# Compound interest cure

So I guess I never got around to summarizing our paper published last year in Scientific Reports (PAPER). The paper was a long time in the making. It began as a project with my colleague Elizabeth Duke, and was inspired by an idea of our good friend Florian Hladik and our advisor Josh Schiffer. Florian’s idea was that because many other folks think HIV is persisting due to proliferation of latently infected cells, it might be a reasonable curative strategy to give patients who are already suppressed on HIV antiretroviral therapy some form of an anti-proliferative agent. Seems simple enough, but to the best of our knowledge, it has never been tried quite like this. There are some papers from the literature where an anti-proliferative drug was given to HIV patients, and these papers even show that perhaps this decreased the reservoir size (see Chapuis et al. Nat Med 2000 and García et al. AIDS 2003). But, those experiments were done before a real understanding of the reservoir existed, and there was certainly no mention that proliferation of latently infected cells was the mechanism that the drug was preventing. SO, in that context, Liz and I began developing a model to describe the slow disappearance of the latent reservoir that included cellular proliferation. It turns out such a model can really just be seen as an exponential decay of the size of the latent reservoir $L=L_0e^{\theta_L t}$ where we can then think about the rate $\theta_L$ as being made up of some combination of birth and death rates. This is where compound interest comes into play. If you are familiar with introductory finance, you will recognize the exponential formula as that of continuously compounding interest.

Huge digression on finance, skip on if you like: Continuous compounding interest arises when interest is constantly reinvested. It has massive implications for amassing wealth. For example, investing some amount in a fund with a 1% interest rate (Ally bank has a perfect savings account for this incidentally) would result in a 1.1x multiple of your wealth after 10 years. 30 years, 1.35x. Now, as that rate climbs, this roughly linear relationship (remember $e^{x}\sim1+x+x^2/2!+\ldots$) begins to be massively nonlinear. The same 10 years but a 10% interest rate (MAYBE doable with the S&P500) would admit a 2.7x gain, and 30 years a 20x gain. Start with 50,000\$, well that makes you a millionaire in 30 years. Human intuition struggles with this kind of function, as I mention in a previous post about nonlinear science, our brains don’t seem to get how steep this function really is. Paying credit card interest does the exact same thing in taking your money. It really pays to try to understand this concept in personal finance. Einstein even purportedly said “compound interest is the 8th wonder of the world, those who understand it earn it, those who don’t pay it”.

So, even though we have trouble understanding the exponential function, we at least are familiar with it enough to know that changing the rate is far more valuable than changing the principal amount. This was the intuition behind our paper, let’s change the proliferation rate by applying a medication continuously, and the payoff in terms of HIV reservoir reduction is fast and impressive. See the paper for many quantitative predictions, but the important thing for us is that this paper generated enough attention to allow us to get a clinical trial funded by the American Foundation for AIDS Research (AmFAR). We are currently enrolling participants and administering MMF, a clinically approved cancer drug. If the trial works at all, it will be a fantastic contribution to HIV research, especially because the legwork of getting a drug FDA approved is so hard and using a pre-approved drug short cuts that massively.

There is so much more on HIV persistence and particularly cell proliferation as a mechanism for HIV persistence that I won’t address here, but please see the work of Sarah Palmer, Thor Wagner, Lisa Frenkel, Jim Mullins, Frank Maldarelli, Alison Hill, Bob Siliciano and many others I’m probably forgetting right now.