A Mathematical Model to Demonstrate the Spread of an Epidemic

Authors

  • Jannatun Nayeem Department of Arts and Sciences, Ahsanullah University of Science and Technology, Dhaka
  • Kazi Aminur Rahman Department of Mathematics, Dhaka University, Dhaka
  • Md Abu Salek Department of Natural Science, United International University, Dhaka

DOI:

https://doi.org/10.3329/ganit.v29i0.8522

Keywords:

Non-linear dynamical method, infectious diseases, epidemic stability, HIV/AIDS

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 

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How to Cite

Nayeem, J., Rahman, K. A., & Salek, M. A. (2011). A Mathematical Model to Demonstrate the Spread of an Epidemic. GANIT: Journal of Bangladesh Mathematical Society, 29, 127–138. https://doi.org/10.3329/ganit.v29i0.8522

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