Stability Analysis of Dengue Epidemic Model with Vertical Transmission Function

Lakhan Nagar¹ , V. K. Gupta² , S. K. Tiwari³

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.315-324, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.315324

Online published on Apr 30, 2019

Copyright © Lakhan Nagar, V. K. Gupta, S. K. Tiwari . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we consider a mathematical model to investigate the dynamics of spread of Dengue fever in both human and mosquito population. We find equilibrium of the model and basic re-production number. We also derive the necessary condition of the model are locally asymptotically stable, globally asymptotically stable or unstable. Global stability of the model is provided by constructing a Lyapunov function. We consider epidemic model with vertical transmission in mosquito population and shows that increases as p increases.

Key-Words / Index Term :
Epidemic Model, Saturated Incidence rate, Basic Reproduction number, Stability

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