Mathematical Sciences: Models for the Spread of HIV;        Equations with Piecewise Continuous Argument; Dynamics of   Discretizations
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
This project will focus on three scientific areas.  The                    first concerns mathematical analysis of epidemiological models                  for the spread of HIV (human immunodeficiency virus).                           Mathematical models for the spread of the virus will be                         developed and evaluated.  The models will be based on dividing                  the population into groups according to criteria such as sex,                   sexual behavior and socioeconomic categories.  They will be                     represented in terms of ordinary and delay-differential                         equations.  Stability and bifurcation phenomenon will be                        analyzed, simulations performed and comparisons made among the                  predictions of the different models.                                                 A second line of investigation concerns differential                       equations with piecewise continuous delays.  Such equations arise               in a number of physical contexts governed by memory effects.  An                objective of this work is to develop theory and applications of                 initial and boundary-value problems.  Conditions for stability                  will be sought; periodic and oscillation phenomena will be                      studied for equations with bounded and unbounded delay.  General                functional differential equations of alternating type will also                 be considered.                                                                       Work will also be done investigating Liapunov functions and                the qualitative behavior of discretizations.  This research will                focus on stability questions related to nonlinear difference                    equations using an extension of Liapunov's direct method and the                invariance principle.  The relation between the asymptotic                      dynamics of classes of differential equations and the dynamics of               discretized and semidiscretized versions of these equations will                be explored.  Applications to population dynamics and chemical                  kinetics will be sought.
{'FirstName': 'Kenneth', 'LastName': 'Cooke', 'PI_MID_INIT': 'L', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Kenneth L Cooke', 'EmailAddress': None, 'NSF_ID': '000399920', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Pomona College', 'CityName': 'CLAREMONT', 'ZipCode': '917114434', 'PhoneNumber': '9096218328', 'StreetAddress': '550 N COLLEGE AVE # 244', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '28', 'CONGRESS_DISTRICT_ORG': 'CA28', 'ORG_UEI_NUM': 'Q9VBQSV2CBY5', 'ORG_LGL_BUS_NAME': 'POMONA COLLEGE', 'ORG_PRNT_UEI_NUM': None}
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[{'Code': '112700', 'Text': 'Evolutionary Processes'}, {'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8807478.xml'}