Dynamic Modeling and Control of Biomedical Systems - Avoiding the Cure Being Worse Than the Disease

Optimization-based control strategies, such as Model Predictive Control (MPC), are today a leading paradigm for addressing a range of critical biomedical problems that include COVID-19, both at the cellular and epidemiological level, HIV, tuberculosis, Type 1 Diabetes Mellitus, and even cancer and antibiotic resistance.

The standard approach to determining optimal interventions—essentially, the most effective way to adjust the controllable parameters of models over time—is to use a set of ordinary differential equations (ODEs) and formulate an optimal control problem aimed at minimizing or maximizing certain key variables. However, modeling real biomedical systems is much more complex than simply setting up a system of equations and an associated optimal control problem. Modeling real-world scenarios requires fully understanding them, which includes characterizing equilibria, invariant regions, and their stability, while also considering realistic constraints on both variables and parameters.

This characterization is, in fact, a core part of the optimization process, as it helps define objective functions and constraints that are consistent with the real-world phenomena we aim to influence. Without this kind of formal analysis, an optimal control problem would be incomplete—inevitably leading to ineffective or even counterproductive interventions, as the recent COVID-19 pandemic has tragically shown.

In this talk, we will review the dynamic characterization and control of some biomedical problems, both at the epidemiological and cellular levels. The goal is to identify appropriate interventions (both pharmaceutical and non-pharmaceutical), using formal procedures, adhering to realistic conditions, and—whenever possible—avoiding a situation where the cure is worse than the disease.