An introduction to optimal control with an application in disease modeling. (English) Zbl 1352.92164

Neilan, Rachael Miller; Lenhart, Suzanne

Gumel, Abba B. (ed.) et al., Modeling paradigms and analysis of disease transmission models. Selected papers based on the presentations at the U.S.-African advanced study institute on mathematical modeling of infectious desease in Africa, Muizenberg, South Africa, June 11–22, 2007 and the DIMACS workshop, Stellenbosch, South Africa, June 25–27, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4384-0/hbk). DIMACS. Series in Discrete Mathematics and Theoretical Computer Science 75, 67-81 (2010).

Summary: This paper serves as an introduction to the theory of optimal control applied to systems of ordinary differential equations with emphasis on disease models. We outline the steps in formulating an optimal control problem and derive necessary conditions. Several simple examples provide detailed methodology in characterizing the optimal control through use of Pontryagin’s maximum principle. An SEIR (Susceptible, Exposed, Infected, Recovered) model with control acting as a rate of vaccination is presented and an optimal control problem is formulated to include an isoperimetric constraint on the vaccine supply. Numerical results illustrate how such a constraint alters the optimal vaccination schedule and its effect on the population.
For the entire collection see [Zbl 1201.92038].

MSC:

92D30	Epidemiology
49N90	Applications of optimal control and differential games

Keywords:

optimal control; isoperimetric constraint; disease model