of CD8 T cell search for malaria infection in the liver Malaria, a disease caused by parasites of the Plasmodium genus, begins when Plasmodium-infected mosquitoes inject malaria sporozoites while searching for blood. Sporozoites migrate from the skin via blood to the liver, infect hepatocytes, and form liver stages. In mice, sufficient numbers of …
Insights into oscillatory neural dynamics using a phase-amplitude framework Model reduction techniques can provide useful insight into the dynamics behaviour of high dimensional oscillatory systems such as networks of neurons or neural field models. However, the utility of the classical technique of phase reduction is limited by the assumption that the local dynamics for each …
Bistability between acute and chronic states in a Model of Hepatitis B Virus Dynamics Understanding the mechanisms responsible for different clinical outcomes following hepatitis B infection requires a systems investigation of dynamical interactions between the virus and the immune system. To help elucidate mechanisms of protection and those responsible from transition from acute to chronic …