So if you are going to put in those controls in the model, how would you do it? My suggestion is to have a term multiply to beta. That term could consist of parameters informing the coverage and efficacy of the intervention. That term is taking the value between 0 and 1, for example we can say
let x be the effective coverage of needle sharing prevention scheme.
Let beta be the transmission rate of Hep C

(beta)(1-x) is updated transmission as a result of intervention