Tuckwell Henry C, Shipman Patrick D, Perelson Alan S
Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, Leipzig D-04103, Germany.
Math Biosci. 2008 Jul-Aug;214(1-2):81-6. doi: 10.1016/j.mbs.2008.03.005. Epub 2008 Mar 28.
We use a simple mathematical model to estimate the probability and its time dependence that one or more HIV virions successfully infect target cells. For the transfer of a given number of virions to target cells we derive expressions for the probability P(inf), of infection. Thus, in the case of needlestick transfer we determine P(inf) and an approximate time window for post-exposure prophylaxis (PEP). For heterosexual transmission, where the transfer process is more complicated, a parameter gamma is employed which measures the strength of the infection process. For the smaller value of gamma, P(inf) is from 6 x 10(-5) to 0.93 or from 7.82 x 10(-6) to 0.29, where the lower figures are for the transfer of 100 virions and the upper figures are for the transfer of 4.4 million virions. We estimate the reductions in P(inf) which occur with a microbicide of a given efficacy. It is found that reductions may be approximately as stated when the number of virions transferred is less than about 10(5), but declines to zero for viral loads above that number. It is concluded that PEP should always be applied immediately after a needlestick incident. Further, manufacturers of microbicides should be encouraged to investigate and report their effectiveness at various transferred viral burdens.
我们使用一个简单的数学模型来估计一个或多个HIV病毒粒子成功感染靶细胞的概率及其时间依赖性。对于给定数量的病毒粒子向靶细胞的转移，我们推导出了感染概率P(inf)的表达式。因此，在针刺转移的情况下，我们确定了P(inf)以及暴露后预防（PEP）的近似时间窗。对于异性传播，其转移过程更为复杂，我们采用了一个参数γ来衡量感染过程的强度。对于较小的γ值，P(inf)为6×10⁻⁵至0.93，或7.82×10⁻⁶至0.29，其中较低的数字是针对100个病毒粒子的转移，较高的数字是针对440万个病毒粒子的转移。我们估计了使用具有给定效力的杀微生物剂时P(inf)的降低情况。结果发现，当转移的病毒粒子数量小于约10⁵时，降低情况可能大致如所述，但对于高于该数量的病毒载量，降低情况降至零。得出的结论是，针刺事件发生后应立即进行PEP。此外，应鼓励杀微生物剂制造商调查并报告其在各种转移病毒载量下的有效性。
