Health and disease are regulated, to a large extent, by our immune system. Current challenges for health and disease that would benefit from mathematical, statistical, and computational approaches to integrate experimental and clinical data include:

(1) What are the relevant mechanisms of viral pathogenesis and immune responses, and how do these relate to a pathogenic and molecular characterisation of the virus,

(2) What are the mechanisms that regulate immune cell differentiation and fate, as well as ageing,

(3) How does receptor-mediated signalling correlate with cellular responses, and

(4) How can we quantify the gene diversity of a species with pathogenic potential, such as M. tuberculosis.

These questions can now be addressed with dual experimental/clinical and mathematical/computational approaches. In particular, modelling (mathematical and computational) helps to (i) interpret and integrate experimental data, (ii) frame and test hypotheses, (iii) suggest novel experiments allowing for more conclusive and quantitative interpretations of biological, immunological and disease-related processes, and (iv) help towards the 3Rs objectives to reduce, refine and develop replacement strategies as alternatives to animal testing.

More concretely, the main research objective of this research network is to develop, by means of the Marie Curie Research Staff Exchange Scheme, four long-term directions in Mathematics for Health and Disease. Given the clinical and experimental expertise of the

Indian, EU and Australian partners, and the mathematical and computational expertise of the Indian, EU, USA and Canadian partners, we plan

(i) to develop mathematical and computational models of host-pathogen and virus dynamics, with a focus on pathogenic and molecular characterisation of HIV-1, and the distribution of virulence in intra-host HIV quasispecies, in order to understand if regulation of immune activation can be a potentially optimum way for disease management,

(ii) to develop mathematical and computational models of immune cellular processes, such as differentiation and cellular fate, as well as ageing, validated by experimental data, with a focus on T cells,

(iii) to develop stochastic mathematical models of receptor-mediated processes in health and disease, with a focus on the CCR5 receptor, VEGF receptor, T cell receptor and B cell receptor, and

(iv) to develop statistical tools and methods, using evolutionary game theory, to characterise the genomic fluidity of human pathogens, in order to understand microbial pathogen evolution and what constitutes the boundary between commensal and pathogenic organisms.