Conditions for invasion of synapse-forming HIV variants

Infection by Human Immunodeficiency Virus is a widespread cause of progressive immunodeficiency and death. The mechanisms of virus transmission and infection are well-documented from many experimental studies. These show that the infection of CD4+ T Cells by HIV happens by two distinct mechanisms: transmission by free viruses, and cell-cell transmission in which viral particles are transmitted directly across a tight junction or synapse between an infected and an uninfected cell. In this paper, a mathematical model of HIV transmission including both the free virus and cell-cell transmission pathways is introduced. A variation of this model is considered including two populations of virus. The first infects cells only by the free virus pathway, and the second infects cells by either the free virus or the cell-cell pathway. Steady-state and bifurcation analyses are performed on this model. A simple formula is presented describing the bifurcation point for local stability of a steady-state solution consisting entirely of the first viral subtype. This is equivalent to the conditions for invasion by a synapse-forming HIV variant. Synapse-forming HIV is shown to provide an evolutionary advantage relative to non synapse-forming virus when the average number of virus transmitted across a synapse is a sufficiently small fraction of the burst size. The exact bifurcation point depends on the fitness of the non synapse-forming virus and the likelihood of successful infection as a function of multiplicity of infection. These results are important for understanding synaptic transmission in HIV, which has been identified as a possible cause of continued replication during antiviral therapy.