Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries

Morganne Igoe; Renato Casagrandi; Marino Gatto; Christopher M Hoover; Lorenzo Mari; Calistus N Ngonghala; Justin V Remais; James N Sanchirico; Susanne H Sokolow; Suzanne Lenhart; Giulio de Leo

doi:10.1007/s11538-023-01137-4

Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries

Bull Math Biol. 2023 Mar 12;85(4):31. doi: 10.1007/s11538-023-01137-4.

Affiliations

¹ Department of Mathematics, University of Tennessee, Knoxville, TN, USA. migoe@utk.edu.
² Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy.
³ Division of Environmental Health Sciences, University of California, Berkeley, Berkeley, CA, USA.
⁴ Department of Mathematics, University of Florida, Gainesville, FL, USA.
⁵ Environmental Science and Policy, University of California, Davis, Davis, CA, USA.
⁶ Stanford Program for Diseases Ecology, Health and the Environment, Stanford University, Pacific Grove, CA, USA.
⁷ Department of Mathematics, University of Tennessee, Knoxville, TN, USA.
⁸ Department of Earth System Science and Department of Oceans, Hopkins Marine Station, Stanford Doerr School of Sustainability, Stanford University, Pacific Grove, CA, USA.

Abstract

Optimal control theory can be a useful tool to identify the best strategies for the management of infectious diseases. In most of the applications to disease control with ordinary differential equations, the objective functional to be optimized is formulated in monetary terms as the sum of intervention costs and the cost associated with the burden of disease. We present alternate formulations that express epidemiological outcomes via health metrics and reframe the problem to include features such as budget constraints and epidemiological targets. These alternate formulations are illustrated with a compartmental cholera model. The alternate formulations permit us to better explore the sensitivity of the optimal control solutions to changes in available budget or the desired epidemiological target. We also discuss some limitations of comprehensive cost assessment in epidemiology.

Keywords: Epidemiological management goals; Optimal control of differential equations.

Publication types

Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

Cholera / epidemiology
Cholera / prevention & control
Cholera / therapy
Developing Countries
Humans
Infections* / therapy
Treatment Outcome