If you are interested in receiving a copy of any of my articles, please email me at dan...@gmail.com.
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Predicting HIV treatment outcomes
The growth and spread of a viral infection within an individual follows well-defined mathematical rules. I am working to analyze these rules to understand and predict outcomes of proposed cures as well as combination antiretroviral drug regiments. Computer simulations of the infection can help us predict long-term outcomes from easily measurable short-term consequences of treatment. Perhaps a cure for HIV is possible?
Hill, Rosenbloom, Fu, Nowak & Siliciano (PNAS, 2014): Simulated clinical trials of HIV cure therapies can help predict outcomes of these exciting new treatments. Cure therapies must contend with the reservoir of latent provirus that is not susceptible to current treatment.
- Rouzine, Razooky & Weinberger (PNAS, 2014): A review of our article, highlighting important unknowns about how viral clones grow out of cells that have recently activated from the latent reservoir.
-  Nature Medicine News on this and other work presented at CROI 2013 (Non-paywall version).
- Ho et al. (Cell, 2013): This article contends with understanding the size of the latent reservoir, which is believed to be the primary barrier to a cure.
Rosenbloom, Hill, Rabi, Siliciano & Nowak (Nature Medicine, 2012): A mathematical model of HIV infection dynamics with fluctuating drug concentrations. Extension of this model may be used to personalize treatment (Presentation at Adherence 2013).
Hill, Rosenbloom & Nowak (Journal of Molecular Medicine, 2012): Review of HIV evolution, with a section on understanding and modeling the spread of drug resistance.
Related work by others:
- Siliciano & Siliciano (Curr. Opin. Virology 2013). HIV drug resistance is receding in patients on top-line therapy, but puzzles remain about ongoing viral replication and treatment failure.
- Shen et al. (Nature Medicine 2008), Sampah et al. (PNAS 2011), Jilek et al. (Nature Medicine 2012). Data on the effectiveness of different drug regimens as well as the strengths of various resistance mutations.
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Investigating viral evolution using computational topology
Recombination is a major force in the evolution of HIV and other pathogens. This mode of evolution enables the rise of new virus strains that can challenge the immune system and resist drugs. Yet recombination greatly complicates evolutionary histories of viral populations, making it difficult to study. In particular, it is difficult to measure recombination when it occurs between closely related viruses, as can happen, for instance, during the course of a chronic viral infection. We are using new mathematical tools, based on the rapidly advancing field of topological data analysis, to tackle this problem.
Emmett, Rosenbloom & Rabadan (ICML 2014). Using coalescent models, we can detect recombination that occurs in influenza populations, both between distantly-related parents (inter-strain recombination), and closely-related parents (intra-strain recombination).
Related work: Chan, Carlsson & Rabadan (PNAS 2013). Proposes a topological method for studying viral recombination and provides a fundamental theorem justifying this method.
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Evolution of high mutation rates under "rock-paper-scissors" and other types of competition
Populations sometimes evolve extraordinarily high mutation rates -- for instance, E. coli lab strains often give rise to "hypermutator" lineages that can more quickly adapt to novel conditions. In some situations, high mutation rates may be particularly important for pathogens' ability to adapt to host defenses.
When will a population's mutation rate evolve upwards, and when will it decrease? By using the frameworks of evolutionary game theory and adaptive dynamics, we can explore how "rock-paper-scissors" competitive interactions favor high mutation rates, while "stable" interactions favor low rates.
Allen & Rosenbloom (Bulletin of Mathematical Biology, 2012): This article introduces our theoretical framework for studying the evolution of mutation rates, and we explore a curious scenario in which two different mutation rates can coexist indefinitely.
Rosenbloom & Allen (American Naturalist, 2014): This article further explores our model of mutation rate evolution, showing how cyclical competition leads to an evolutionarily stable mutation rate and describing particular biological scenarios.
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Epidemiology and the spread of vaccination through social groups
When many individuals in a population are vaccinated, even those who forego vaccination can be protected, by "herd immunity." Yet this population-wide protection is fragile: after a vaccination program has been successful for a long time, individuals may forget the painful consequences of the disease itself and neglect to vaccinate. Worse still, personal anecdotes about perceived negative consequences of vaccination can lead to "vaccine scares." This behavior can lead to the decay of herd immunity and subsequent disease outbreaks, after which self-interested individuals again may choose to vaccinate. I am interested in understanding the patterns behind this cycle of vaccination and disease outbreak.
Fu, Rosenbloom, Wang & Nowak (Proceedings of the Royal Society B, 2011): This article offers a simple model of seasonal influenza epidemics and vaccination in social groups. When individuals use anecdotal accounts from their neighbors about flu prevalence and success of vaccination, herd immunity can break down quickly.
- University press release: Harvard Gazette
- Other information: Wikipedia
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