Basic Reproduction Number - Limitations of R₀

Limitations of R₀

When calculated from mathematical models, particularly ordinary differential equations, what is often claimed to be R₀ is, in fact, simply a threshold, not the average number of secondary infections. There are many methods used to derive such a threshold from a mathematical model, but few of them always give the true value of R₀. This is particularly problematic if there are intermediate vectors between hosts, such as malaria.

What these thresholds will do is determine whether a disease will die out (if R₀ < 1) or whether it may become endemic (if R₀ > 1), but they generally can not compare different diseases. Therefore, the values from the table above should be used with caution, especially if the values were calculated from mathematical models.

Methods include the survival function, rearranging the largest eigenvalue of the Jacobian matrix, the next-generation method, calculations from the intrinsic growth rate, existence of the endemic equilibrium, the number of susceptibles at the endemic equilibrium, the average age of infection and the final size equation. Few of these methods agree with one another, even when starting with the same system of differential equations. Even fewer actually calculate the average number of secondary infections. Since R₀ is rarely observed in the field and is usually calculated via a mathematical model, this severely limits its usefulness.