Stability analysis of epidemic models of Ebola hemorrhagic fever with non-linear transmission
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Authors
Emile Franc Doungmo Goufo
- Department of Mathematical Sciences, University of South Africa, Florida Sciences Campus, 003 South Africa.
Morgan Kamga Pene
- Department of Mathematical Sciences, University of South Africa, Florida Sciences Campus, 003 South Africa.
Stella Mugisha
- Department of Mathematical Sciences, University of South Africa, Florida Sciences Campus, 003 South Africa.
Abstract
Some Epidemic models with fractional derivatives were proved to be well-defined, well-posed and more
accurate (Brockmann et al. [D. Brockmann, L. Hufnagel, Phys. Review Lett., 98 (2007), 17-27]; Doungmo
Goufo et al. [E. F. Doungmo Goufo, R. Maritz, J. Munganga, Adv. Diff. Equ., 2014 (2014), 9 pages];
Pooseh et al. [S. Pooseh, H. S. Rodrigues, D. F. M. Torres, In: Numerical Analysis and Applied Mathematics, ICNAAM, American Institute of Physics, Melville, (2011), 739-742]), compared to models with the
conventional derivative. In this paper, an Ebola epidemic model with non linear transmission is analyzed.
The model is expressed with the conventional time derivative with a new parameter included, which happens
to be fractional. We proved that the model is well-defined, well-posed. Moreover, conditions for boundedness and dissipativity of the trajectories are established. Exploiting the generalized Routh-Hurwitz Criteria,
existence and stability analysis of equilibrium points for Ebola model are performed to show that they are
strongly dependent on the non-linear transmission. In particular, conditions for existence and stability of
a unique endemic equilibrium to the Ebola system are given. Finally, numerical simulations are provided
for particular expressions of the non-linear transmission (with parameters \(\kappa = 0:01, \kappa = 1\) and \(p = 2\)).
The obtained simulations are in concordance with the usual threshold behavior. The results obtained here
are significant for the fight and prevention against Ebola haemorrhagic fever that has so far exterminated
hundreds of families and is still infecting many people in West-Africa.
Share and Cite
ISRP Style
Emile Franc Doungmo Goufo, Morgan Kamga Pene, Stella Mugisha, Stability analysis of epidemic models of Ebola hemorrhagic fever with non-linear transmission, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4191--4205
AMA Style
Goufo Emile Franc Doungmo, Pene Morgan Kamga, Mugisha Stella, Stability analysis of epidemic models of Ebola hemorrhagic fever with non-linear transmission. J. Nonlinear Sci. Appl. (2016); 9(6):4191--4205
Chicago/Turabian Style
Goufo, Emile Franc Doungmo, Pene, Morgan Kamga, Mugisha, Stella. "Stability analysis of epidemic models of Ebola hemorrhagic fever with non-linear transmission." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4191--4205
Keywords
- Conventional derivative with a new parameter
- Ebola epidemic model
- non-linear incidence
- existence
- stability.
MSC
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