An International Publications House

Albert Science International Organization

Connecting People With Pioneering Thought

Albert Science International Organization (ASIO) is international , peer-reviewed , open access , cum print version & online journals.
JOURNALS || ASIO Journal of Chemistry, Physics, Mathematics & Applied Sciences (ASIO-JCPMAS) [ISSN: 2455-7064 ]
STABILITY ANALYSIS OF A SEIR EPIDEMIC MODEL WITH INFECTIOUS FORCE IN LATENT, INFECTED AND IMMUNE STATES

Author Names : Prof. (Dr.) Sumit Kumar Banerjee
Page No. : 10-13
Read Hit : 789
Pdf Downloads Hit : 11  volume 1 issue 2
Article Overview

ARTICLE DESCRIPTION: 

Dr. Sumit Kumar Banerjee, Stability Analysis of a SEIR Epidemic Model with Infectious Force in Latent, Infected and Immune States, ASIO Journal of Chemistry, Physics, Mathematics & Applied Sciences (ASIO-JCPMAS), 2016, 1(2): 10-13.

ARTICLE TYPE: Research

dids/doi No.: 03.2016-26169319

dids link:  http://dids.info/didslink/04.2016-81576388/


ABSTRACT:  

In this paper local and global dynamics of a SEIR epidemic model have been studied in which latent, infected and immune states were studied. With the help of basic reproduction rate R0 the conditions for local and global stability of equilibrium points have been derived. Furthermore the condition for global stability of endemic equilibrium point has been derived.

Key words: Epidemic model, Immune state, Reproduction, Global stability, Endemic

Reference

[1] Zhang J (2003). Global analysis of SEI epidemic model with the constant inflows of different compartments. J xian Jiaotong University, PP. 653-656.

[2] Yuan SL (2001). A kind of epidemic model having infectious force in both latent period and infected period. J Biomath, PP. 392-398.

[3] Li G, Jin Z (2004). Global stability of an SEI epidemic model, chaos, Solutions & Fractals, PP. 925-931.

[4] Li G, Jin Z (2005). Global stability of an SEI epidemic model with general contact rate, chaos, Solutions & Fractals, PP. 997-1004. 

[5] Aron JL (1988). Acquired immunity dependent upon exposure in an SIRS epidemic model. Math Biosci, PP. 37-47.

[6] Thieme HR (1992). Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations, Math Biosci, PP. 87-94.

[7] Brauer F, Van den Driessche P (2001). Models for transmission of disease with immigration of infectives, Math Biosc, PP. 143-151.

[8] Mena-Lorca J, Hethcote HW (1992). Dynamic models of infectious diseases as regulators of population sizes, J Math Biol, PP. 693-702.

[9] Greenhalgh D (1992). Some results for a SEIR epidemic model with density dependence in the death rate, IMA J Math. Appl Med Biol, PP. 67-73.

[10] Cooke K, Van dan Driessche P (1996). Analysis of an SEIRS epidemic model with two delays, J Math Biol PP. 240-248.

[11] Greenhalgh D (1997). Hopf bifurcation in epidemic models with a latent period and nonpermanent immunity, Math Comput Model, PP. 85-91.

[12] Li My, Smith HL, wang L (2001). Global dynamics of an SEIR epidemic model with vertical transmission, SIAM J APPL Math, PP. 58-66.

[13] Hale JK (1969). Ordinary differential equations, New York: Wiley-Interscience, PP. 296-307.