Stability Analysis of a SEIV Epidemic Model with Saturated Incidence Rate
O. Adebimpe *
Department of Mathematics and Physical Science, Osun State University, Oshogbo, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a SEIV epidemic model with saturated incidence rate that incorporates polynomial information on current and past states of the disease is investigated. The model exhibits two equilibria, disease-free equilibrium (DFE) and the endemic equilibrium (EE). It is shown that if the basic reproduction number, R0< 1, the DFE is locally asymptotically stable and by the use of Lyapunov function, DFE is globally asymptotically stable and in such a case, the EE is unstable. Moreover, if R0>1, the endemic equilibrium is locally asymptotically stable. The effects of the rate at which vaccine wanes (ω) are investigated through numerical stimulations.
Keywords: SEIV epidemic model, saturated incidence rate, basic reproduction number, locally and globally stable.