A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay. (English) Zbl 1023.92011

Culshaw, Rebecca V.; Webb, Glenn

J. Math. Biol. 46, No. 5, 425-444 (2003).

Summary: We consider a two-dimensional model of cell-to-cell spread of HIV-1 in tissue cultures, assuming that infection is spread directly from infected cells to healthy cells and neglecting the effects of free virus. The intracellular incubation period is modeled by a gamma distribution and the model is a system of two differential equations with distributed delay, which includes the differential equations model with a discrete delay and the ordinary differential equations model as special cases.
We study the stability in all three types of models. It is shown that the ODE model is globally stable while both delay models exhibit Hopf bifurcations by using the (average) delay as a bifurcation parameter. The results indicate that, differing from the cell-to-free virus spread models, the cell-to-cell spread models can produce infective oscillations in typical tissue culture parameter regimes and the latently infected cells are instrumental in sustaining the infection. Our delayed cell-to-cell models may be applicable to study other types of viral infections such as human T-cell leukaemia virus type 1 (HTLV-1).

MSC:

92C50	Medical applications (general)
34K60	Qualitative investigation and simulation of models involving functional-differential equations
92C60	Medical epidemiology
34K18	Bifurcation theory of functional-differential equations
34D23	Global stability of solutions to ordinary differential equations