Sorry, maybe we're all making this too difficult. "Increase" is fine.
For me, bacili is an unusual word - it isn't used in everyday conversation. It is correct and valid, but it doesn't come into my daily conversation. When I read your sentence "a" I skim over the word bacilli, not immediately realizing it is the plural of bacillus. Then, when I get to the verb "increase" it seems strange. It almost looks like it goes with the word "straw", so in my mind I think, "what is a straw increase"? . I have to reread the sentence to understand that increase goes with bacilli.
Paradoxically, changing it to "increases" solves this problem. In my mind I immediately realize it is linked to the word bacilli - even though it is in conflict with the plural word bacilli. I think maybe Wonko and I are in agreement on this. It sounds right, but it is, in fact, wrong (as Indojindesu correctly pointed out).
Regarding the word multiply, it seems to be more appropriate when talking about propagation, breeding, procreation, etc... Maybe it feels more appropriate because it hints at exponential increase, rather than a simple addition, or linear increase. So when you are talking about bacteria, you are probably talking about exponential increase, rather than just the addition of one or two bacterium.