Parameter Estimation in Hybrid Machine Learning and Mechanistic Models of Infectious Diseases

Abstract

Infectious diseases are one of the biggest public health threats. The development of new avenues to integrate the complex interactions between pathogens and the host immune system is central to tackle outbreaks and pandemics. In the last two decades, mathematical modeling by differential equations has played an important role to interpret experimental results on quantitative grounds providing relevant insights to understand several infectious diseases. However, abstracting the complex mechanisms of the immune system can result in models with a large number of equations and consequently parameters to be estimated.Parameter fitting consists on the estimation of model parameters based on experimental data from the studied process, which can be considered as a nonlinear optimization problem. Hybrid models with machine learning methods have the potential to incorporate data sets of different immune mechanisms and scales in a black-box manner, while the well-known process-related principles are represented by mechanistic models. However, identifiability can be a key obstacle to overcome towards mathematical models with predictive value. Based on the differential evolution algorithm, this paper evaluates the potential use of hybrid models while keeping the capacity to recover the parameters in the mechanistic models to represent viral infections at a host level.