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.