Related papers: Global and local asymptotic stability of an epidem…
This paper analyzes the stability of a reactiondiffusion equation coupled with a finite-dimensional controller through Dirichlet boundary input and Neumann boundary output. Going against the flow, we intend to propose numerical certificates…
We propose a lattice dynamical system that arises in a discrete diffusive two-group epidemic model with latency in a patchy environment. The model considers the SIS form and latency of the disease in group 1, while the SIR form without…
The global stability of the nonhomogeneous positive steady state solution to a diffusive Holling-Tanner predator-prey model in a heterogeneous environment is proved by using a newly constructed Lyapunov function and estimates of nonconstant…
In this paper, we investigate the global asymptotic stability of an age-structured population dynamics model with a Ricker's type of birth function. This model is a hyperbolic partial differential equation with a nonlinear and nonlocal…
In this paper, Lyapunov-Razumikhin technique, design of state-dependent switching laws, a fixed point theorem and variational methods are employed to derive the existence and the unique existence results of globally exponentially stable…
One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the…
The conceptual difference between equilibrium and non-equilibrium steady state (NESS) is well established in physics and chemistry. This distinction, however, is not widely appreciated in dynamical descriptions of biological populations in…
In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of…
In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
A significant proportion of the infections driving the current {SARS-CoV-2} pandemic are transmitted asymptomatically. Here we introduce and study a simple epidemic model with separate compartments comprising asymptomatic and symptomatic…
This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…
The question of biological stability (permanence) of a replicator reaction-diffusion system is considered. Sufficient conditions of biological stability are found. It is proved that there are situations when biologically unstable…
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…
In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a…
This paper studies qualitative properties of solutions of nonlocal infectious SIR epidemic models (1.3)-(1.5), with the homogeneous Neumann boundary conditions, Dirichlet boundary conditions and free boundary, respectively. We first use the…
In this study, a new and natural way of constructing a stochastic Susceptible-Infected-Susceptible (SIS) model is proposed. This approach is natural in the sense that the disease transmission rate, $\beta$, is substituted with a generic,…
We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their…
We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…
In this paper, we investigate a class of non-monotone reaction-diffusion equations with distributed delay and a homogenous boundary Neumann condition, which have a positive steady state. The main concern is the global attractivity of the…
We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…