Computational methods for multiscale modeling of virus infections

The dynamics of virus infections are governed by a variety of processes at multiple scales. In the report, the developed computational methods for studying virus infections through hybrid stochastic multiscale modeling will be presented. The multiscale model includes: (1) multi-compartment transport in the organism, (2) 3D reaction-diffusion equations with moving sources for virion and molecule transport in the tissues (finite element method), (3) 3D model of immune cell locomotion in lymphoid tissues with stochastic motility (symplectic numerical methods), (4) the models of virus intracellular replication in target cells, which are calibrated as systems of ordinary differential equations and then transformed into the stochastic discrete-state continuous-time Markov chains with time-inhomogeneous propensities that depend on the extracellular virion concentrations. Stochastic intracellular models are simulated using the integral- or uniformization-based Monte Carlo algorithms, as well as the hybrid discrete-continuous approximation methods. The multiscale model components are applied for studying certain aspects of HIV-1, SARS-CoV-2 and LCMV infection dynamics. The study is supported by the Russian Science Foundation (grant No. 23-11-00116).