Stability Analysis of a Human-Mosquito Model of Malaria with Infective Immigrants
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.
 Andrei Korobeinikov: Lyapunov functions and global properties for
SEIR and SEIS epidemic models. Mathematical Medicine and Biology,
21 (2004) 75-83.
 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.
 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.
 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.
 L. Guihua and J. Zhen: Global stability of an SEI epidemic model.
Chaos, Solitons and Fractals, Volume 21, Number-4, (2009), 925-931.
 G. Li, W. Wang, Z. Jin: Global stability of an SEIR epidemic model
with constant immigration.Chaos Solitons Fractals, 30 (4), (2006), 1012-
 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.
 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.
 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),
 Muhammad Ozair and Takasar Hussain: Analysis of Vector-Host Model
with Latent Stage Having Partial Immunity. Applied Mathematical
Sciences, Vol. 8, (2014), 1569 - 1584.
 J. LaSalle and S. Lefschetz: Stability by Liapunov’s Direct Method.
NewYork Academic (1961).
 LaSalle J. P: The Stability of Dynamical system, SIAM, Philadelphia.(
 Sunita Daniel and Nisha Budhwar:An SEIR Model for Malaria with
Infective Immigrants, (submitted).
 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.