Small variations in multiple parameters account for wide variations in HIV–1 set–points: a novel modelling approach

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Abstract
Steady–state levels of HIV–1 viraemia in the plasma vary more than a 1000–fold between HIV–positive patients and are thought to be influenced by several different host and viral factors such as host target cell availability, host anti–HIV immune response and the virulence of the virus. Previous mathematical models have taken the form of classical ecological food–chain models and are unable to account for this multifactorial nature of the disease. These models suggest that the steady–state viral load (i.e. the setpoint) is determined by immune response parameters only. We have devised a generalized consensus model in which the conventional parameters are replaced by so–called ‘process functions’. This very general approach yields results that are insensitive to the precise form of the mathematical model. Here we applied the approach to HIV–1 infections by estimating the steady–state values of several process functions from published patient data. Importantly, these estimates are generic because they are independent of the precise form of the underlying processes. We recorded the variation in the estimated steady–state values of the process functions in a group of HIV–1patients. We developed a novel model by providing explicit expressions for the process functions having the highest patient–to–patient variation in their estimated values. Small variations from patient to patient for several parameters of the new model collectively accounted for the large variations observed in the steady–state viral burden. The novel model remains in full agreement with previous models and data.