Parameter Sensitivity Methodology in the Context of HIV Delay Equation Models

摘要

Over the past several years, the use of mathematical models as an aid in understanding features of HIV and other virus infection dynamics has been substantial. Several papers published in the mid nineties provided strong evidence for the high rate of HIV-1 replication and clearance in infected individuals 16, 37, 51. By the end of the decade, the general consensus was that in vivo, on the order of 10(10) virions are assembled and cleared every day 25, 35, 39. In many of these papers, the viral clearance rate c was identified by modeling the disease pathogenesis with a system of deterministic differential equations, numerically calculating a solution, and then fitting the results with experimental data (using a nonlinear least squares (NLS) approach), e.g., see 35, 37, 39. The existence of such a high replication/clearance rate implies a high mutation rate, thus indicating that pharmacological mono-therapy will ultimately fail, since the virus can rapidly manifest a resistance to any one drug. More importantly, this knowledge directly contributed to the current practice of simultaneously administering multiple drugs to HIV positive individuals in an effort to counteract the high mutation rate of the virus.