Disease Spread - With Immunity

You are given an R×C grid that represents a population. Each cell can be in one of four states: Healthy (0), Infected (1), Recovered (2), or Immune (3). At time 0 you receive the initial configuration plus two integers N and M. Every minute the following happens in order:

1. Recovery & immunity – any cell that has been Infected for exactly N consecutive minutes becomes Recovered and immediately turns Immune (state 3). Immune cells can never be infected again and do not spread disease.
2. Infection – a Healthy cell becomes Infected if at least one of its four orthogonal neighbors was Infected at the start of this minute (Moore neighborhood is not used).
3. Increment time and repeat.

Write a function that returns the first minute at which every non-immune cell is Healthy, or –1 if the infection never dies out.