Jñānābha, Vol. 50 (2) (2020), (75-83)
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)
DOI: https://doi.org/10.58250/jnanabha.2020.50209
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.