So worse case of two T-Cells

They can bounce around, each spinning at its rate, and after 35 bounces around the virus, they hit pay dirt.  Macrophage is eating any of the small objects, which is the urgency. So what is the distribution of five-seven sequences on the typical virus ball? Why ae the T-cell paris likely to find a soltuion on this ball vs others? What is the probability that a seven rate Poisson has one update pending?  Very small.  Ditto for five.  So if the five seven sequence was unique, the ball has larger N, approaching flat Poisson.  So let us assume the solution not unique.    The total variety of edible available in he blood stream cannot be that complex.     T-cells needs to kill more virus than good stuff. Add terms to the markov, xyz, zx^2 zy^2.   Rework the Poinsson approximation with a different equation polynomial degree two. Floor the solution to select ratios.  The value,k, in Poisson, the expected number in the queue, has more values, known from above. Change therelatived  concentrations to reflect the choice. But we can see the resolution, or compression losses, have gone by by three approximately. Bu we still run a three counter. Z goes up, it carries arbitrage.
The trade is to get the virus before the macrophage eats everything..

We re still dealing with power of two.  There is not 23^5 power. There is a possible 400 arrangements of five seven sequences available before path merging. There is really four times that because the pacrophage have lowered resolution globally.  But with N increasing in the Poisson sense, we can set the ratio such that the duplicates match the targeted virus ratio, moment matching. We will most likely kill off excess virus than excess good stuff.

Then we let N go to the exact count of the virus ball, known to some close approximation.   The two white cell loads in the proper concentration will count the virus without duplicates, except deletions.  The stable pairs will tend to congregate on the virus surface, to minimize cost of cytokine.  The doc can set absolute concentration by checking for loose T-cells.