Global dynamics of an infinite dimensional epidemic model with nonlocal state structures
This paper studies the global dynamics of an infinite-dimensional epidemic model with nonlocal state structures. To describe a continuous state model, the population is partitioned into susceptible and recovered, and a state-structured SIR model is introduced. Under certain balance conditions and smooth conditions, a sharp threshold result characterizing the global dynamics in terms of basic reproduction number \(R_0\) is presented. The model is a general multi-stage one in which infected individuals are allowed to transfer among different stages and new infections are distributed into all stages with certain probability. The existence and local stability of stationary solutions such as the disease-free equilibrium and endemic equilibria are discussed. The authors establish the global stability of the disease-free equilibrium when \(R_0<1\) and uniform persistence when \(R_0>1\). Some examples are also provided to illustrate the theoretical results.
scientific article; zbMATH DE number 6931740
scientific article