Reproduction number of a SIR model with mortality
The only answer that makes numerical sense is 1. The product of two rates beta and delta (recovery * death) doesn't mean anything in SIR. And in answer three you're doubling the rate of infection (alpha). Looking at the other way, for R_0 it doesn't matter how people leave the Infected class, once you're either dead or recovered you no longer are transmitting the disease. Therefore you can say that some value Zeta is the exit from Infected class and Zeta would be the sum of all rates which remove a person from being Infectious