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Lev Ginzburg started Applied Biomathematics, private research, and software firm in East Setauket, New York, in 1982. Applied Biomathematics focuses on ecology, health, and engineering. The company is principally funded by research grants and contracts from the U.S. government and private industry. Dr. Ginzburg's work in risk analysis and applied ecology has been conducted at Applied Biomathematics in collaboration with Dr. Scott Ferson and Dr. Resit Akcakaya, who are now professors, respectively, at the University of Liverpool, UK, and Stony Brook University, New York, USA.

Dr. Ginzburg’s most known academic work (most of it at Stony Brook University, 1977-2015) is a theory of predation (the ratio-dependent or Arditi-Ginzburg equations) that is an alternative to the classic prey-dependent Lotka-Volterra and MacArthur-Rosenzweig models. His book with Roger Arditi, How Species Interact, summarizes their proposed alteration of the standard view. The recent editions of the standard college Ecology textbook devote equal space to the Lotka-Volterra and Arditi-Ginzburg equations. Next in recognition has been the idea of inertial growth or an explanation of population cycles, based upon the maternal effect model, the main point of the book with Mark Colyvan, Ecological Orbits, and a more recent paper co-authored with Charley Krebs. One of Dr. Ginzburg’s current interests is an evolutionary theory of non-adaptive selection (selective disappearance of unstable configurations). A book in progress (Nonadaptive Selection: an evolutionary source of ecological laws, joint with John Damuth) is about to be published in 2020.

A 2018 study published in Nature: Ecology & Evolution has listed the Drs. Ginzburg and Jensen's 2004 paper is one of the 100 must-reads in the history of Ecology, a selection out of half a million papers since Darwin.