Example 9.2.5 of the textbook continues with our model of SARS from Example 9.1.12 (also see the associated BB material on this website). Recall that the basic reproduction number R0 is an important quantity in mathematical models of infectious diseases because any intervention that can reduce R0 below 1 will eradicate the disease. Thus, all else equal, public health officials usually want to invest in interventions that cause the greatest reduction in R0. As this example of the textbook shows, we can assess the effectiveness of an intervention for reducing R0 by calculating the partial derivative of R0 with respect to the variable representing this intervention (Glasser 2008).
References
Glasser, J.W. 2008. Clinical and public health applications of mathematical models, pp. 129-165 in “Mathematical Understanding of Infectious Disease Dynamics” S. Ma and Y. Xia (eds.). Volume 16 of Lecture Note Series, Institute for Mathematical Sciences, National University of Singapore.