I would like to do simulations using cellular automata to describe the behavior of influenza. What software do you recommend?
Well Mathematica provides a reasonable amount of intrinsic functionality for working with Cellular Automata. It's not an area of the system I have extensive experience of and I don't know how it compares with other software with similar functionality. You might learn more about it's CA capabilities before breaking open your piggy-bank (maybe digging into your trust fund too, Mathematica's not cheap) over at the sister site https://mathematica.stackexchange.com.
Beyond that, I'd have thunk that programming CA's isn't tremendously difficult in many programming languages.
You may want to try Ready https://gollygang.github.io/ready/ especially if you are going for continous valued/reaction diffusion/FDTD type systems:
Ready is a program for exploring continuous and discrete cellular automata, including reaction-diffusion systems, on grids and arbitrary meshes.
For discrete systems, hashlife is a great algorithm to be able to efficiently step through millions of iterations, especially if parts of the pattern just oscillate. It is implemented in Golly http://golly.sourceforge.net/
CellularAutomata.jl is a fairly efficient CA simulation package.