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

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 ( ${\tilde{R}}_1$, ${\tilde{R}}_A$), 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.