# How many macrophages does it take to kill a virus?

Some organisms move around more or less at random, so we can use diffusion to "model" how these cells move. This works fine, as long as you accept the assumption / simplification that these organisms are mindless little robots that walk around changing directions randomly. Sometimes this is a reasonable concession to make in exchange for the simplicity and power of the diffusion model, other times it is not. It’s a choice that you, the person implementing the model, need to make.

Here is an example of using diffusion to model a cell moving (adapted from Essential Mathematical Biology by N. F. Britton):

The macrophage is a specialized cell that defends that body against foreign materials. Within the lungs, macrophages engulf inhaled viruses and digest them. Macrophages move in a way that is very similar to diffusion – they ooze along at a stately 3 micrometers per minute, but change directions more or less randomly about every 5 minutes.

### Consider an alveolus (diameter = 300 micrometers) that contains a single macrophage and a single virus. Assume the phage and virus start at opposite ends of the cell and the phage moves in a straight line (not similar to diffusion) towards the virus. How long will it take for the phage to arrive?

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• I need a hint ... : Remember from physics:

speed = distance / time!

• ...another hint ... : Moving that equation around....we get:

time = distance / speed!