Spatially resolved modelling of immune responses following a multiscale approach: from computational implementation to quantitative predictions
Abstract In this work we formulate a hybrid multiscale model for describing the fundamental immune processes in human immunodeficiency type 1 (HIV) infection. These include (i) the T cell migration in the lymphoid tissue, (ii) the replication cycle of HIV within an infected cell, (iii) the type I interferon (IFN) response of the target cells, and (iv) the spatiotemporal dynamics of the HIV and type I IFN fields. Computational implementation of the hybrid multiscale model is presented. It is based on the use of semi-implicit first-order symplectic Euler method for solving the equations of the second Newton’s law for cell migration and the alternating direction method for the initial-boundary value problem for reaction–diffusion equations governing the spatial evolution of the virus and IFN fields in 2D domain representing the lymph node (LN) tissue. Both, the stochastic and deterministic descriptions of the intracellular HIV infection and the IFN reaction are developed. The potential of the calibrated multiscale hybrid model is illustrated by predicting the dynamics of the local HIV infection bursts in LN tissue.