  We investigate the use of hybrid techniques in complex processes of
infectious diseases. Since predictive disease models in biomedicine require a
multiscale approach for understanding the molecule-cell-tissue-organ-body
interactions, heterogeneous methodologies are often employed for describing the
different biological scales. Hybrid models provide effective means for complex
disease modelling where the action and dosage of a drug or a therapy could be
meaningfully investigated: the infection dynamics can be classically described
in a continuous fashion, while the scheduling of multiple treatment discretely.
We define an algebraic language for specifying general disease processes and
multiple treatments, from which a semantics in terms of hybrid dynamical system
can be derived. Then, the application of control-theoretic tools is proposed in
order to compute the optimal scheduling of multiple therapies. The
potentialities of our approach are shown in the case study of the SIR epidemic
model and we discuss its applicability on osteomyelitis, a bacterial infection
affecting the bone remodelling system in a specific and multiscale manner. We
report that formal languages are helpful in giving a general homogeneous
formulation for the different scales involved in a multiscale disease process;
and that the combination of hybrid modelling and control theory provides solid
grounds for computational medicine.
