Asya Pritsker's Summer 2010 REU Homepage
Summer 2010 Office:
|Rutgers University, New Brunswick|
This website was created in the summer of 2010 as part of the DIMACS Research Experience for Undergraduates. It is mostly here to tell a little about the projects I work on, and it is a temporary homepage of sorts for me. I am very grateful to DIMACS, the organizers of this program, and the various foundations which provide financial support this REU. I am also extremely grateful to my mentors for the time they spent helping me with my projects and advising me in general. The summer has been both enjoyable and very helpful in focusing my desires. To any undergraduate students who may be looking at this website to learn more about the program, you are welcome to contact me with any questions you may have- I highly recommend applying.
We are interested in studying the effects of various resource allocation strategies to battle with the HIV epidemic in sub-saharan Africa. We are doing this by building an SIR-type model while incorporating economics- we include a distinction between producers and consumers, roughly speaking, adults and children. Epidemiologists have been recently concerned about the possibility of demographic collapse in the regions- nations of children, or simply a heavy imbalance of children who cannot be provided sufficiently for. The clearest result we have seen in working with this model is that it is far more important to treat adults with antiretrovirals than it is children because this does a great deal more to prevent the spread of disease both vertically and horizontally, and it makes the economics of the society far more robust. Furthermore, by treating a target subpopulation, it takes longer for the society to run out of money for treatment, making treatment for the same people more continuous, and thus more effective. The model has also shown, with quite realistic parameters, that societies with HIV run out of money quite quickly because of the need to provide medication. I am particularly interested in how the behaviour of the system changes as the prevalence of the disease changes- is there a point early on where we can stop the epidemic because prevalence is low and we can treat everyone? There does not appear to be. Currently, we are working on doing stability analysis on a slightly simplified version of the model which is just a system of ordinary differential equations.
This project was started by Immanuel Williams, a DIMACS REU student from U. of Maryland in 2009, and also worked on by Senelani Hove-Musekwa, a DIMACS visitor from U. of Zimbabwe in the winter of 2009Presentation 1, 11 June 2010
Mentors: Nina Fefferman, fefferman (at) aesop.rutgers.edu, Ecology and Tamra Carpenter, tcar at dimacs.rutgers.edu, DIMACS
Project Title: Allocation of Monetary Resources in HIV-Infected Communities
In many impoverished nations, monetary resources to treat HIV are severely limited, so communities are unable to treat all of the infected population. While much research focuses on specific treatment strategies  or more macro-scale modeling , recent research is also looking at finer models of equitability  and economics . We will develop and refine a mathematical epidemiological model that ties community economics with HIV progression. Through computer simulation, the model will be used to gain intuition and potentially inform policy decisions on how to allocate treatment resources. We will refine this model to capture features of populations in specific areas (e.g., sub-Saharan Africa) and use it to explore the impact of different treatment strategies with the goal of identifying those that best assure the stability and long-term survival of the community.
R. F. Baggaley, G. P. Garnett, and N. M. Ferguson, "Modeling the Impact of Antiretroviral Use in Resource-Poor Settings," PLoS Medicine 3(4):e124, 2006.
Cuddington, J. Hancock, and C. Rogers, "A Dynamic Aggregative Model of the AIDS Epidemic with Possible Policy Interventions," Journal of Policy Modeling 16(5) (1994), 473-496.
D. Wilson, and S. Blower, "Designing Equitable Antiretroviral Allocation Strategies in Resource-Constrained Countries," PLoS Medicine 2(2):e50, 2005.
N. H. Fefferman, and J. N. Kibambe, "A Household Resource Model for Epidemic Control in Financially Constrained Populations," (Under Review).
* You must be a U.S. Citizen or Permanent Resident to be eligible for this project.
We would like to analyze the extent to which human risk estimation affects the spread of HIV through sexual transmission. We have used game theory to build a simulation in which every sexual encounter is a game, and we separate the population into those who get regularly tested and those who rarely get tested for infection. The type of game played depends on the knowledge available to the players. The overall mathematical model becomes a Markov process; the simulation was implemented in MATLAB. We will analyze sensitivity to parameters such as individual utility of sexual contact and risk estimation, as well as frequency of testing for infection. This model could provide insight into design of public awareness campaigns, to incorporate the impact of risk estimation on behavior and resulting exposure. In collaboration with Dr. Fefferman and Dr. Amira Kebir