Abstract:
In this paper, we examine a novel SEIVS epidemiological model involving an incubation period and temporary immunity. The dynamics of the model is governed by the threshold behavior determined by the control reproductive number $R_c$. The existence and uniqueness of the endemic equilibrium are rigorously proved; this implies that an endemic state arises if and only if $R_c>1$. The local asymptotic stability of this equilibrium is established by analyzing the Jacobian matrix and the Routh–Hurwitz criterion. Theorems on sufficient and necessary conditions for the stability of solutions are proved.
Fulltext:
PDF file (187 kB)