An SVEIR epidemic model with continuous age-dependent vaccination, latency, infection, and disease relapse is proposed and analyzed in this paper. The dynamical behaviors including the derivation of basic reproduction number 0 , the existence and the stability of steady states, and the uniform persistence of the model are investigated. The results indicate that if 0 ≤ 1, the disease-free steady state is globally asymptotically stable, and the disease dies out, whereas if 0 > 1, the disease is uniformly persistent, and the endemic steady state is also globally asymptotically stable, and the disease remains at the endemic level. The research shows the global dynamics of the model are sharply determined by its basic reproduction number 0 . Finally, numerical examples support our main theoretical results.
In this study, an SIRE epidemic model including infection age, relapse age, and effect of protection for susceptible in environmental virus infectious diseases is investigated. We use the function ffalse(Sfalse)$f(S)$ to represent the protection of susceptible so as to reduce the probability that susceptible are exposed to the polluted environment and become infected, and the function gfalse(Sfalse)$g(S)$ represents the protection of susceptible so as to reduce the probability that susceptible are directly contact with infected persons and become infected. We obtain threshold R0$R_{0}$ and the basic properties of solutions. Further, we see that when R0<1$R_{0}<1$ the disease‐free equilibrium exists and is unique and globally asymptotically stable, and when R0>1$R_{0}> 1$, besides the disease‐free equilibrium, the model has a unique endemic equilibrium that is locally asymptotically stable. Furthermore, we only obtained the system is uniformly persistence without the global asymptotical stability of endemic equilibrium when R0>1$R_0>1$. The numerical examples show that there exists a stable manifold of endemic equilibrium when R0>1$R_0>1$.
SVEIR epidemic model; age-dependence; basic reproduction number; local and global stability; uniform persistence Hosted file \begin{CJK}{UTF8}{gbsn}\end{CJK}\selectlanguage{english}SVEIR\begin{CJK}{UTF8}{gbsn}-\end{CJK}\selectlan available at https://authorea.com/users/369351/articles/488234-dynamical-properties-in-ansveir-epidemic-model-with-age-dependent-vaccination-latent-infected-and-relapse
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