Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 21, Issue.: 4

Original Research Article

GLOBAL DYNAMICS OF AN SIQR EPIDEMIC MODEL WITH SATURATED INCIDENCE RATE

 

HARISH JOSHI1*, R. K. SHARMA2 AND GEND LAL PRAJAPATI  

1Acropolis Institute of Technology and Research, Indore (M.P.), India.

2Govt. (Modal, Autonomous) Holkar Science College, DAVV, Indore (M.P.), India.

3Institute of Engineering and Technology, DAVV, Indore (M.P.), India.

Abstracts

In this paper, an SIQR epidemic model is constructed and analyzed which incorporates saturated incidence rate with quarantine. Threshold Rq determines the outcome of the disease. If Rq < 1, the infection disappears and disease dies out. If Rq > 1, the infection persists and disease becomes endemic. The local stability of the equilibrium is studied by Routh-Hurwitz criteria. The global stability of disease-free and endemic equilibrium are proved with the help of Lyapunov function and Dulac criteria. Finally numerical simulations are carried out.

Keywords :

 Endemic; saturated incidence; reproduction number; global stability; quarantine.