Steady-state analysis of networked epidemic models

Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two positive feedback frameworks that are applicable to the study of steady-state values in a wide range of compartmental epidemic models, including both group and networked processes. In the case of a group (resp. networked) model, we show that the convergence limit of the susceptible proportion of the population (resp. the susceptible proportion in at least one of the subgroups) is upper bounded by the reciprocal of the basic reproduction number (BRN) of the model. The BRN, when it is greater than unity, thus demonstrates the level of penetration into a subpopulation by the disease. Both non-strict and strict bounds on the convergence limits are derived and shown to correspond to substantially distinct scenarios in the epidemic processes, one in the presence of the endemic state and another without. Formulae for calculating the limits are provided in the latter case. We apply the developed framework to examining various group and networked epidemic models commonly seen in the literature to verify the validity of our conclusions

On the exponential convergence of input-output signals of nonlinear feedback systems

We show that the integral-constraint-based robust feedback stability theorem for certain Lurye systems exhibits the property that the endogenous input-output signals enjoy an exponential convergence rate for all initial conditions of the linear time-invariant subsystem. More generally, we provide conditions under which a feedback interconnection of possibly open-loop unbounded subsystems to admit such an exponential convergence property, using perturbation analysis and a combination of tools including integral quadratic constraints, directed gap measure, and exponential weightings. As an application, we apply the result to first-order convex optimisation methods. In particular, by making use of the Zames-Falb multipliers, we state conditions for these methods to converge exponentially when applied to strongly convex functions with Lipschitz gradients.Comment: This paper has been submitted to Automatic

B and T Lymphocyte Attenuator Down-regulation by HIV-1 Depends on Type I Interferon and Contributes to T-Cell Hyperactivation

Background. Nonspecific T-cell hyperactivation is the main driving force for human immunodeficiency virus (HIV)–1 disease progression, but the reasons why the excess immune response is not properly shut off are poorly defined

Geochemical reactions altering the mineralogical and multiscale pore characteristics of uranium-bearing reservoirs during CO2 + O2in situ leaching

CO2 + O2in situ leaching has been extensively applied in uranium recovery in sandstone-type uranium deposits of China. The geochemical processes impact and constrain the leaching reaction and leaching solution migration; thus, it is necessary to study the CO2 + O2–water–rock geochemical reaction process and its influence on the physical properties of uranium-bearing reservoirs. In this work, a CO2 + O2–water–rock geochemical reaction simulation experiment was carried out, and the mineralogical and multiscale pore characteristics of typical samples before and after this simulation experiment were compared by X-ray diffraction and high-pressure mercury intrusion porosimetry (HPMIP). The results show that the CO2 + O2–water–rock geochemical reaction has complicated effects on the mineral compositions due to the various reaction modes and types. After the CO2 + O2–water–rock geochemical reaction, the femic minerals decrease and the clay minerals in the coarse sandstone, medium sandstone, fine sandstone, and siltstone increase, while the femic minerals and clay minerals in sandy mudstone show a contrary changing trend. The CO2 + O2–water–rock geochemical reaction decreases the total pore volume of uranium-bearing reservoirs and then promotes pore transformation from small scale to large scale. The fractal dimensions of macropores are decreased, and the fractal dimensions of mesopores, transition pores, and micropores are increased. The effects of felsic mineral and carbonate dissolution, secondary mineral precipitate, clay mineral swelling, and mineral particle migration are simultaneously present in the CO2 + O2in situ leaching process, which exhibit the positive transformation and the negative transformation for the uranium-bearing reservoirs. The mineral dissolution may improve reservoir permeability to a certain degree, while the siltation effect will gradually reveal with the extension of CO2 + O2in situ leaching. This research will provide a deep understanding of the physical property response of uranium-bearing reservoirs during CO2 + O2in situ leaching and indicate the direction for the efficient recovery of uranium resources

Robust stability of uncertain linear systems with input and output quantization and packet loss

This paper investigates the robust stability of uncertain discrete-time linear systems subject to input and output quantization and packet loss. First, a necessary and sufficient condition in terms of LMIs is proposed for the quadratic stability of the closed-loop system with double quantization and norm bounded uncertainty in the plant. Moreover, it is shown that the proposed condition can be exploited to derive the coarsest logarithmic quantization density under which the uncertain plant can be quadratically stabilized via quantized state feedback. Second, a new class of Lyapunov function which depends on the quantization errors in a multilinear way is developed to obtain less conservative results. Lastly, the case with input and output packet-loss channels is investigated.<br