The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

Background The global spread of the novel coronavirus pneumonia is still continuing, and a new round of more serious outbreaks has even begun in some countries. In this context, this paper studies the dynamics of a type of delayed reaction-diffusion novel coronavirus pneumonia model with relapse and self-limiting treatment in a temporal-spatial heterogeneous environment. Methods First, focus on the self-limiting characteristics of COVID-19, incorporate the relapse and self-limiting treatment factors into the diffusion model, and study the influence of self-limiting treatment on the diffusion of the epidemic. Second, because the traditional Lyapunov stability method is difficult to determine the spread of the epidemic with relapse and self-limiting treatment, we introduce a completely different method, relying on the existence conditions of the exponential attractor of our newly established in the infinite-dimensional dynamic system to determine the diffusion of novel coronavirus pneumonia. Third, relapse and self-limiting treatment have led to a change in the structure of the delayed diffusion COVID-19 model, and the traditional basic reproduction number $$R_0$$ R 0 no longer has threshold characteristics. With the help of the Krein-Rutman theorem and the eigenvalue method, we studied the threshold characteristics of the principal eigenvalue and found that it can be used as a new threshold to describe the diffusion of the epidemic. Results Our results prove that the principal eigenvalue $$\uplambda ^{*}$$ λ ∗ of the delayed reaction-diffusion COVID-19 system with relapse and self-limiting treatment can replace the basic reproduction number $$R_0$$ R 0 to describe the threshold effect of disease transmission. Combine with the latest official data and the prevention and control strategies, some numerical simulations on the stability and global exponential attractiveness of the diffusion of the COVID-19 epidemic in China and the USA are given. Conclusions Through the comparison of numerical simulations, we find that self-limiting treatment can significantly promote the prevention and control of the epidemic. And if the free activities of asymptomatic infected persons are not restricted, it will seriously hinder the progress of epidemic prevention and control.

Exponential Attractors for the 3D Fractional-order Bardina Turbulence Model With Memory and Horizontal Filtering

We consider the 3D simplified Bardina turbulence model with horizontal filtering, fractional dissipation, and the presence of a memory term incorporating hereditary effects. We analyze the regularity properties and the dissipative nature of the considered system and, in our main result, we show the existence of a global exponential attractor in a suitable phase space.

Strong attractors and their robustness for an extensible beam model with energy damping

<p style='text-indent:20px;'>This paper investigates the existence of <i>strong</i> global and exponential attractors and their robustness on the perturbed parameter for an extensible beam equation with nonlocal energy damping in <inline-formula><tex-math id="M1">\begin{document}$ \Omega\subset{\mathbb R}^N $\end{document}</tex-math></inline-formula>: <inline-formula><tex-math id="M2">\begin{document}$ u_{tt}+\Delta^2 u-\kappa\phi(\|\nabla u\|^2)\Delta u-M(\|\Delta u\|^2+\|u_t\|^2)\Delta u_t+f(u) = h $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M3">\begin{document}$ \kappa \in \Lambda $\end{document}</tex-math></inline-formula> (index set) is an extensibility parameter, and where the "<i>strong</i>" means that the compactness, the attractiveness and the finiteness of the fractal dimension of the attractors are all in the topology of the stronger space <inline-formula><tex-math id="M4">\begin{document}$ {\mathcal H}_2 $\end{document}</tex-math></inline-formula> where the attractors lie in. Under the assumptions that either the nonlinearity <inline-formula><tex-math id="M5">\begin{document}$ f(u) $\end{document}</tex-math></inline-formula> is of optimal subcritical growth or even <inline-formula><tex-math id="M6">\begin{document}$ f(u) $\end{document}</tex-math></inline-formula> is a true source term, we show that (ⅰ) the semi-flow originating from any point in the natural energy space <inline-formula><tex-math id="M7">\begin{document}$ {\mathcal H} $\end{document}</tex-math></inline-formula> lies in the stronger strong solution space <inline-formula><tex-math id="M8">\begin{document}$ {\mathcal H}_2 $\end{document}</tex-math></inline-formula> when <inline-formula><tex-math id="M9">\begin{document}$ t&gt;0 $\end{document}</tex-math></inline-formula>; (ⅱ) the related solution semigroup <inline-formula><tex-math id="M10">\begin{document}$ S^\kappa(t) $\end{document}</tex-math></inline-formula> has a strong <inline-formula><tex-math id="M11">\begin{document}$ ({\mathcal H},{\mathcal H}_2) $\end{document}</tex-math></inline-formula>-global attractor <inline-formula><tex-math id="M12">\begin{document}$ {\mathscr A}^\kappa $\end{document}</tex-math></inline-formula> for each <inline-formula><tex-math id="M13">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula> and the family of <inline-formula><tex-math id="M14">\begin{document}$ {\mathscr A}^\kappa, \kappa\in \Lambda $\end{document}</tex-math></inline-formula> is upper semicontinuous on <inline-formula><tex-math id="M15">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula> in the topology of stronger space <inline-formula><tex-math id="M16">\begin{document}$ {\mathcal H}_2 $\end{document}</tex-math></inline-formula>; (ⅲ) <inline-formula><tex-math id="M17">\begin{document}$ S^\kappa(t) $\end{document}</tex-math></inline-formula> has a strong <inline-formula><tex-math id="M18">\begin{document}$ ({\mathcal H},{\mathcal H}_2) $\end{document}</tex-math></inline-formula>-exponential attractor <inline-formula><tex-math id="M19">\begin{document}$ \mathfrak {A}^\kappa_{exp} $\end{document}</tex-math></inline-formula> for each <inline-formula><tex-math id="M20">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula> and it is Hölder continuous on <inline-formula><tex-math id="M21">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula> in the topology of <inline-formula><tex-math id="M22">\begin{document}$ {\mathcal H}_2 $\end{document}</tex-math></inline-formula>. These results break through long-standing existed restriction for the attractors of the extensible beam models in energy space and show the optimal topology properties of them in the stronger phase space.</p>

Pullback attractors via quasi-stability for non-autonomous lattice dynamical systems

<p style='text-indent:20px;'>In this paper we study long-time behavior of first-order non-autono-mous lattice dynamical systems in square summable space of double-sided sequences using the cooperation between the discretized diffusion operator and the discretized reaction term. We obtain existence of a pullback global attractor and construct pullback exponential attractor applying the introduced notion of quasi-stability of the corresponding evolution process.</p>

Study of the dissipativity, global attractor and exponential attractor for a hyperbolic relaxation of the Caginalp phase-field system with singular nonlinear terms

In this paper, we study of the dissipativity, global attractor and exponential attractor for a hyperbolic relaxation of the Caginalp phase-field system with singular nonlinear terms, with initial and homogenous Dirichlet boundary condition.

Strong Exponential Attractors for Weakly Damped Semilinear Wave Equations

In this paper, we investigate the longtime dynamics for the damped wave equation in a bounded smooth domain of ℝ3. The exponential attractor is investigated in a strong energy space for the case of subquintic nonlinearity, which is based on the recent extension of the Strichartz estimate for the case of a bounded domain. The results obtained complete some previous works.