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Stability Analysis of a Human-Mosquito Model of Malaria with Infective Immigrants

Authors: Nisha Budhwar, Sunita Daniel

Abstract:

In this paper, we analyse the stability of the SEIR model of malaria with infective immigrants which was recently formulated by the authors. The model consists of an SEIR model for the human population and SI Model for the mosquitoes. Susceptible humans become infected after they are bitten by infectious mosquitoes and move on to the Exposed, Infected and Recovered classes respectively. The susceptible mosquito becomes infected after biting an infected person and remains infected till death. We calculate the reproduction number R0 using the next generation method and then discuss about the stability of the equilibrium points. We use the Lyapunov function to show the global stability of the equilibrium points.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1129181

References:

[1] Andrei Korobeinikov: Lyapunov functions and global properties for SEIR and SEIS epidemic models. Mathematical Medicine and Biology, 21 (2004) 75-83.
[2] Diekmann O., J. A. P. Heesterbeek, and J. A. J. Metz: On the definition and the computation of the basic reproduction ratio Ro in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28 (1990) 365-382.
[3] Fan M,, M.Y. Li, K. Wang: Global stability of an SEIS epidemic model with recruitment and a varying population size. Mathematical Bioscience, 171 (2001) 143-154.
[4] A.George Maria Selvam, A. Jenifer Priya: Analysis of a Discrete SEIR Epidemic Model. International Journal of Emerging Technologies in Computational and Applied Science,12(1), (2015) pp. 73-76.
[5] L. Guihua and J. Zhen: Global stability of an SEI epidemic model. Chaos, Solitons and Fractals, Volume 21, Number-4, (2009), 925-931.
[6] G. Li, W. Wang, Z. Jin: Global stability of an SEIR epidemic model with constant immigration.Chaos Solitons Fractals, 30 (4), (2006), 1012- 1019.
[7] Li MY, Smith HL, Wang L: Global dynamics of an SEIR epidemic model with vertical transmission. SIAM Journal of Applied Mathematics 62(1), (2001), 58-69.
[8] Manju Agarwal, Vinay Verma: Stability analysis of an SEIRS model for the spread of malaria. International Journal of Applied Mathematics and Computation Journal, Volume 4(1), (2012), 64-76.
[9] Muhammad Altaf Khan, Abdul Wahid, Saeed Islam, Ilyas Khan, Sharidan Shafie, Taza Gul: Stability analysis of an SEIR epidemic model with non-linear saturated incidence and temporary immunity.International Journal of Advances in Applied Mathematics and Mechanics, 2(3), (2015), 1-14.
[10] Muhammad Ozair and Takasar Hussain: Analysis of Vector-Host Model with Latent Stage Having Partial Immunity. Applied Mathematical Sciences, Vol. 8, (2014), 1569 - 1584.
[11] J. LaSalle and S. Lefschetz: Stability by Liapunovâ€™s Direct Method. NewYork Academic (1961).
[12] LaSalle J. P: The Stability of Dynamical system, SIAM, Philadelphia.( 1976).
[13] Sunita Daniel and Nisha Budhwar:An SEIR Model for Malaria with Infective Immigrants, (submitted).
[14] J. Tumwiine , J. Y. T. Mugisha , L. S. Luboobi: A host-vector model for malaria with infective immigrants. Journal of Mathematical Analysis and Applications, 361, (2010), 139-149.