Global dynamics of a three-species spatial food chain model

HY Jin, ZA Wang, L Wu - Journal of Differential Equations, 2022 - Elsevier
In this paper, we study the following initial-boundary value problem of a three-species
spatial food chain model {ut= d 1 Δ u+ u (1− u)− b 1 uv, x∈ Ω, t> 0 vt= d 2 Δ v−∇⋅(ξ v∇ u)+ …

Global stability of infectious disease models using Lyapunov functions

Z Shuai, P van den Driessche - SIAM Journal on Applied Mathematics, 2013 - SIAM
Two systematic methods are presented to guide the construction of Lyapunov functions for
general infectious disease models and are thus applicable to establish their global …

Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics

X Bai, M Winkler - Indiana University Mathematics Journal, 2016 - JSTOR
The fully parabolic two-species chemotaxis system (∗) u_t=d_1Δu-χ_1\triangledown⋅(u\
triangledownw)+μ_1u(1-u-a_1v)\quadx∈Ω,t\textgreater0,\v_t=d_2Δv-χ_2\triangledown⋅(v …

Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator–prey system

F Yi, J Wei, J Shi - Journal of Differential Equations, 2009 - Elsevier
A diffusive predator–prey system with Holling type-II predator functional response subject to
Neumann boundary conditions is considered. Hopf and steady state bifurcation analysis are …

Global dynamics of the Lotka‐Volterra competition‐diffusion system: diffusion and spatial heterogeneity I

X He, WM Ni - Communications on Pure and Applied …, 2016 - Wiley Online Library
In the first part of this series of three papers, we investigate the combined effects of diffusion,
spatial variation, and competition ability on the global dynamics of a classical Lotka‐Volterra …

Dynamics and pattern formation of a diffusive predator–prey model with predator-taxis

S Wu, J Wang, J Shi - Mathematical Models and Methods in Applied …, 2018 - World Scientific
We propose a new reaction–diffusion predator–prey model system with predator-taxis in
which the preys could move in the opposite direction of predator gradient. A similar situation …

Global solvability and stability of an alarm-taxis system

HY Jin, ZA Wang, L Wu - SIAM Journal on Mathematical Analysis, 2023 - SIAM
This paper is concerned with the global boundedness and stability of classical solutions to
an alarm-taxis system describing the burglar alarm hypothesis as an important mechanism …

[HTML][HTML] Stability analysis of a chemostat model with maintenance energy

T Zhang, T Zhang, X Meng - Applied Mathematics Letters, 2017 - Elsevier
In this paper, we dedicate ourselves to the study of a diffusive model for unstirred membrane
reactors with maintenance energy and subject to a homogeneous Neumann boundary …

A host-vector model for malaria with infective immigrants

J Tumwiine, JYT Mugisha, LS Luboobi - Journal of Mathematical Analysis …, 2010 - Elsevier
This paper considers a host-vector mathematical model for the spread of malaria that
incorporates recruitment of human population through a constant immigration, with a fraction …

Multiscale model within-host and between-host for viral infectious diseases

AES Almocera, VK Nguyen… - Journal of Mathematical …, 2018 - Springer
Multiscale models possess the potential to uncover new insights into infectious diseases.
Here, a rigorous stability analysis of a multiscale model within-host and between-host is …