WAKE FOREST UNIVERSITY
DEPARTMENT OF MATHEMATICS & STATISTICS
George Mason University
March 7, 2019
Manchester Hall, Room 018
“The role of PDEs and integro-differential equations in biomedical and materials models”
The talk will survey some recent theoretical developments in the realm of random walks and generalized master equations for TRWs with non-stationary jump and waiting times distributions, and draw connections between their materials science and biomedical applications. In particular, the presentation will focus on: (1) recent advances in mathematical modeling of materials microstructures, where distributions of misorientations, their steady-states and their time evolution may be inferred from generalized master equations, and (2) new applications of this theory to a problem of malaria transmission, where antibody levels in blood may be modeled via a similar continuous time jump process, presenting new epidemiological insights and pathways for intervention. Results of numerical experiments will be provided to demonstrate the use of this methodology in both contexts.