Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 22, Issue.: 2

Original Research Article

GLOBAL ANALYSIS OF AN SEIRS EPIDEMIC MODEL WITH SATURATED INCIDENCE AND SATURATED TREATMENT

 

ANKIT AGRAWAL1*, ABHA TENGURIA2 AND GEETA MODI1

1Department of Mathematics, Govt. Motilal Vigyan Mahavidyalaya, Bhopal, India.

2Department of Mathematics, Govt. Maharani Laxmi Bai Girls P. G. (Autonomous) College, Bhopal, India.

Abstracts

In this paper, we studied an SEIRS epidemic model with saturated incidence and saturated treatment function. The threshold condition of the equilibrium point is obtained. The local and global stability of the disease free equilibrium and the endemic equilibrium of the model are discussed. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. Finally, numerical simulations are given to support some of the theoretical results.

Keywords :

Lyapunov function; saturated treatment and incidence; Routh-Hurwitz.