The combination of two factors gives early HIV infection an especially strong influence on transmission dynamics: (a) increased transmission probabilities and (b) increased transmission potential of partners infected during this period. Most attention has been focused on the first factor because it fits the way we usually think about risk factors affecting individuals. The second factor acts not on individuals, but across chains of transmission. It is missed by models with constant partnership formation rates over an individual's life or with random mixing. It cannot be assessed from available data collected from individuals. Its assessment requires data from both individuals in a partnership. We demonstrate that this second effect can be so strong that early infection can dominate transmission dynamics even when transmission probabilities are only modestly increased. This second effect is not directly parameterized in our models but arises from two realistic types of temporal variation in partnership formation: (a) Partnership formation rates vary by age with preferential partnership formation in one's own age group, and (b) individuals of any age can experience transient periods of high-risk partnership formation. In a model with only the age-related effect, early infection is observed to dominate transmission dynamics when 20% of transmissible virus is allocated to the first 6 weeks of infection, 7% to middle infection, and 73% to late infection. This domination occurs both early in the course of an epidemic and later when endemic infection levels have been reached. When the second effect is added, early infection is seen to dominate transmission in a model allocating 10% of transmissible virus to the first 6 months, 40% to middle infection, and 50% to late infection. In this model, transmission probabilities during early infection are only 4.17 times those of middle infection and half those of late-stage infection.

A target moves between two regions in a Markovian fashion, the parameters of which are known to the searcher. Discrete amounts of search effort (“looks”) may be allocated to one region at a time. This paper gives equations that characterize (a) the minimum expected number of looks to detect the target, and (b) the maximum probability of detecting the target within a given number of looks. These are solved completely for special cases, and numerical approximate solutions are described for general cases.

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