Abstract

Spread of Contagious Diseases in Heterogenous Population

D. Muthuramakrishnan1 and A. Martin2*

1Associate Professor, 2Assistant Professor 1Department of Mathematics, 2Department of Mathematics, 1National College, Tiruchirapalli - 620001, INDIA. 2Avvaiyar Government College for Women, Karaikal 609602, INDIA.

DOI : http://dx.doi.org/10.29055/jcms/985

ABSTRACT

In this paper we discuss in detail about the model of the invasion and spread of diseases in heterogeneous environments. This is organized in the form such that it contains the heterogeneous population structured into homogeneous subgroups, with the application modeling TB and HIV epidemics, then give a new approach to analyze epidemics in well-mixed populations in which individual-level variations in infectiousness is represented by a distributed reproductive number in particular the expected number of secondary cases due to each individual is drawn from a gamma distribution, yielding a negative binomial distribution after stochastisity in transmission is taken into account.

Keywords :Reproduction number, Tuberculosis (TB), Gamma Distribution, Human immunodeficiency virus (HIV).

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