Optimal long-run control of endemic infections: bang-bang threshold policies in a stochastic SIS model
Abstract
We study long-run optimal intervention strategies for endemic infections in a stochastic susceptible-infected-susceptible (SIS) model. The proportion of infected individuals evolves as a diffusion process with random fluctuations, while a control variable ζt∈[0,ζ̃max] represents the intensity of public health interventions that reduce transmission for some intervention threshold ζ̃max∈ (0,1]. The objective is to minimize the long-run average societal cost, balancing the burden of infection against the costs of interventions. Under a concave intervention cost structure the problem can be formulated as an ergodic stochastic control problem, whose structure implies (under certain additional conditions) that optimal interventions are of bang-bang type, switching between no intervention and the maximal admissible intervention at a single switching threshold in the infection level. We construct candidate value functions, rigorously verify optimality in this single-threshold case, and relate the results to extinction and persistence properties of the underlying SIS dynamics in the absence of control. In our framework, the analysis provides a rigorous justification for the threshold-based intervention rules commonly used in epidemic management.
Related
- Stochastic Decision Policy Is Optimal Under Costly Control
- Stochastic Procrastination and Optimal Task Division
- Phenology-driven dynamic threshold iot control for hydroponic garlic sprout production
- Optimal Control of Vaccine Therapy in a Tumor-Immune-Vaccine Model for Pituitary Neuroendocrine Tumors
- Antibiotic Exposure and Risk of MDR Urinary Tract Infections: A Case-Control Study
BibTeX
@misc{buckland2026optimal,
title = {{Optimal long-run control of endemic infections: bang-bang threshold policies in a stochastic SIS model}},
author = {Matthew Buckland and Sören Christensen and Philip Le Borne and Cornelia Pokalyuk},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05495},
eprint = {2609.05495},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05495},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Optimal long-run control of endemic infections: bang-bang threshold policies in a stochastic SIS model
AU - Matthew Buckland
AU - Sören Christensen
AU - Philip Le Borne
AU - Cornelia Pokalyuk
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.05495
UR - https://arxiv.org/abs/2609.05495
AB - We study long-run optimal intervention strategies for endemic infections in a stochastic susceptible-infected-susceptible (SIS) model. The proportion of infected individuals evolves as a diffusion process with random fluctuations, while a control variable ζ_t∈[0,ζ̃_max] represents the intensity of public health interventions that reduce transmission for some intervention threshold ζ̃_max∈ (0,1]. The objective is to minimize the long-run average societal cost, balancing the burden of infection against the costs of interventions. Under a concave intervention cost structure the problem can be formulated as an ergodic stochastic control problem, whose structure implies (under certain additional conditions) that optimal interventions are of bang-bang type, switching between no intervention and the maximal admissible intervention at a single switching threshold in the infection level. We construct candidate value functions, rigorously verify optimality in this single-threshold case, and relate the results to extinction and persistence properties of the underlying SIS dynamics in the absence of control. In our framework, the analysis provides a rigorous justification for the threshold-based intervention rules commonly used in epidemic management.
ER -