Optimally ending an epidemic. (4th March 2018)

• Record Type: Journal Article
• Authors: Lefebvre, Mario
• Is Part Of: Optimization. Volume 67:Number 3(2018)
• Page Start: 399
• Page End: 407
• Publication Date: 2018-03-04
• Subjects: Dynamic programming -- first-passage time -- Brownian motion -- partial differential equations -- method of similarity solutions; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1397147
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: A stochastic and controlled version of the classic three-dimensional Kermack–McKendrick model for the spread of epidemics is considered. The aim is to end the epidemic as soon as possible, taking the quadratic control costs into account. An exact and explicit solution is found in a particular case by making use of the method of similarity solutions to solve the partial differential equation satisfied by the value function, subject to the appropriate conditions.