What is Antiviral drugs and vaccines?

Example 13.6 (HIV before and after the equations)

Until 1995 the years of clinical latency of HIV infection — a stable viral load of $10^{4}$–$10^{6}$ copies per millilitre and a slow fall of T cells — were read as a quiescent virus. Ho, Perelson and colleagues gave patients a protease inhibitor and fitted the decline of the viral load to the theorem: the fast phase gave $c \approx 3\,\mathrm{d}^{-1}$ (a virion half-life of about six hours), the slow phase $\delta \approx 0.5\,\mathrm{d}^{-1}$ (an infected cell lives about a day and a half). A steady load of $10^{5}$ per millilitre in $15\,\mathrm{L}$ of body fluid, cleared at $c$, therefore requires the production of about $10^{10}$ virions a day, every day, for years: the “latent” period is a furious steady state of infection and death, with the T cell pool replaced daily until it fails. The mutation arithmetic of the next section then follows at once, and with it the reason single drugs failed and three did not.

Example 13.9 (Why HIV needed three drugs)

HIV’s reverse transcriptase errs about once in $10^{5}$ nucleotides, so each $9700\,\mathrm{nt}$ genome copied carries about $0.1$ mutations, and $10^{10}$ new genomes a day carry $10^{9}$ mutations among them: every one of the $3\times 9700 \approx 30\,000$ possible single point mutations arises many times every day, before any drug is given. A drug that a single mutation defeats — as one mutation defeats most reverse-transcriptase and protease inhibitors — is therefore defeated within weeks, which is what happened to AZT in 1987. Two independent mutations arise together at $10^{-10}$ per genome, about once a day; three at $10^{-15}$, once in a thousand days — and a patient on three drugs whose load has fallen a thousandfold produces $10^{7}$ genomes a day, so the triple mutant never appears. That, and the theorem’s demonstration that the virus was replicating at full speed, made combination therapy from 1996 the treatment that turned AIDS into a chronic condition.