On transient effects in the HIV/AIDS epidemic

Area of Science:

• Epidemiology
• Mathematical Modeling of Infectious Diseases

Background:

• The spread of human immunodeficiency virus (HIV) and the resulting acquired immunodeficiency syndrome (AIDS) presented complex epidemiological dynamics.
• Understanding the growth rates and transients of both HIV infections and AIDS cases is crucial for public health interventions.

Purpose of the Study:

• To analyze the growth rate dynamics of AIDS cases during the initial phase of the HIV epidemic.
• To investigate the relationship between HIV and AIDS growth rates, particularly during periods of changing HIV incidence.
• To determine the conditions under which AIDS growth rates exhibit monotonic decrease and to assess the timing of these transients in the US and Europe.

Main Methods:

• Sensitivity analysis of HIV epidemic parameters (e.g., incubation period, doubling time).
• Mathematical modeling, including analysis of growth rates and transients under different HIV spread scenarios (exponential and logistic).
• Examination of density functions for the incubation period of AIDS.

Main Results:

• The initial positive transient in AIDS growth rate becomes negligible as case numbers increase.
• Under the assumption of non-increasing HIV growth rates, AIDS growth rate consistently exceeds HIV growth rate.
• A pathological incubation period can lead to non-monotonic AIDS growth even with exponential HIV spread.
• The positive transient in the US likely ended by 1982, and in five major European countries by 1986-1987.

Conclusions:

• The early phase of the HIV epidemic exhibited complex growth rate transients for AIDS cases.
• The relationship between HIV and AIDS growth rates is nuanced, with AIDS growth often exceeding HIV growth under specific conditions.
• Mathematical modeling provides valuable insights into the epidemiological trajectory of HIV/AIDS, aiding in understanding historical trends and future projections.