MATHEMATICAL MODEL FOR THE SPREAD OF EPIDEMICS

Authors:

Md. Zaidur Rahman,2Md. Abul Kalam Azad ,Md. Nazmul Hasan,

DOI NO:

https://doi.org/10.26782/jmcms.2012.01.00003

Keywords:

epidemiological models ,reaction-diffusion model, Fisher’s equation,public health policy,

Abstract

n most recent time worrying epidemic was HIV, Influenza, Tuberculosis etc. While there are many complicating factors, simple mathematical models can provide much insight into the dynamics of disease epidemics and help officials make decisions about public health policy in this subject matter. We shall discuss two of the classical and still much used, deterministic epidemiological models which are responsible for spreading diseases in an area. We shall then consider a reaction-diffusion model, Fisher’s equation, a new integro-differential equation model for the spread of an epidemic in space and to evaluate strategies to control an epidemic.

Refference:

I. Bailey N.T., The mathematical Theory of Infectious Disease (2nd edition), Charles Griffin and co. Ltd (1975)

II. Anderson R.M. and R.M. May. Infectious Diseases of Humans: Dynamics and Control. Oxford UniversityPress, Oxford, UK, 1991.

III. Bailey N.T.J.. The Mathematical Theory of Infectious Diseases. Hafner, New York, 2nd Edition, 1975.

IV. Banks R.B.. Growth and Diffusion Phenomena. Springer-Verlag, New York, 1994.

V. Daley D.J. and Gani J.. Epidemic Modelling: An Introduction. Cambridge University Press, Cambridge,UK, 1999.

VI. Murray J.D., Mathematical Biology. Springer-Verlag, New York, 2nd Edition, 1993.

VII.SIR model: Online experiments with JSX Graph (http://jsxgraph.unibayreuth.de/wiki/index/Epidemiology:_The_SIR_model)

VIII. Capasso V., The ,mathematical structure of Epidemic system, Springer Varlag (1993)

IX. Trottier, H.,& Phillippe, P. (2001). Deterministic modeling of Infectious diseases : Theory and methods. The Internet Journal of Infectious Diseases. Retrieved Dec. 3,2007, from http://www.ispub.com/ostio/index.php?xmlFilePath=journals/ ijid/volln2/model.xml.

X. Brauer, F.& Castillo-Chavez,C.(2001). Mathematical Models in Population Biology and Epidemiology.NY: Springer.

Md. Zaidur Rahman, Md. Abul Kalam Azad ,Md. Nazmul Hasan. View Download