Most quantitative models in biomedical research have been formulated by ordinary differential equations (ODEs). Despite the great contributions ODEs have made to biology and beyond, the high-dimensional, time-dependent factors of the immune system still pose a significant challenge to the predictive value of ODEs as it would require several hundred equations and thousands of parameters to be estimated. The recent rise of machine learning as a powerful computational tool to integrate large datasets presents a special opportunity to deal with the inherent complexity of biological systems. However, machine learning approaches do not consider the mechanistic knowledge of the underlying interactions. Preliminary studies that combine ODEs and machine learning highlight that these computational algorithms could be on the cusp of a major revolution. Remarkably enough, however, no parameter estimation theory exists to integrate simultaneously both approaches. We propose to create new hybrid models and test their predictions in a mouse viral coinfection system to address a central vexation for infection biology which is how and when to modulate immune responses to mitigate mortality during lethal respiratory viral infection. At the interface between mathematical and life sciences, we will develop and analyze a novel suite of computational models that will integrate the underlying biological mechanisms to manage ill-posed problems and explore massive design spaces, allowing for robust predictions from complex biological systems. To validate and test our novel and foundational mathematical approaches, we will generate the biological data from a mouse infection system with a mild viral pathogen (rhinovirus) two days before infection with a lethal viral pathogen (influenza) that results in reduced disease compared to single infection alone. We hypothesize that this system can train our mathematical models in a natural way how the innate immune system can be manipulated to reduce mortality to lethal infections and beyond. Key model predictions will be tested by targeted immune system manipulation during lethal infection, paving the way to understanding the role of complex immune interactions in respiratory viral disease pathology.