1. A Mathematical Model to Demonstrate the Spread of an Epidemic
- Author
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Jannatun Nayeem, Abu Salek, and Kazi Aminur Rahman
- Subjects
education.field_of_study ,Susceptible individual ,Transmission (medicine) ,Population ,Statistics ,Human immunodeficiency virus (HIV) ,medicine ,Disease ,Biology ,medicine.disease_cause ,education ,Basic reproduction number ,Virology - Abstract
Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Non-linear dynamical method of projecting the transmission of an epidemic is accurate if the input parameters are reliable. In this paper, a mathematical model is constructed for predicting an epidemic of HIV/AIDS with respect to the presence of infected individuals in the population. For the model, a formula for the basic reproduction number, R 0 (the expected number of secondary infectious caused by a single new infective introduced into a susceptible population) is determined. The six dimensional model is analyzed qualitatively to determine the stability of equilibria. Analysis of this model includes identifying the threshold R 0 that determines whether the disease dies out or an epidemic occurs. Key words: Non-linear dynamical method; infectious diseases; epidemic stability; HIV/AIDS. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 127-138 DOI: http://dx.doi.org/10.3329/ganit.v29i0.8522
- Published
- 1970