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A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation. (English) Zbl 1211.93010

Summary: We derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturation function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then infected cells are cleared and the disease dies out. Otherwise, the infection is persistent with the existence of an infected equilibrium. Numerical simulations indicate that, depending on the fraction of cells surviving the incubation period, the solutions approach either an infected steady state or a periodic orbit.

MSC:

93A30 Mathematical modelling of systems (MSC2010)
92C50 Medical applications (general)
92C17 Cell movement (chemotaxis, etc.)
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