# You need a lot of macrophages - or one smart one!

So. It would take about an hour and a half for the phage to meet with and
devour the hapless bacteria. Except that the phage does ** not**
ooze in a straight line. Instead it goes in a variety of random-looking directions,
resulting in a diffusion coefficient of 11 micrometers

^{2}/ minute. Therefore, the real time to viral annihilation is more like:

### Assuming that the phages movement is similar to diffusion, how long will
it take the phage to reach the virus (on average) ?

D = 11 µm^{2}/min. Distance = 300 µm

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- I need a hint ... : (300 µm)
^{2}/ (2*11 µm^{2}/min) =

4500 min

#### I think I have the answer: About 3 days.

Three days is too long to wait around getting rid of a cold!

You might say that this calculation is not realistic – even a phage does
not move completely at random. And you would be right, the phage can home in
on the virus to some extent (called chemotaxis).** Nevertheless, this simple model
points out something important:**

- either you need many phages
- or the phages need to be able to direct themselves towards the viruses.

As it happens, the answer in this case is a little of both.

**There are many other systems, particularly in ecology, that use diffusion as
a simple model of organismal movement. **The organisms modeled include **trees** (which
“move” via seed dispersal), **insects**, and even larger animals like
muskrats. Diffusion is one way that biologists are looking at the likely effects
of large-scale stressors like global warming – can oak trees disperse
north fast enough to escape the pressures of a warmer world? However, these
models are mathematically more complicated than the diffusion we have been talking
about: the organisms do not only move around, they also reproduce.

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