Traveling waves and spreading properties for a reaction-diffusion competition model with seasonal succession*

In this paper, we investigate the propagation dynamics of a reaction–diffusion competition model with seasonal succession in the whole space. Under the weak competition condition, the corresponding kinetic system admits a globally stable positive periodic solution ( u ^ ( t ) , v ^ ( t ) ) . By the method of upper and lower solutions and the Schauder fixed point theorem, we first obtain the existence and nonexistence of traveling wave solutions connecting (0, 0) to ( u ^ ( t ) , v ^ ( t ) ) . Then we use the comparison arguments to establish the spreading properties for a large class of solutions.

Closed Churches during the Pandemic: Liberal versus Conservative and Christian versus Atheist Argumentation in Media

The current COVID-19 pandemic has led to the introduction of various epidemiological measures, including the ban on public worship. The problem of closed churches has become an intensely debated subject across several countries and a hotly debated question in recent media discourse. This paper provides an analysis of the arguments presented on the subject of closed churches by the media in Slovakia and the Czech Republic. In addition to the detailed analysis of the argumentation used, it also presents a twofold comparison: arguments presented in liberal versus conservative media, and arguments presented in the Slovak media versus Czech media. Twenty-eight years ago, these two countries were part of one state and after the split, the countries became a model of a peaceful dissolution (the so-called ‘velvet divorce’). However, from a religious perspective, they are quite different: whereas Slovakia is one of the most Christian (Catholic) countries, the Czech Republic is one of the most atheist countries in Europe. Three research dimensions are presented as part of this study: (1) media argumentation on the problem of closed churches; (2) comparison of liberal versus conservative arguments; (3) comparison of the media coverage in a strongly Christian country versus a strongly atheist country.

Global stability of an SEIR epidemic model with vaccination

In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results.

Stability and Hopf Bifurcation in Delayed Predator-Prey System with Ratio Dependent

A delayed predator-prey model with stage structure for predator and ratio dependent response function is considered. By calculating characteristic equations and analyzing characteristic roots, the sufficient conditions for local stability of all the equilibria and Hopf bifurcation are obtained. Moreover, We use an iteration technique and comparison arguments to derive the sufficient conditions of the global stability of the boundary and positive equilibrium.

Analysis of a delayed epidemic model with non-monotonic incidence rate and vertical transmission

A delayed SEIR epidemic model with vertical transmission and non-monotonic incidence is formulated. The equilibria and the threshold of the model have been determined on the bases of the basic reproduction number. The local stability of disease-free equilibrium and endemic equilibrium is established by analyzing the corresponding characteristic equations. By comparison arguments, it is proved that, if R0 < 1, the disease-free equilibrium is globally asymptotically stable. Whereas, the disease-free equilibrium is unstable if R0 > 1. Moreover, we show that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium when R0 > 1.

Existence and non-existence of solutions to elliptic equations with a general convection term

In this paper we consider the nonlinear elliptic problem −Δu + αu = g(∣∇u∣) + λh(x) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain of ℝN, α ≥ 0, g is an arbitrary C1 increasing function and h ∈ C1() is non-negative. We completely analyse the existence and non-existence of (positive) classical solutions in terms of the parameter λ. We show that there exist solutions for every λ when α = 0 and the integral 1/g(s)ds = ∞, or when α > 0 and the integral s/g(s)ds = ∞. Conversely, when the respective integrals converge and h is non-trivial on ∂Ω, existence depends on the size of λ. Moreover, non-existence holds for large λ. Our proofs mainly rely on comparison arguments, and on the construction of suitable supersolutions in annuli. Our results include some cases where the function g is superquadratic and existence still holds without assuming any smallness condition on λ.

Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays

We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.

Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge

A ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey population is formulated and analyzed. The effects of time delay due to the gestation of the predator and stage structure for the predator on the dynamics of the system are concerned. By analyzing the corresponding characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the system is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the coexistence equilibrium, whenτ=τ0. By comparison arguments, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium. By using an iteration technique, sufficient conditions are derived for the global attractivity of the coexistence equilibrium of the proposed system.

Analysis of a HBV Model with Diffusion and Time Delay

This paper discussed a hepatitis B virus infection with delay, spatial diffusion, and standard incidence function. The local stability of equilibrium is obtained via characteristic equations. By using comparison arguments, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproductive number is greater than unity, by means of an iteration technique, sufficiently conditions are obtained for the global asymptotic stability of the infected steady state. Numerical simulations are carried out to illustrate our findings.