Mechanisms accounting for Allee effects during HIV-1 infection.

The infection of target cells by viruses involves several positive feedback loops. Many viruses increase the likelihood of infecting a target cell by increasing the local multiplicity of infection (MOI), and viruses like HIV-1 increase the availability of target cells by activating quiescent CD4+ cells. Positive feedbacks during viral infection can lead to bistability phenomena, meaning that a stable uninfected steady state co-exists with a stable infected steady state. This could have the consequence that too small viral inocula are unable to infect a host, which is a so-called Allee effect, and that crippled viruses with a low fitness are nevertheless able to persist. By mathematically modeling the acute phase of human HIV-1 infections with a form of immune activation that increases target cell levels, and an infection rate that increases with the MOI, we find that Allee effects can occur for a wide range of parameter values. Because the MOI feedback is instantaneous and immune activation feedback takes time, this parameter range is somewhat larger for MOI feedback. Combining both feedbacks increases the parameter domain. As Allee effects allow the growth rate to increase over time, viral infections can grow faster than exponential, which sometimes occurs during the rebound of virus when treatment is interrupted. Bistability due to immune exhaustion can coexist with the bistability due to a positive feedback, and approaching the exhausted state can be subjected to similar Allee effects as approaching an immune-controlled chronic infection.