Modeling and optimal control of ADE-prone dual-strain influenza: balancing costs, risks, and interventions

Zongmin Yue; Yi Dong; Hui Cao; Zongmin Yue; Yi Dong; Hui Cao

doi:10.3934/era.2026195

Electronic Research Archive

2026, Volume 34, Issue 7: 4410-4447. doi: 10.3934/era.2026195

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Research article

Modeling and optimal control of ADE-prone dual-strain influenza: balancing costs, risks, and interventions

School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi'an 710021, China

Received: 30 January 2026 Revised: 20 April 2026 Accepted: 06 May 2026 Published: 22 May 2026

Antibody-dependent enhancement (ADE) is a major safety challenge in multiserotype disease control, involving complex trade-offs among infection burden, cost, and vaccine safety. This study develops a two-strain influenza model that integrates both host immunity (endogenous) and viral cross-reactivity (exogenous) as dual mechanisms underlying ADE. Threshold analysis shows that exogenous ADE lowers transmission thresholds ($ \widetilde{R}_{1} $, $ \widetilde{R}_{A} $), promoting strain coexistence, whereas endogenous ADE reverses this trend. We further establish a multiobjective optimal control framework to balance outbreak control, ADE risk, and intervention costs. The resulting strategy combines early targeted measures with sustained behavioral precautions (e.g., 51–79% mask-wearing compliance), effectively reducing the peak infection rate. Crucially, we identify an optimal risk-aversion level ($ \alpha \approx 2 $), which halves the ADE risk with only a 2.3% increase in infections and minimal extra cost—demonstrating a clear Pareto-optimal trade-off. This quantitative framework can be applied to other contexts, such as multivalent vaccine design for dengue fever, and provides a decision-making basis for risk-benefit assessment of vaccines against emerging infectious diseases.
- antibody-dependent enhancement (ADE),
- dual-strain influenza model,
- basic reproduction number,
- stability,
- optimal control
Citation: Zongmin Yue, Yi Dong, Hui Cao. Modeling and optimal control of ADE-prone dual-strain influenza: balancing costs, risks, and interventions[J]. Electronic Research Archive, 2026, 34(7): 4410-4447. doi: 10.3934/era.2026195

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Abstract

Antibody-dependent enhancement (ADE) is a major safety challenge in multiserotype disease control, involving complex trade-offs among infection burden, cost, and vaccine safety. This study develops a two-strain influenza model that integrates both host immunity (endogenous) and viral cross-reactivity (exogenous) as dual mechanisms underlying ADE. Threshold analysis shows that exogenous ADE lowers transmission thresholds ($ \widetilde{R}_{1} $, $ \widetilde{R}_{A} $), promoting strain coexistence, whereas endogenous ADE reverses this trend. We further establish a multiobjective optimal control framework to balance outbreak control, ADE risk, and intervention costs. The resulting strategy combines early targeted measures with sustained behavioral precautions (e.g., 51–79% mask-wearing compliance), effectively reducing the peak infection rate. Crucially, we identify an optimal risk-aversion level ($ \alpha \approx 2 $), which halves the ADE risk with only a 2.3% increase in infections and minimal extra cost—demonstrating a clear Pareto-optimal trade-off. This quantitative framework can be applied to other contexts, such as multivalent vaccine design for dengue fever, and provides a decision-making basis for risk-benefit assessment of vaccines against emerging infectious diseases.

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