iosr-Jm   Volume-6 ~ Issue-3

Abstract: In this Paper, the effect of the variation of recruitment rate on the transmission dynamics of tuberculosis was studied by modifying an existing model. While the recruitment rate into the susceptible class of the existing model is constant, in our modified model we used a varying recruitment rate. The models were analyzed analytically and numerically and these results were compared. The Disease Free Equilibrium (DFE) state of the existing model was found to be          ,0,0,0  , the DFE of the modified model was found to be ( ,0,0,0) * S where * S is arbitrary. While all the eigenvalue of the existing model are negative, one of the eigenvalues of the modified model is zero. The basic reproduction number o R of both models are established to be the same. The numerical experiments show a gradual decline in the infected and exposed populations as the recruitment rates increase in both models but the decline is more in the modified model than in the existing model. This implies that eradication will be achieved faster using the model with a varying recruitment rate.

Keywords: tuberculosis, variation, recruitment rate, constant, effect, reproduction number, stability

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Abstract:In this paper, I have invented the formulae for finding the area of an Isosceles triangle. My finding is based on pythagoras theorem.

1 Geometry concepts and Pythagoras theorem.

Abstract: This pape r d e l i n e a t e s existence, characterizations and st rong unicity of best uniform approximations in real linear 2-normed spaces. AMS Su ject Classification: 41A50, 41A52, 41A99, 41A28.

Key Words and Phrases: Best approximation, existence, 2-normed linear spaces.

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Abstract: In this paper, first we define β*-open sets and β*-interior in topological spaces.J.Antony Rex Rodrigo[3] has studied the topological properties of 𝜂 * -derived, 𝜂 * -border, 𝜂 * -frontier and 𝜂 * exterior of a set using the concept of 𝜂 * -open following M.Caldas,S.Jafari and T.Noiri[5]. By the same technique the concept of β*-derived, β*-border, β*-frontier and β*exterior of a set using the concept of β*-open sets are introduced.Some interesting results that shows the relationships between these concepts are brought about.

Key words: 𝜂 * -border, 𝜂 * -frontier and 𝜂 * exterior, β*-derived, β*-border, β*-frontier and β*exterior

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