Exploring epidemic control policies using nonlinear programming and mathematical models

The useful part

Frost Optimal control theory in epidemiology has been used to establish the most effective intervention strategies for managing and mitigating the spread of infectious diseases while considering constraints and costs. Using Pontryagin's Maximum Principle, indirect methods provide necessary optimality conditions by transforming the control problem into a two-point boundary value problem. However, these approaches are often sensitive to initial guesses and can be computationally challenging, especially when dealing with complex constraints.

How it works

• However, despite their potential, the widespread adoption of these techniques has been limited.
• direct methods, which discretise the optimal control problem into a nonlinear programming (NLP) formulation, hold potential for automation and could offer suitable, adaptable solutions for real-time...
• Several factors may contribute to this challenge, including limited access to specialised software, a perception of high computational costs, or a general unfamiliarity with these methods.
• While indirect methods provide useful theoretical insights, direct approaches may be a better fit for the fast-evolving challenges of real-world epidemiology.

Details worth keeping

Through case studies, we demonstrate the use of NLP solvers to determine the optimal application of interventions based on single objectives, such as minimising total infections, "flattening the curve", or reducing peak infection levels, as well as multi-objective optimisation to achieve the best combination of interventions.