DYNAMICS OF AN SIRS EPIDEMIC MODEL WITH PARTICULAR NON-LINEAR INCIDENCE RATE AND MEDIA EFFECTS

By

Garima Saxena

Institute of Engineering and Technology

Devi Ahilya Vishwavidyalaya

Indore-452020, Madhya Pradesh, India

Email: rimasa.1907@gmail.com

R. K. Sharma

Department of Mathematics, Government Holkar Science College

Devi Ahilya Vishwavidyalaya

Indore-452001, Madhya Pradesh, India

Email: raj_rma@yahoo.co.in

Ankit Agrawal

Department of Mathematics, Acropolis Institute of Technology and Research, Indore-453771, Madhya Pradesh, India

Email: ankit_agrawal458@yahoo.com

(Received : May 24, 2020; Revised : September 26, 2020; Final Form : December 18, 2020)

This paper deals with the nonlinear dynamics of Susceptible, Infected, Recovered epidemic model with a particular non linear incidence rate and the consequences of media awareness program. The model analysis shows that the spread of an infectious disease can be controlled by using awareness programs. Different equilibrium points and their stability are discussed. The basic reproduction number R₀ is obtained. We also apply Lasalle’s invariance principle to show that the disease-free equilibrium is globally asymptotically stable if R₀<1 and we use a geometric approach to find out the global stability of the endemic equilibrium. In addition, to our analytical results, several numerical simulations are also illustrated.

2010 Mathematics Subject Classifications: 34D20, 34D23, 92B05, 92D05.

Keywords and phrases: social distancing, wearing protective masks, geometric approach, stability, media, COVID-19.