Artificial intelligence-driven stability-constrained optimum control of phylodynamic systems with Hopf bifurcations
Document Type : Original Article
Authors
- 1 Chemical Engineering Department, University of Puerto Rico, Mayaguez, Puerto Rico
Abstract
Background: Phylodynamic systems combine epidemiological dynamics and pathogen evolution, and they can display complicated nonlinear characteristics such as oscillations and instability. Hopf bifurcations are particularly interesting because they represent the shift from stable disease dynamics to long-term epidemic cycles.
Methods: In MATCONT, a continuous phylodynamic susceptible-infected-recovered model with adaptive pathogen evolution was examined through numerical continuation. Computing the maximum real part of the Jacobian eigenvalues yielded a stability dataset from equilibrium branches. A feedforward neural network was trained to approximate this stability measure and then integrated into a Pyomo-based optimum control formulation. The dynamic optimization problem was handled utilizing orthogonal collocation and nonlinear programming.
Results: Bifurcation analysis revealed a Hopf bifurcation point at (0.126448, 1.543549, 7.016131, 0.085120, 0.842161). The first Lyapunov coefficient was -3.41 × 10⁻², indicating a supercritical Hopf bifurcation and the formation of a stable limit cycle. The neural network surrogate successfully approximated the stability boundary, allowing stability information to be included in the optimization problem without requiring explicit eigenvalue calculations. The stability-constrained optimum control formulation yielded an objective value of around 0.0787, which represents the cost of maintaining stability while meeting disease-control objectives.
Conclusion: The proposed framework combines bifurcation analysis, artificial intelligence, and optimum control to create a coherent technique for phylodynamic systems. By punishing trajectories that approach instability, the strategy produces dynamically stable control policies that restrict oscillatory behavior while lowering infection levels. The framework offers a practical way to managing changing infectious illnesses while maintaining stability.
Methods: In MATCONT, a continuous phylodynamic susceptible-infected-recovered model with adaptive pathogen evolution was examined through numerical continuation. Computing the maximum real part of the Jacobian eigenvalues yielded a stability dataset from equilibrium branches. A feedforward neural network was trained to approximate this stability measure and then integrated into a Pyomo-based optimum control formulation. The dynamic optimization problem was handled utilizing orthogonal collocation and nonlinear programming.
Results: Bifurcation analysis revealed a Hopf bifurcation point at (0.126448, 1.543549, 7.016131, 0.085120, 0.842161). The first Lyapunov coefficient was -3.41 × 10⁻², indicating a supercritical Hopf bifurcation and the formation of a stable limit cycle. The neural network surrogate successfully approximated the stability boundary, allowing stability information to be included in the optimization problem without requiring explicit eigenvalue calculations. The stability-constrained optimum control formulation yielded an objective value of around 0.0787, which represents the cost of maintaining stability while meeting disease-control objectives.
Conclusion: The proposed framework combines bifurcation analysis, artificial intelligence, and optimum control to create a coherent technique for phylodynamic systems. By punishing trajectories that approach instability, the strategy produces dynamically stable control policies that restrict oscillatory behavior while lowering infection levels. The framework offers a practical way to managing changing infectious illnesses while maintaining stability.
Keywords
Phylodynamics
Hopf bifurcation
optimal control
artificial intelligence
Neural Networks
Stability analysis
Puerto Rico