Mathematical study of SEIR model with functional rates of incidence and treatment
Downloads
DOI:
https://doi.org/10.26637/MJM0804/0105Abstract
In this paper, with nonlinear inhibitory effect and saturated treatment rate, an SEIR epidemic model is proposed. The basic reproduction number R0, is calculated when determining the threshold value for the disease and the dynamics of the model. The criteria for the existence of all the points of equilibrium are established and we also found that the conditions depend on them. The stability of equilibrium is discussed in terms of local and global. All attempted were made to present the numerical simulations for the model we suggested. The theoretical findings are clearly predicted to be supported and evaluated.
Keywords:
SEIR model, equilibrium point, stability analysisMathematics Subject Classification:
Mathematics- Pages: 1953-1960
- Date Published: 01-10-2020
- Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)
Lourdes Esteva And Mariano Matias, A Model For Vector Transmitted Diseases With Saturation Incidence, Journal of Biological Systems, 9(4)(2001), 235-245.
Fred Brauer Carlos Castillo-Chavez Zhilan Feng, Mathematical Models in Epidemiology, Texts in Applied Mathematics, (69), Springer, 2019.
Michael Y. Li, An Introduction to Mathematical Modeling of Infectious Diseases, Mathematics of Planet Earth 2, Springer, 2018.
Julie C. Blackwood and Lauren M. Childs, An introduction to compartmental modeling for the budding infectious disease modeler, Letters in Biomathematics, 5(1)(2018), 195-221.
B. Dubey, Atasi Patra, P. K. Srivastava and Uma S. Dubey, Modeling And Analysis Of An Seir Model With Different Types Of Nonlinear Treatment Rates, Journal of Biological Systems, 21(3)(2013), Article ID 1350023.
Xinli Wang, An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence Rate, Discrete Dynamics in Nature and Society, 2015(2015), Article ID 720682.
Jinhong Zhang, Jianwen Jia and Xinyu Song, Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function, The Scientific World Journal, 2014(2014), Article ID 910421.
R.M. Anderson, R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1992.
H. W. Hethcote, The Mathematics Of Infectious Diseases, Siamreview, 42(4)(2000), 599-653.
Bo Li, Sanling Yuan And Weiguo Zhang, Analysis On An Epidemic Model With A Ratio Dependent Nonlinear Incidence Rate, International Journal of Biomathematics, 4(2)(2011), 227-239.
Ottar N. Bjørnstad, Epidemics Models and Data using R, Springer, 2018.
Maia Martcheva, An Introduction to Mathematical Epidemiology, Springer, 2015.
${ }^{[13]} mathrm{W}$. Wang and S. Ruan, Bifurcation in an epidemic model with constant removal rate of the invectives, Journal of Mathematical Analysis and Applications, 291(2)(2004), 775-793.
Z. Zhang, S. Suo, Qualitative analysis of a SIR epidemic model with saturated treatment rate, $J mathrm{Appl}$ Math Comput, 34(2010), 177-194.
H. I. Freedman, J. W. H. So, Global stability and persistence of simple food chain, Math Biosci, 76(1983), 69-86.
- NA
Similar Articles
- P. Amsini, R. Uma Rani, Cancer cell detection using advanced fuzzy set theories , Malaya Journal of Matematik: Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
