Analytic solutions to compartmental models of the HIV/AIDS epidemic
| Autor: | Janet Elizabeth Williams, Jeff Griffiths, Tracey England |
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| Rok vydání: | 2000 |
| Předmět: |
State variable
Control and Optimization Computer science Human immunodeficiency virus (HIV) HIV Infections medicine.disease_cause Models Biological General Biochemistry Genetics and Molecular Biology Disease Outbreaks medicine Humans Applied mathematics Sensitivity (control systems) Set (psychology) General Environmental Science Pharmacology Acquired Immunodeficiency Syndrome General Immunology and Microbiology Estimation theory General Neuroscience Applied Mathematics Numerical Analysis Computer-Assisted General Medicine Control and Systems Engineering Modeling and Simulation Piecewise Analytic solution Hiv aids epidemic |
| Zdroj: | IMA Journal of Mathematical Control and Information. 17:295-310 |
| ISSN: | 1471-6887 0265-0754 |
| Popis: | For many years compartmental models have provided useful insights into the spread of epidemics. Such models are usually fairly easy to set up, but even the simpler models have the disadvantage that they are intractable to analytic solution. In this paper we examine models of the HIV/AIDS epidemic, and show that the equations may be linearized in a piecewise manner over time, thus allowing analytic solutions to be obtained. Indications of the usefulness of this approach are provided. In particular, an analytic solution gives insight into the mechanism of the epidemic, together with a clearer picture of the sensitivity of results to changes in parameter values. Further, the processes of parameter estimation and the methodology of back-calculation also benefit from the provision of functional forms for the state variables. |
| Databáze: | OpenAIRE |
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