Distributed Incubation and Infectious Periods in Models of the Transmission Dynamics of the Human Immunodeficiency Virus (HIV)

Distributions describing variation in the incubation and infectious periods of the human immunodeficiency virus (HIV) are derived from a series of risk or hazard functions. Four possible forms of the probability density function are considered, namely, exponential, Weibull, Erlang/gamma, and rectangular, and the properties and underlying risk functions are compared and contrasted. Models of the transmission dynamics of the virus, encapsulating different assumptions concerning the distributed incubation and infectious periods, are analysed, and their properties compared by steady-state and local-stability analyses and numerical methods.