Research Interests
My research includes
dynamical systems modeling of the micro-parasite, Plasmodium,
with host immune response. A model I have analyzed consists of a system
of delay
differential equations with state variables being the antigenically
distinct variants of Plasmodium and the two corresponding
phenomenological variables representing specific and cross-reactive
immune responses. I have had published the results concerning
synchronous oscillations [1]
in the Bulletin of Mathematical Biology
while a paper concerning the globally-coupled model allowing both
synchronous and asynchronous oscillations is under review
[2].
I am also researching a generalized predator-prey
model for which the prey is regulated by a state-dependent delay. It is
common for equilibria in such delay models to bifurcate to persistent
periodic solutions. Using a multiple-scales analysis, I show how the
definition of the delay influences the nonlinear behavior of the
system, be it subcritical or supercritical. I am applying the result to
a few different examples of delays to substantiate the analysis.
Publications
- J. L. Mitchell and T. W. Carr, Oscillations in an Intrahost Model
of Plasmodium falciparum
Malaria due to Cross-reactive Immune Response, Bull. Math. Biol.,
August, 2009.
DOI
10.1007/s11538-009-9462-2
- J. L. Mitchell and T. W. Carr, Asynchronous behavior in a
globally-coupled system of delaydifferential equations modeling
Plasmodium falciparum infection (submitted to Mathematical
Biosciences
12/20/09).