A Mathematical Model to Demonstrate the Spread of an Epidemic

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, R₀ (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 R₀ 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