Age-structured viral dynamics in a host with multiple compartments.

Several studies have reported dual pathways for HIV cell infection, namely the binding of free virions to target cell receptors (cell-free), and direct transmission from infected cells to uninfected cells through virological synapse (cell-to-cell). Furthermore, understanding spread of the infection may require a relatively in-depth comprehension of how the connection between organs, each with characteristic cell composition and infection kinetics, affects viral dynamics. We propose a virus model consisting of multiple compartments with cell populations subject to distinct infectivity kernels as a function of cell infection-age, in order to imitate the infection spread through various organs. When the within-host structure is strongly connected, we formulate the basic reproduction number to be the threshold value determining the viral persistence or extinction. On the other hand, in non-strongly connected cases, we also formulate a sequence of threshold values to find out the infection pattern in the whole system. Numerical results of derivative examples show that: (1) In a strongly connected system but lacking some directional connection between compartments therein, the migration of cells certainly affects the viral dynamics and it may not monotonously depend on the value of migration rate. (2) In a non-strongly connected structure, increasing migration rate may first change persistence of the virus to extinction in the whole system, and then for even larger migration rate, trigger the infection in a subset of compartments. (3) For data-informed cases of intracellular delay and gamma-distributed cell infectivity kernels, compartments with faster kinetics representative of cell-to-cell transmission mode, as opposed to cell-free, can promote persistence of the virus.