An SEIT epidemic model with new modulated saturated incidence and time delay

Abstract

In this paper, we have considered an SEIT epidemic model with new modulated saturated incidence and discrete time delay. From our motivation first we prepare the mathematical model and the effect of time delay is investigated. Our main motivation that the disease is transmitted only by contact with the infected individuals of the same species. The model convey two equilibria namely, a disease free equilibrium and an endemic equilibrium. With the help of basic reproductive number we discuss the transmission dynamics of the disease. Analyzing the model we have found out the mathematical results like invariant region boundedness and local stability of both the delayed and non-delayed system. In our details study we can say that bifurcation occurs due to time delay. Also we are trying to examine what will happen if we increase the time delay. The stability of the endemic equilibrium point breaks of the delay system and Hopf bifurcation occurs. When the bifurcation parameter passes through the critical value, E∗ losses its stability and a family of periodic solutions bifurcate from E∗. With the support of competent value of the parameter we have calculated the value of basic reproductive number. The proposed model has been solved numerically and it verify the analytical results.  

Author Biographies

Debashis Biswas, Calcutta Girls’ College

Debashis Biswas did his Ph.D. in the year 2018 from University of Kalyani. The title of his thesis is "Population dynamics of horizontally and vertically transmitted diseases with non-linear incidence: model based study". He has joined as an Assistant Professoor in the Department of Mathematics, Calcutta Girls’ College, Kolkata-700013, India.

Nanda Das, Maulana Azad College, Kolkata- 700013, India

Nanda Das did his Ph.D. in the year 2014 from University of Kalyani. The title of his thesis is "Role of virus infection in bacterial population and plankton species-Model based study". He is now serving  Department of Mathematics, Maulana Azad College, Kolkata- 700013, India as an Associate Professoor.

Samares Pal, Professor

Mathematical Modelling in Ecology, Epidemiology

Published
2022-02-20