The role of PDEs and integro-differential equations in biomedical and materials models

WAKE FOREST UNIVERSITY
DEPARTMENT OF MATHEMATICS & STATISTICS

Presents
Maria Emelianenko
George Mason University

March 7, 2019
11:00am
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.

 

 

 

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