Modeling HIV Infections
One of the most popular mathematical modeling topics in immunology is that the slow crumbling (over the course of almost a decade) of the immune system in an HIV infected patient, specifically the decline of “helper T cells” (technically known as the CD4+ lymphocytes). There are many hypotheses about how and why this happens, but each model has difficulty explaining all aspects of the disease.
Recently, in PLoS Medicine, a cool mathematical model rules out one of the hypotheses, the “runaway” theory. In that model, helper T cells, which recognize infections and activate other cells in the immune system, keep getting destroyed because each T cell gets infected, which produces more HIV, and which activates more T cells, which get infected, and so on, like a grain of sand snowballing into a giant avalanche. The mathematical model captures the essence of the immunological processes, and although (Camelot!) it is only a model, the whole point was to show that, at least based on our current understanding of the immune system, the “runaway” hypothesis would predict T cells numbers to fall very quickly (in a few months), rather than taking many years to fall.
Strangely, they do not mention Martin Nowak’s pioneering work in HIV population dynamics, which is well summarized in a review article from Bioessays (D. Wodarz, M. A. Nowak (2002), Bioessays 24, p. 1178-87). I took a great mathematical evolutionary dynamics course from him last semester, and he walked us through the logic for his phenomenological model. Essentially, he hypothesizes that any specific form of HIV is hunted down by the immune system relatively quickly and destroyed, which can be seen by the sharp drop in a patient’s viral levels shortly after infection. The human body generates very specific T and B immune cells to hunt down that version of HIV. The problem is that HIV mutates so rapidly that new forms of HIV are constantly being evolved within the patient, and over time, as the immune system tries to generate more and more different versions of T and B cells to go after each of the different cell types, the immune system just stops being able to keep up with the evolutionary rate of the HIV virus. Eventually, the HIV just mutates fast enough that all the different versions, together, overwhelm the immune system and cause AIDS. Using some experimental estimates, Nowak actually simulated his model on a computer, and found that it reproduces the time course of the disease, the slow drop in helper T cell levels, and so on.
I find it interesting that even after all these years, people are still “discovering” this mechanism for HIV, who seem to be unfamiliar with Nowak’s work. These physicists from 2006, for example, seem to just reproduce Nowak’s work, and don’t cite him at all. Note that Nowak came up with his model in the mid-1990s, so it’s been almost ten years, and still his model gets missed!
