Stopping the Coronavirus puzzle [closed]

Claim: On an $n$ by $n$ grid, if there are fewer than $n$ squares initially infected, then the infection will not spread to the entire region.

Define a edge of a square to be a frontier edge if one side of the edge is infected but the other side is uninfected. (The region outside the entire $n$ by $n$ grid is considered to always be uninfected.)

Key lemma: As the infection propagates, the number of frontier edges can never increase.

Proof of key lemma: Whenever the infection spreads to a new square, then at least two of its neighbors was already infected, hence you lose at least two frontier edges and gain at most two. End of proof.

Proof of claim: Suppose the infection spreads to the entire region. At that time, the number of frontier edges is $4n$ (the entire outer edge of the board). By the key lemma, the number of initial frontier edges must be at least $4n$. Therefore, there must have been at least $n$ initial squares infected. Put another way, if there were fewer than $n$ squares initially infected, then the infection will not propagate to the entire region.

(By the way, there are many initial configurations of size $n$ that lead to the whole board becoming infected, not just the diagonals.)