Stability Analysis of a Vector-borne Disease Model with Nonlinear and Bilinear Incidences

Seema Khekare   and Sujatha Janardhan

doi:10.17485/ijst/2015/v8i13/58749

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Stability Analysis of a Vector-borne Disease Model with Nonlinear and Bilinear Incidences

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i13/58749

Year: 2015, Volume: 8, Issue: 13, Pages: 1-6

Original Article

Stability Analysis of a Vector-borne Disease Model with Nonlinear and Bilinear Incidences

Seema Khekare^1* and Sujatha Janardhan²

¹Department of Applied Mathematics, G. H. Raisoni Institute of Engineering and Technology for Women, Nagpur - 440016, Maharashtra, India; [email protected]

² Department of Mathematics, St. Francis De Sales College, Nagpur - 440006, Maharashtra, India; [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Background/Objectives: To formulate and analyze a vector host epidemic model with non-monotonic and bilinear incidences.
Methods/Statistical Analysis: The stability conditions of disease free equilibrium and endemic equilibrium are investigated by constructing suitable Lyapunov functions. Numerical simulation is carried out to justify the theoretical results.
Results/Findings: The disease becomes endemic when the basic reproduction number is greater than one and it fades out when it is less than one.
Conclusion/Application: In endemic state of the disease, number of infective host decreases as awareness of vaccination and preventive measures increases and number of vectors approaches zero as the awareness of use of insecticides and cleanliness tends to infinity.

Keywords: Basic Reproduction Number, Disease Free Equilibrium, Endemic Equilibrium, Stability, Vector Borne Diseases