A stochastic programming model of vaccine preparation and administration for seasonal influenza interventions

Sheng-I Chen; Chia-Yuan Wu; Sheng-I Chen; Chia-Yuan Wu

doi:10.3934/mbe.2020169

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 2984-2997. doi: 10.3934/mbe.2020169

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A stochastic programming model of vaccine preparation and administration for seasonal influenza interventions

Sheng-I Chen ^,,
Chia-Yuan Wu

Department of Industrial Engineering and Management, National Chiao-Tung University, 1001University Road, HsinChu, 30010, Taiwan

Received: 26 November 2019 Accepted: 10 March 2020 Published: 31 March 2020

This study considers the integration of vaccine preparation and administration decisions for seasonal influenza interventions. We examine actual vaccination activities of sharing multiple vaccine products and supplementary vaccinations. A two-stage stochastic program is formulated to determine the optimal ordering and allocation of vaccines under uncertain attack rates, vaccine efficacies, and demands. We present an algorithm based on the sample average approximation and warm-start solution to solve the stochastic integer program with continuous random variables. Furthermore, the optimal solution for the deterministic model using the expected value is analyzed and obtained directly. Our analysis compares the deterministic and stochastic solutions to assess the impact of uncertainties on the immunization outcomes and costs. The result shows that the stochastic programming model provides a more robust solution than the deterministic model, and uncertain characteristics should consider when making public health decisions.
- seasonal influenza,
- vaccination activities,
- stochastic integer programming,
- sample-average approximation
Citation: Sheng-I Chen, Chia-Yuan Wu. A stochastic programming model of vaccine preparation and administration for seasonal influenza interventions[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 2984-2997. doi: 10.3934/mbe.2020169

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Abstract

This study considers the integration of vaccine preparation and administration decisions for seasonal influenza interventions. We examine actual vaccination activities of sharing multiple vaccine products and supplementary vaccinations. A two-stage stochastic program is formulated to determine the optimal ordering and allocation of vaccines under uncertain attack rates, vaccine efficacies, and demands. We present an algorithm based on the sample average approximation and warm-start solution to solve the stochastic integer program with continuous random variables. Furthermore, the optimal solution for the deterministic model using the expected value is analyzed and obtained directly. Our analysis compares the deterministic and stochastic solutions to assess the impact of uncertainties on the immunization outcomes and costs. The result shows that the stochastic programming model provides a more robust solution than the deterministic model, and uncertain characteristics should consider when making public health decisions.

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