Stability analysis of a stage‐structure model with spatial heterogeneity

Abstract

A stage‐structure competition‐diffusion model with spatial heterogeneity is investigated in this paper. Under some suitable assumptions, the existence of spatially non‐homogeneous steady‐state solutions is established by investigating eigenvalue problems with indefinite weight and employing Lyapunov‐Schmidt reduction. The stability of spatially nonhomogeneous steady‐state solutions is obtained by analyzing the set of the spectrum of the associated infinitesimal generator. In particular, the global stability of the steady‐state solutions is described in weak competition case.

Qualitative analysis of a diffusive SEIR epidemic model with linear external source and asymptomatic infection in heterogeneous environment

“…Note that m, M are independent of n, then m ≤ S n ≤ M for all n ∈ N and the claim holds. Hence, one can use the similar arguments as those of [8] together with (34) to prove that S n → S * > 0 uniformly onΩ, where S * satisfies (48), which implies that S * = F (x, E * , I * , R * ).…”

“…Therefore, it is of great significance to use mathematical models to study infectious diseases. In recent years, based on the fact that environmental heterogeneity and individual migration have a significant impact on the spread of disease and the permanence of populations [3,34], many scholars have made extensive and profound research by using mathematical models [1,2,8,14,20,26,30,31,38,40,43,45,48]. In 2008, Allen et al [2] proposed the following frequencydependent SIS (susceptible-infected-susceptible) epidemic reaction-diffusion system with space-dependent disease transmission rate β(x) and recovery rate γ(x):…”

Dynamics of a delayed Lotka-Volterra model with two predators competing for one prey

“…In this model the populations of predator and prey permanently oscillate for almost all positive initial conditions. Recently, there have been some excellent works on global dynamics of resource competitive models (see [4,5,11,16,17,19,24,22,25,30,31,32,33,34]), which are important in understanding of the mechanism of natural selection: the principle of competitive exclusion (see [1,3,10,26,27,28,35,36]) or the coexistence of competing species. For example, Volterra [29] observed that the coexistence of two or more predators competing for fewer prey resources is impossible.…”