Dynamics of a delayed within host model for dengue infection with immune response and Beddington–DeAngelis incidence

In this paper, a new delayed within host model for dengue fever with immune response and Beddington–DeAngelis incidence is investigated. The basic reproduction number is computed. In addition, a detailed analysis on the local and global dynamics of the model is conducted. Finally, sensitivity analysis is carried out on basic reproduction number and numerical simulations are given to elucidate our theoretical results.

Transmission Dynamics of Coronavirus Pandemic: Modeling and Stability Analysis

Covid-19, as a pandemic disease around the world, has generated great threat to human society and caused enormous mortality with weak surveillance system. In this paper, we propose a mathematical model to describe the transmission of Covid-19. Moreover, basic reproduction number and the local and global dynamics of the dynamical model are obtained. Then we apply our model to characterize the transmission process of Covid-19 in Nigeria. It was found that, in order to avoid its outbreak in Nigeria, it may be better to adhere to government policy to curtail the spread through person-to-person transmission and make effort to improve personal hygiene as well as early detection and reporting. Our results may provide some new insights for elimination of Covid-19.

Analysis of a Predator-Prey Model with Distributed Delay

In this paper, we consider a predator-prey model, where we assumed that the model to be an infected predator-free equilibrium one. The model includes a distributed delay to describe the time between the predator’s capture of the prey and its conversion to biomass for predators. When the delay is absent, the model exhibits asymptotic convergence to an equilibrium. Therefore, any nonequilibrium dynamics in the model when the delay is included can be attributed to the delay’s inclusion. We assume that the delay is distributed and model the delay using integrodifferential equations. We established the well-posedness and basic properties of solutions of the model with nonspecified delay. Then, we analyzed the local and global dynamics as the mean delay varies.

An Island for Everyone: Poveglia as contested public space in the Venetian Lagoon

This article focuses on the story of the proposed privatisation of Poveglia, a small uninhabited island in the Venetian Lagoon. In March 2014 the Italian State Property Office announced that a 99-year lease on Poveglia would be offered for sale in an online auction. The reaction of some citizens led to the formation of the association Poveglia per Tutti (Poveglia for Everyone), whose activists and supporters wanted the island to be preserved as a public space and blocked the acquisition. The article firstly frames Poveglia in the processes that are particular to the small islands of the Venetian Lagoon, from abandonment to tourism-related ‘land grabbing’, and then contextualises the story of this minor island in a more general discussion regarding broader ‘right to the island’ narratives and practices with reference to some other European cases. Finally, the article presents the results of a an ethnographically informed analysis of the association Poveglia per Tutti to discuss the capacity and potentialities of some small islands - as separate, limited, and identifiable spaces - to be part of territorialisation processes dealing with active citizenship, resistance to tourist monoculture and the usability of public space. In this way, Poveglia becomes a synecdoche for the whole of Venice and its lagoon, ‘condensing’, at the same time, local and global dynamics.

COMPETITION AND COOPERATION ON PREDATION: BIFURCATION THEORY OF MUTUALISM

In this paper, we investigate two predator–prey models which take into consideration hunting cooperation (i.e., mutualism) between two different predators and within one predator species, respectively. Local and global dynamics are obtained for the model systems. By a detailed bifurcation analysis, we investigate the dependence of predation dynamics on mutualism (cooperative predation). From our study, we prove that mutualism may enhance the survival of mutualist predators in a severe condition and break the competitive exclusion principle. We further provide quantitative information about how the cooperative predation (mutualism) may (i) establish multiple stability switches on the positive equilibrium; (ii) generate backward bifurcation on equilibria; (iii) induce supercritical or subcritical Hopf bifurcations; and (iv) establish bi-stability phenomenon between the predator-free equilibrium and a positive equilibrium (or a limit cycle).

Stability Properties of 1-Dimensional Hamiltonian Lattices with Nonanalytic Potentials

We investigate the local and global dynamics of two 1-Dimensional (1D) Hamiltonian lattices whose inter-particle forces are derived from nonanalytic potentials. In particular, we study the dynamics of a model governed by a “graphene-type” force law and one inspired by Hollomon’s law describing “work-hardening” effects in certain elastic materials. Our main aim is to show that, although similarities with the analytic case exist, some of the local and global stability properties of nonanalytic potentials are very different than those encountered in systems with polynomial interactions, as in the case of 1D Fermi–Pasta–Ulam–Tsingou (FPUT) lattices. Our approach is to study the motion in the neighborhood of simple periodic orbits representing continuations of normal modes of the corresponding linear system, as the number of particles [Formula: see text] and the total energy [Formula: see text] are increased. We find that the graphene-type model is remarkably stable up to escape energy levels where breakdown is expected, while the Hollomon lattice never breaks, yet is unstable at low energies and only attains stability at energies where the harmonic force becomes dominant. We suggest that, since our results hold for large [Formula: see text], it would be interesting to study analogous phenomena in the continuum limit where 1D lattices become strings.

Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game

The Bischi–Naimzada game is a market competition between two firms with the objective of maximizing profits under limited information. In this article, we study a more generalized and realistic situation that takes into account the sales constraints. we generalize the economic model suggested by Bischi–Naimzada by introducing and studying the maximization of profits based on sales constraints. Our motivation in this paper is the studying of profit and sales constraints maximization and their influences on the game’s dynamics. The local stability of the equilibrium points of the proposed model is discussed. It examines how the dynamics of the proposed two-dimensional competition game model focusing on changes in both the speed of the adjustment and the sales constraint parameters. The map describing the game is proven to be noninvertible and yields many multi-stable, complex dynamics and the coexistence chaotic attractors may arise. The global behavior of the map is achieved by studying the critical curves. The numerical simulations demonstrate the coexistence of two attractors and complex structures of the attraction basins. Several examples are discussed in order to confirm all the analytical results obtained.