Warren M. Hirsch, a developer of a mathematical model predicting schistosomiasisa tropical diseasethat became a foundational concept in mathematical epidemiology, died Mon., July 9 in Sarasota, Fla. Hirsch, professor emeritus of mathematics at New York Universitys Courant Institute of Mathematical Sciences, was 88.
The cause of death was complications of progressive supra-nuclear palsy.
Best known for his work in mathematical biology, particularly on the transmission of parasitic diseases, his wide-ranging research spanned the fields of optimization and operations research, cannibalization theory, probability theory, statistics, biostatistics, and mathematical epidemiology.
Hirschs early work on the fixed charge problem with George Dantzig was first published as a RAND report in 1954. The Hirsch-Dantzig algorithm that emerged from this work is widely recognized in economics and business, providing a method of analysis for companies who seek to enhance profitability in the presence of fixed costs.
In 1957 he proposed the Hirsch conjecture that has played an intriguing role in the theory of linear programming and has posed an enduring challenge for many students and researchers over the years. It states that the edge-vertex graph of an n-facet polytope in d-dimensional Euclidean space has diameter no more than n-d. Although, resolved in some special cases, it remains an open problem in the general case and has remained so for 50 years.
Several of Hirschs papers concerned optimization questions; he was one of the pioneers in mathematical cannibalization theory. The main focus of his research, however, was probability theory where he derived significant results about sums of random variables and measures in denumerable spaces.
Always intrigued by the challenge of mathematically modeling important real world phenomena, he was inspired to venture into epidemiology following a casual dinner-party conversation in the late 1960s with a public health physician from Surinam who described to him the devastating consequences of schistosomiasis, a tropical disease produced by a parasitic worm. Hirsch became absorbed in the prospect of mathematically modeling the transmission dynamics of these parasites; but, in order to understand deeply the biology before undertaking model construction, he took a sabbatical year at Yale to prepare himself in parasitology and tropical medicine.
In the early 1970s, with his Ph.D. student, Ingemar Nasell, Hirsch developed a mathematical model based on a prior paper by George Macdonald, who had proposed a quantitative approach to schistosomiasis and had focused on the worms sexuality. The Nasell-Hirsch model introduced Markov chains to represent the state of the infection in the definitive and intermediate host populations and linked them in a non-linear way with a useful rule: every external variable involved in a transition probability is replaced by its expected value, a semi-stochastic link. This assumption, supported by phenomenological reasoning, provided a tractable analysis of underlying stochastic processes. In addition, the worms sexuality turned out to be related to modified Bessel functions of the first type. The models conclusions confirmed some of Macdonalds inferences, such as that in fighting the spread of schistosomiasis safe water supplies are more important than latrines.
The Nasell-Hirsch model is regarded as a seminal work and became a foundational concept in mathematical epidemiology. A subsequent model dealt with hermaphroditic worms and revealed fundamental differences in the structure of equilibrium points and the transmission dynamics.
Together with Jean-Pierre Gabriel and Herman Hanisch, Hirsch next considered transmission models for a very general class of worms. Their reproductive strategies were captured mathematically in the notion of oviposition function, a new sexual classification of worms emerged from their mathematical considerations; depending on behavior, hermaphroditic parasites can induce dynamics similar to those of the doecious worm. An important link emerged between the pre-patent period of the intermediate host and the transmission dynamics of the parasite. The pre-patent period is the delay between infection and response of the intermediate host; its introduction into the model led to the study of functional differential equations with delay. These approaches provided new methods for the study of asymptotic behavior of solutions of ordinary and delay differential equations. The now commonly used fluctionation lemma came out of this research.
Hirschs collaborator, Ingemar Nasell, now a professor at the Royal Institute of Technology in Stockholm, recently reflected on Hirschs overall contributions to mathematical epidemiology: The branch of applied mathematics known as mathematical epidemiology has experienced a steady growth in the last half century. Warren Hirsch had a very strong role in this. Part of his role is reflected in the several research papers in the area that he wrote. But his personal and informal influence on researchers in the field was equally important for the progress in the field. His enthusiasm for new ideas, his knowledge in both mathematics and biological sciences, and his strong personality combined to give a lasting contribution to this area of applied mathematics.
Hirsch was appointed a professor of mathematics at NYUs Courant Institute of Mathematical Sciences in 1953. On retirement in 1988, he joined the biomathematical sciences faculty at the Mt. Sinai School of Medicine where, for the next 11 years, he taught mathematics and epidemiology in the MD/PhD joint degree program preparing future physicians for careers in biomedical research.
Hirsch was born on Aug. 3, 1918 in New York City. He was a graduate of the City College and NYU, where he earned his Ph.D. in 1952. He received an honorary degree from the University of Fribourg in Switzerland in 1989.
In 1942, he was commissioned in the U.S. Army Air Forces and attended the Army Air Forces Statistical Officers School at Harvard University. Hirsch then served at AAF Headquarters as assistant chief of the Combat Operations Branch of the Office of Statistical Control. He was commended for major contributions in operational analysis and logistical planning, for a creative slide-rule computing device, and for the maximum sortie study used to plan heavy bombing during the Normandy invasion. As a member of the AAF Evaluation Board in Europe from 1944-1946 and director of its Analysis Section, he studied the effects of bombing German targets in France and Germany and drew conclusions for the continuous improvement of bombing strategies.
Dr. Hirschs first wife, Karen Haber, died in 1955. He is survived by his wife of 48 years, Gail Glavin Hirsch of Sarasota, Fla.; his son, Adam Hirsch, a Florida State University law professor, of Tallahassee, Fla.; his daughter, Lisa Eisner, of Wallingford, Conn.; and his granddaughter, Caitlin Mitchell, of St. Petersburg, Fla.