Viral Burst
Viruses infect cells, and hijack the machinery of the cell to create new virons. The burst size is defined as the number of virons created when a cell finally bursts to release the accumulated virons.
Incredibly, the burst factor is on the order of $10^2..10^5$ in multicellular hosts - which gives a new grounding to the term “going viral:”
- We established in cellular muatation that there are on the order of $10^{13}$ cells in the body, with a volumetric argument and a weighted-sum argument by cell type.
- If every viron emerging from a bursting cell, could burst another cell with the same burst factor, it would take somewhere between 3-6 rounds of bursting to destory every cell in a typical human.
Further, there is even more headroom for the burst factor to grow, considering just 2-5% of the host cell’s volume becomes dedicated to housing the virus.
Of course, getting the flu (for example) doesn’t typically end in the destruction of every cell in the body within a matter of hours, so there must be some powerful, negative feedback to counteract such a jaw-dropping growth factor. Here are some dynamics on the viron population $V$, as a function of time:
| Phenomenon | Feedback on $\frac{\mathrm{d} V}{\mathrm{d}t}$ | Description | Viral Work-around |
|---|---|---|---|
| Burst Factor | $V$ | The more virons, the more bursting possible. | (Working as intended) |
| Immune Response | $-V$ | The more virons, the better the immune response | Attack the immune system (HIV), slow incubation time |
| Passivity | $-k$ | Viruses can’t move; at $10^{-8}m$ OoM, they’re 100x-1000x smaller than e. coli. flagella. | Infect high-movement cells, like blood |
| Removal Rate | $-\beta \times V$ | Viruses have a fixed lifespan; they will die off at a scale-invariant rate $\beta$. | Live longer, become latent |
| Limited Cell Domain | $-V$ | Viruses tend to infect some cells better than others; once the preferred cell type is exhausted, there may be significant friction to further expansion. | Adapt to many cell types (SARS-CoV-2) |
| Local Exhaustion | $-V$ | Too many virons in a small region causes competition, leading to predator-prey dynamics that ultimately “starve” many viruses (e.g. they infect the same cell, destroy too many cells, ..). | Respiratory system allows easy escape/spread to fresh, unsaturated hosts |