Saturday, October 3, 2009
Anderson and May
I know this paper is old, but it covers a lot of the basic ideas of HIV epidemiology and illustrates some of the ways of estimating parameters from data. Comments/questions please. Along with your question, also please provide a tentative idea for a project on dynamics -- the easiest things would be to work on an aspect of HIV dynamics in vivo or an epidemiological project, but you are also welcome to work on a topic from any area of biology, provided that it seems feasible to set up a simple model in Excel within the time frame of a few weeks (project presentations in class on October 21). You will be working in groups of 2 to 4.
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Anderson/May discussion:
ReplyDeleteI don't understand Figure 5. I'd really like to take some time to talk about gamma distributions in class. I'm just flat out struggling to follow the logic used to characterize the gamma distribution in fig 5. (see p.140 3rd paragraph).
project idea for modeling:
I'd like to work on developing a model to explore the affects of premature immunosenescence in HIV patients. The Yates paper gave us a foundational framework for CD4 T-cell dynamics and showed that immunosenescence (cell exhaustion) could play an important role in the slow progression towards AIDS. A search of the literature on immunosenescence and HIV yielded many sources for additional parameters and parameter values that could improve the Yates model.
Hey all,
ReplyDeleteI'm with Tim on Figure 5- I need some help understanding what these values of CV represent.
Also, I found the idea of highly sexually active individuals being 'weeded' out early on in the epidemic really interesting too- pg. 140, middle of the first column. That makes a lot of sense to me, that those who are most vulnerable, and also, pass along the disease most efficiently, die off fairly early on because they get infected early, while those who have fewer partners and live a more conservative lifestyle may be important over the long term in progressing the epidemic at a slower rate.
As a potential project, I was thinking about gender dynamics in the disease and how they differ in Africa compared to the UK and US. Maybe more specifically, how HIV transmission to babies differ in these two groups because of the differences in HIV prevalence in females. So, I am still a little vague about what I would have in each of the boxes in this model, but I'm interested in the population-level dynamics.
Christine
Anderson and May, 1987:
ReplyDeleteI am also slightly confused by Figure 5--Does this mean that as the variance in sexual activity decreases and the mean in sexual activity increases, the spread of infection through the population increases at lower Ro? If so, is this simply showing that sexual activity can offset the reproductive rate of the infection?
I also find myself more confused on what Ro is after reading this paper. I noticed that Ro was referred to as both the "net transmission of the virus" and the "net reproductive rate of the virus" (top right, page 140). Isn't this referring to two different values? I thought Ro was simply the amount of cells that are infected by a single infected cell, not whether these cells are transmitted to another person....
For a modeling project, I would be interested in shifting gears toward community ecology. I would like to construct a model that looks at how abiotic conditions are related to grazing/predation pressure. More specifically, if I can find sufficient data, I would like to look at how nutrient concentrations stimulate epiphye growth and, in turn, grazing pressure in seagrass meadows and how such epiphyte grazing affects seagrass abundance. However, since we are working in groups, I would be interested in modeling ideas on other topics in population/community ecology...
-Mike
It seems that everyone in this blog has problems with fig 5; Is CV not the a part of the rate of activity?. If that is true, why is the the Curve at CV=0 have a fraction of 1, I would predict, the opposite
ReplyDeleteFig 6 b is also problematic to understand. It tells you that the incidence per year will drop after 20 years. How is that possible?
Iwan
@Iwan: because we have run out of susceptible people, or at least depleted the pool somewhat, so we can't sustain an epidemic as large as the initial HIV epidemic.
ReplyDeleteWe can certainly spend time discussing gamma distributions and Figure 5. The basic idea is that with the mean contact rate held constant, increasing variability increases R0 but *not* (much) the total number infected: thus, holding R0 and mean contact rate constant decreases the total number infected.
How did they arrive at their calculation of the doubling time (td=(ln 2)/A)? (Middle column, p. 138) Also, on p. 142 (middle column) they mention that "the epidemiologically relevant quantity is not the mean number of new partners but, rather, the mean-square divided by the mean." Was this incorporated into the model anywhere? My best guess is that this is what they were aiming for in equation 2 (p. 137).
ReplyDeleteI'd also be interested in modifying the model in Yates et al. 2007 with the goal of predicting the decline of CD4+ cells better. In particular, how will predictions about the rate of CD4+ T-cell decay vary if parameters (such as a [the rate of resting cell division] and lambda [the virion production rate]) are allowed to vary around a mean, OR decay as the CD4+ population decreases?
Hi all!
ReplyDeleteI believe that CV in figure 5 could represent the variation respect sexual activity. Because both the "monogamous" and "non-monogamous" group or people could be infected by HIV. It is fascinating to show due to that behavior the rate of infection never will be minor than 1.
In general, I wonder how models could represent the biological mechanisms. Even though how the biologic mechanisms could be mathematically modeled. This question emerges from the fig 6, The prediction shows that there isn´t any people below 10 years old that could be seropositive. In the present time we now that any people in the world could be HIV infected.
that is all for now!
See you guys!
For the modeling project: I would like to work a simple model about the dynamics of gene expression for measuring the performance of a phenotype.
ReplyDeleteFor the modeling project, I would like to use a SIRS model to explore the dynamics of avian influenza in wild bird populations. It is a latent threat to bird communities and humans, but it has been sparsely explored.
ReplyDelete