Within-host virus infections through high-order interactions

The human lymphatic organs are the primary sites where HIV infection occurs and are interconnected within the body in specific structures. These organs are closely linked within the entire lymphatic system, which can increase the risk of HIV infection. The increased interactions between cells in these organs can affect the overall behavior of the virus. When considering these interconnected lymphatic organs as simplicial structures, the entire system becomes a complex network. To study how high-order infections impact viral dynamics, we simplify the network system to a mean-field equation that describes coordinated viral dynamics across multiple infection sites. Even the simplified model may display a backward bifurcation, leading to bistable dynamics. This means that a mild initial infection may disappear, but a severe initial infection can cause the virus to persist. We study the characteristic equations to examine the local stability of the infection-free equilibrium. The equilibria’s global stabilities are demonstrated using the Poincaré–Bendixson theorem for three-dimensional competitive systems and the theory of second compound equations. Furthermore, the complex interactions among lymphatic organs can result in periodic viral dynamics. We conduct numerical simulations of the mean-field equation and the entire network system to illustrate the bistable viral dynamics resulting from backward bifurcation and periodic viral dynamics.