A MATHEMATICAL MODEL OF DENGUE INTERNAL TRANSMISSION PROCESS

N. Nuraini; E. Soewono; K.A. Sidarto

doi:10.22342/jims.13.1.79.123-132

N. Nuraini ⁽¹⁾ , E. Soewono ⁽²⁾ , K.A. Sidarto ⁽³⁾

(1) Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Nat- ural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia., Indonesia,

(2) Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Nat- ural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia., Indonesia,

(3) Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Nat- ural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia., Indonesia

https://doi.org/10.22342/jims.13.1.79.123-132

Issue
Volume 13 Number 1 (April 2007)

Submitted
May 25, 2012

Accepted
July 24, 2012

Published
July 24, 2012

Keywords:

mathematical model, equilibrium points, threshold parameter, numerical simulation

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Abstract

In this paper we formulate a mathematical model of internal process of dengue virus transmission in the human body. We analyze the dynamic of dengue virus using a system of differential equation. We obtain a local stability of equilibrium for this model base on a threshold parameter. In particular, we prove the stability result for a free-virus and abundance of virus-states. Finally, numerical simulation of the model are performed to study the behaviour of the system for a short period of time.

DOI : http://dx.doi.org/10.22342/jims.13.1.79.123-132

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Authors

N. Nuraini

Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Nat- ural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia.

penulis@jims-a.org (Primary Contact)

E. Soewono

Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Nat- ural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia.

K.A. Sidarto

Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Nat- ural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia.

Nuraini, N., Soewono, E., & Sidarto, K. (2012). A MATHEMATICAL MODEL OF DENGUE INTERNAL TRANSMISSION PROCESS. Journal of the Indonesian Mathematical Society, 13(1), 123–132. https://doi.org/10.22342/jims.13.1.79.123-132