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The COVID-19 pandemic highlighted the need to quickly respond, via public policy, to the onset of an infectious disease breakout. Deciding the type and level of interventions a population must consider to mitigate risk and keep the disease under control could mean saving thousands of lives. Many models were quickly introduced highlighting lockdowns, testing, contact tracing, travel policies, later on vaccination, and other intervention strategies along with costs of implementation. Here, we provided a framework for capturing population heterogeneity whose consideration may be crucial when developing a mitigation strategy based on non-pharmaceutical interventions. Precisely, we used age-stratified data to segment our population into groups with unique interactions that policy can affect such as school children or the oldest of the population, and formulated a corresponding optimal control problem considering the economic cost of lockdowns and deaths. We applied our model and numerical methods to census data for the state of New Jersey and determined the most important factors contributing to the cost and the optimal strategies to contained the pandemic impact.
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This content will become publicly available on March 19, 2026
Optimizing overlapping non-pharmaceutical interventions with a socio-demographic model
Abstract The effectiveness of non-pharmaceutical interventions (NPIs) during a pandemic is challenging to assess due to the multifaceted interactions between interventions and population dynamics. Significant difficulty arises from the overlapping effects of various NPIs applied to different subgroups within a population. To address this, we propose a new mathematical model that incorporates various intervention strategies, including total and partial lockdowns, school closures, and reduced interactions among specific subgroups, such as the elderly. Our model extends previous work by explicitly accounting for the quadratic nature of control costs and the interplay between overlapping controls targeting the same population segments. Using optimal control theory, we identify intervention policies that effectively mitigate disease transmission while balancing economic and societal costs. To demonstrate the utility of our approach, we apply the model to real-world data from the COVID-19 pandemic in the State of New Jersey. Our results provide insights into the trade-offs and synergies of different NPIs and the importance of accurately capturing the relationship between a policy and the population affected.
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- Award ID(s):
- 2033580
- PAR ID:
- 10644770
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Bollettino dell'Unione Matematica Italiana
- ISSN:
- 1972-6724
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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