Biomaterial Database

Mathematical modelling of the spread of HIV/AIDS amongst injecting drug users. 1997

D Greenhalgh, and G Hay

Department of Statistics and Modelling Science, University of Strathclyde, Glasgow, UK.

In this paper we develop and analyse a model for the spread of HIV/AIDS amongst a population of injecting drug users. Our work is based on a model originally due to Kaplan (1989, Rev. Inf. Diseases 11, 289-98). We start off with a brief literature survey and review; this is followed up by a detailed description of Kaplan's model. We then outline a more realistic extension of Kaplan's model. Then we perform an equilibrium and stability analysis on this model. We find that there is a critical threshold parameter Rzero which determines the behaviour of the model. If Rzero < or = 1 there is a unique disease-free equilibrium, and if Rzero < 1 the disease dies out. If Rzero > 1 this disease-free equilibrium is unstable, and in addition there is a unique endemic equilibrium which is locally stable. If a certain condition is satisfied (and for Kaplan's model this condition is always satisfied), additional complete global-stability results are shown. These results are confirmed and explored further by simulation.

UI	MeSH Term	Description	Entries
D008433	Mathematics	The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)	Mathematic
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D003198	Computer Simulation	Computer-based representation of physical systems and phenomena such as chemical processes.	Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000163	Acquired Immunodeficiency Syndrome	An acquired defect of cellular immunity associated with infection by the human immunodeficiency virus (HIV), a CD4-positive T-lymphocyte count under 200 cells/microliter or less than 14% of total lymphocytes, and increased susceptibility to opportunistic infections and malignant neoplasms. Clinical manifestations also include emaciation (wasting) and dementia. These elements reflect criteria for AIDS as defined by the CDC in 1993.	AIDS,Immunodeficiency Syndrome, Acquired,Immunologic Deficiency Syndrome, Acquired,Acquired Immune Deficiency Syndrome,Acquired Immuno-Deficiency Syndrome,Acquired Immuno Deficiency Syndrome,Acquired Immuno-Deficiency Syndromes,Acquired Immunodeficiency Syndromes,Immuno-Deficiency Syndrome, Acquired,Immuno-Deficiency Syndromes, Acquired,Immunodeficiency Syndromes, Acquired,Syndrome, Acquired Immuno-Deficiency,Syndrome, Acquired Immunodeficiency,Syndromes, Acquired Immuno-Deficiency,Syndromes, Acquired Immunodeficiency
D015658	HIV Infections	Includes the spectrum of human immunodeficiency virus infections that range from asymptomatic seropositivity, thru AIDS-related complex (ARC), to acquired immunodeficiency syndrome (AIDS).	HTLV-III Infections,HTLV-III-LAV Infections,T-Lymphotropic Virus Type III Infections, Human,HIV Coinfection,Coinfection, HIV,Coinfections, HIV,HIV Coinfections,HIV Infection,HTLV III Infections,HTLV III LAV Infections,HTLV-III Infection,HTLV-III-LAV Infection,Infection, HIV,Infection, HTLV-III,Infection, HTLV-III-LAV,Infections, HIV,Infections, HTLV-III,Infections, HTLV-III-LAV,T Lymphotropic Virus Type III Infections, Human
D015819	Substance Abuse, Intravenous	Abuse, overuse, or misuse of a substance by its injection into a vein.	Drug Abuse, Intravenous,Drug Abuse, Parenteral,Intravenous Drug Abuse,Intravenous Substance Abuse,Parenteral Drug Abuse
D016485	Needle Sharing	Usage of a single needle among two or more people for injecting drugs. Needle sharing is a high-risk behavior for contracting infectious disease.	Syringe Sharing,Needle-Sharing,Needlesharing,Sharing, Needle,Sharing, Syringe