Quantitative Guidelines for Communicable Disease Control Program: A Complete Synthesis
Biometrics, 30(4), Dec. 1974, 681-691; a detailed Abstract in Statistical Theory and Method Abstracts, 1975
Posted: 5 Jun 2020
Date Written: 1975
Abstract
This paper considers an optimal-control problem for the dynamics of an epidemic spread, the optimal control being the level of medical program effort to achieve a terminal number of infectives within specified limits in a way that minimizes the present value of the social and medical costs over a finite horizon. First, the special polar cases of fixed and free-end points are solved for large as well as small capability of the health delivery system in delivering the medical care. The complete solution to the general problem is then constructed from these polar cases. The fixed-end point case with sufficiently large capability of the health delivery system is solved by using Green's theorem, while the other cases require additional use of switching point analysis based on the maximum principle. The optimal control is characterized by a combination of bang-bang, impulse, and singular control, with the singular are forming a turnpike. It is shown that the turnpike behavior of the optimal control generalizes to short horizon and bounded control situations.
Keywords: Communicable Disease, Epidemic Spread, Infectives, Optimal Control
JEL Classification: J1, I1, C61
Suggested Citation: Suggested Citation