Artzrouni M
Department of Mathematical Sciences, Loyola University, New Orleans, LA 70118.
J Math Biol. 1992;31(1):73-99. doi: 10.1007/BF00163843.
Building on the Weibull distribution, we develop a modeled time-varying density function of the incubation time between exposure to HIV infection and full-blown AIDS. This approach leads to a series of cohort-specific density functions that take into account the increasing impact of new therapies such as zidovudine (AZT). The resulting modeled density functions are studied in detail, particularly with regard to their modes and medians. The mode is sensitive to changes in the period incubation time distribution, with even a possibility of a bimodal distribution for certain combinations of the parameters that determine the rate at which the period median incubation time changes. An important substantive result is that when a period median incubation period slowly increases to some leveling off value, say m(xc), then it is surprisingly early on that cohorts of infected individuals have a median incubation period very close to that ultimate value m(xc).
基于威布尔分布，我们开发了一个关于从接触艾滋病毒感染到发展为全面艾滋病之间潜伏期的模拟时变密度函数。这种方法产生了一系列特定队列的密度函数，其中考虑了齐多夫定（AZT）等新疗法日益增加的影响。我们详细研究了由此产生的模拟密度函数，特别是关于它们的众数和中位数。众数对潜伏期分布时期的变化很敏感，对于某些决定时期中位数潜伏期变化速率的参数组合，甚至可能出现双峰分布。一个重要的实质性结果是，当一个时期的中位数潜伏期缓慢增加到某个趋于平稳的值，比如说m(xc)时，令人惊讶的是，感染个体队列的中位数潜伏期在很早的时候就非常接近那个最终值m(xc)。
