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Stability Analysis of Dengue Disease Using Host–Vector Model

In: Recent Advances in Mathematical Sciences

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  • Eminugroho Ratna Sari

    (Yogyakarta State University, Mathematics Education Department, Faculty of Mathematics and Natural Science)

Abstract

The previous model of dengue disease was discussed only in host population using a simple SIR model. In fact, vectors provide an important role in the spread of dengue fever since a host can be infected by the vector. Hence it is reasonable to build a model of dengue disease in host and vector population. From the model, there are two kinds of equilibrium point: disease free and endemic. Solution behavior of model can be analyzed using the changes of basic reproduction number which is obtained by next generating matrix. If basic reproduction number is less or equal than one, then using LaSalle–Lyapunov Theorem, it is shown that the disease-free equilibrium is globally asymptotically stable. If the basic reproductive number is greater than one, then using Routh–Hurwitz Condition, it is shown that the endemic equilibrium is locally asymptotically stable. In the end, we present the numerical solution with MAPLE.

Suggested Citation

  • Eminugroho Ratna Sari, 2016. "Stability Analysis of Dengue Disease Using Host–Vector Model," Springer Books, in: Adem Kılıçman & Hari M. Srivastava & M. Mursaleen & Zanariah Abdul Majid (ed.), Recent Advances in Mathematical Sciences, pages 83-98, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-0519-0_8
    DOI: 10.1007/978-981-10-0519-0_8
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