Local Stability Analysis Of Dynamic Model On Dengue Transmission
Arista Fitri Diana (1), Lathifatul Aulia (2), Zakaria Bani Ikhtiyar (3)

Department of Actuarial Science, Faculty of Sciences and Technology, Institut Teknologi Statistika dan Bisnis Muhammadiyah Semarang, Jl. Prof. Dr. Hamka No. KM. 1, Ngaliyan, Semarang, 50185

*Corresponding author email: arista.fitri[at]itesa.ac.id

Abstract

Abstract. Dengue fever transmission in Indonesia has an advanced amount. In this article, dynamic model of interaction between human and Aedes aegypti mosquitos is learned. The SEIRRD (Susceptible, Exposed, Infected, Recovery, Deceased) model is used in this article. The prurpose in this model is to describe the stability of dengue transmission, so that we can analyze the developed of epidemic model in mathemtic field. Using NGM method to analyze basic reproduction number and applying Routh-Hurwitz criteria method to show the local stability of model. Then, two equilibrium points, called endemic and non-endemic equilibrium points, are obtained. The result of basic reproduction number is described the stability analysis. If basic reproduction number less then one, the endemic equilibrium point is locally asymptotically stable and otherwise. Local stability analysis at the equilibrium point is determined through parameter analysis. Furthermore, numerical simulations are carried out by fitting the data to obtaine the result of the parameters. The results of numerical simulations explaine the spread of dengue transmission

Keywords: Dynamic Model, Epidemic Model, Equilibrium Point, Local Stability, Routh Hurwitz

Topic: Medicine & Health Sciences