Infection is best described as a stochastic process. Whether a host becomes infected upon exposure has a strong random element. The same applies to cells exposed to virions. In this review, we show how the mathematical formalism for stochastic processes has been used to describe and understand the infection by the Human and Simian Immunodeficiency Virus on different levels. We survey quantitative studies on the establishment of infection in the host (the organismal level) and on the infection of target cells (the cellular and molecular level). We then discuss how a synthesis of the approaches across these levels could give rise to a predictive framework for assessing the efficacy of microbicides and vaccines.
Keywords: Antibody neutralization; Establishment of infection; Human Immunodeficiency Virus; Mathematical modeling; Microbicide; Simian Immunodeficiency Virus; Stochasticity; Vaccination.
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