Global dynamics of a Vector‐Borne disease model with two delays and nonlinear transmission rate

In this paper, we investigate a Vector‐Borne disease model with nonlinear incidence rate and 2 delays: One is the incubation period in the vectors and the other is the incubation period in the host. Under the biologically motivated assumptions, we show that the global dynamics are completely determined by the basic reproduction number R₀. The disease‐free equilibrium is globally asymptotically stable if R₀≤1; when R₀>1, the system is uniformly persistent, and there exists a unique endemic equilibrium that is globally asymptotically. Numerical simulations are conducted to illustrate the theoretical results.     

Geometric approach to global asymptotic stability for the SEIRS models in epidemiology

In this paper, we present a more general criterion for the global asymptotic stability of equilibria for nonlinear autonomous differential equations based on the geometric criterion developed by Li and Muldowney. By applying this criterion, we obtain some results for the global asymptotic stability of SEIRS models with constant recruitment and varying total population size. Based on these results, we give a complete affirmative answer to Liu–Hethcote–Levin conjecture. Furthermore, an affirmative answer to Li–Graef–Wang–Karsai’s problem for SEIR model with permanent immunity and varying total population size is given.     

New results for the Liebau phenomenon via fixed point index

We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a simple model. Our methodology relies on the use of classical fixed point index. Some examples are provided to illustrate our theory. We improve and complement previous results in the literature.     

Study of the aerodynamic characteristics of cone-sphere models in a hypersonic flow

The aerodynamic characteristics of cone-sphere models are studied at Mach numbers M = 6, 8.4, and 12 to 13 over a wide Reynolds number range. Models of a braking device (sphere) were connected with a load (frustum of a cone) by means of shrouds. The dependences of the aerodynamic coefficients C _x and C _y on the angle of attack α were obtained for different relative dimensions of the load and the braking device, shroud lengths, and Mach and Reynolds numbers. The effect of the above-mentioned parameters on the aerodynamic characteristics of the models is analyzed. The C _x (Re_D) dependences of load-parachutemodels in a symmetric flow are determined over the wide Mach and Reynolds number ranges 6 ≤ M ≤ 13 and 3 · 10³ ≤ Re_D ≤ 3 · 10⁶.     

Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems

In the real world, many networks show community structure, i.e., clusters of nodes, which have a high density of links within the same cluster but a lower density of links between different clusters. In this paper, nonlinearly coupled networks with community structure and non-identical nodes and with time-varying delay are considered. By applying pinning control to a fraction of network nodes, and using a suitable Lyapunov function, we obtain some new and useful synchronization criteria, which guarantee that various clusters are synchronized independently. An example is presented to show the application of the criteria obtained in this paper.