Mathematical Modeling of Transmission Dynamics with Periodic Contact Rate and Control by Different Vaccination Rates of Hepatitis B Infection in Ghana

The paper evidenced that Hepatitis B infection is the world's deadliest liver infection and Vaccination is among the principal clinical strategies in fighting it. These have encouraged a lot of researchers to formulate mathematical models to accurately predict the mode of transmission and make deductions for better health decision-making processes. In this paper, an SEIR model is used to model the transmission of the Hepatitis B infection with periodic contact rate and examine the impact of vaccination. The model was validated using estimated data in Ghana and simulated in a MATLAB environment. The results showed that the vaccination rate has a great impact on the transmission mode of the Hepatitis B infection and the periodic contact rate may lead to a chaotic solution which could result in an uncontrolled spreading of the infection. It is concluded that even if the vaccination rate is 70%, the infection rate would reduce to the minimum barest so more newborns must be vaccinated.

Periodic Contact and Mixed Problems of the Elasticity Theory (Review)

Results are reviewed collected in the investigations of periodic contact and mixed problems of the plane, axially symmetric and spatial elasticity theory. Among mixed problems, cut (crack) problems are focused integral equations of which are connected with those for contact problems. The periodic contact problems stimulate research of the discrete contact of rough (wavy) surfaces. Together with classical elastic domains (half-plane, half-space, plane and full space), we consider periodic problems for cylinder, layer, cone and spatial wedge. Most publications including fun-damental ones by Westergaard and Shtaerman deals with plane periodic problems of the elasticity theory. Here, one can mention approaches based on complex variable functions, Fourier series, Green’s functions and potential func-tions. A fracture mechanics approach to the plane periodic contact problem was developed. Methods and approaches are considered which allow us to take friction forces, adhesion and wear into account in the periodic contact. For spatial periodic and doubly periodic contact and properly mixed problems, we describe such methods as the localiza-tion method, the asymptotic methods, the method of nonlinear boundary integral equations, the fast Fourier trans-form. The half-space is the simplest model for elastic solids. But for the simplest straight-line periodic punch system, some three-dimensional contact problems (normal contact or tangential contact for shifted cohesive coatings) turn out to be incorrect because their integral equations contain divergent series. Considering three-dimensional periodic problems, I.G. Goryacheva disposes circular punches in special way (circular orbits, polar coordinated are used for centers of the punches), in this case one can prove convergence of the series in the integral equation (it is important that the punches are circular). For the periodic problems for an elastic layer, V.M. Aleksandrov has shown that the series in integral equations converge but the kernels become more complicated. In the present paper, we demonstrate that for the straight-line periodic punch system of arbitrary form the contact problem for a half-space turns out to be correct in case of more complicated boundary conditions. Namely, it can be sliding support or rigid fixation of a half-plane on the half-space boundary, the half-plane boundary should be parallel to the straight-line (the punch system axis) for arbitrary finite distance between the parallel lines. On this way, for sliding support, the kernel of the period-ic problem integral equation kernel is free of integrals, it consists of single convergent series (normal contact, the kernel is given in two equivalent forms). We consider classical percolation (how neighboring contact domains pene-trate one to another, investigated by K.L. Johnson, V.A. Yastrebov with co-authors) for the three-dimensional periodic contact amplification as well as percolation for the straight-line punch system. A similar approach is suggested for the case of periodic tangential contact (coatings system cohesive with a half-space boundary shifted along its axis or perpendicular to it). Here, one can separate out unique solutions of auxiliary problems because the line of changing boundary conditions on the half-space boundary can provoke non-uniqueness. The method proposed opens possibility to consider more complicated three-dimensional periodic contact problems for straight-line punch systems with changing boundary conditions inside the period.

Olfactory contacts mediate plasticity in male aggression with variable male density

Males typically adjust their reproductive strategies based on the perceived density and relative abilities of nearby competitors. In high-density populations, repeated encounters facilitate reliable, learned associations between individuals and their relative competitive abilities. In contrast, opportunities to form such associations are limited when densities are low or in flux, increasing the risk that individuals will unintentionally engage in potentially costly interactions with higher-quality or aggressive opponents. To maximize their fitness, individuals in low-density and fluctuating populations therefore need a general way to assess their current social environment, and thus their relative competitive ability. Here, we investigate how olfactory social signals (scent marks) might perform this function. We manipulated the perceived social environment of isolated, male house mice ( Mus domesticus ) via their periodic contact with scent marks from 3 or 9 male conspecifics, or a control of no scents, over 15 days. We then paired them with an unknown opponent and examined how the diversity of recent scent contact mediated their behavior towards dominant or subordinate opponents. There was an overall pattern for increasing scent diversity to significantly reduce male mice’s aggression (tail rattling and lunging) towards their opponents, and also their willingness to engage in reciprocal investigation. Such cautiousness was not indicative of perceived subordinance, however; the diversity of recent scent contact did not affect mice’s investigation of their opponent’s scents, and some measures of aggression were greater when mice faced dominant opponents. These results suggest that house mice can use scent signals to assess their current social environment in the absence of physical interactions, modifying their behavior in ways that are predicted to reduce their risks of injury when the likelihood of encountering unknown opponents increases.

A Self-Powered Triboelectric Nanosensor for PH Detection

A self-powered, sliding electrification based triboelectric sensor was developed for detecting PH value from a periodic contact/separation motion. This innovative, cost-effective, simply designed sensor is composed of a fluorinated ethylene propylene thin film and an array of electrodes underneath. The operation of the TENG (triboelectric nanogenerator) sensor relies on a repetitive emerging-submerging process with traveling solution waves, in which the coupling between triboelectrification and electrostatic induction gives rise to alternating flows of electrons between electrodes. On the basis of coupling effect between triboelectrification and electrostatic induction, the sensor generates electric output signals which are associated with PH value. Experimental results show that the output voltage of the TENG sensor increases with the increasing PH value, which indicate that the PH value of different solution can be real-time monitored. This work not only demonstrates a new principle in the field of PH value measurement but also greatly expands the applicability of triboelectric nanogenerator (TENG) as self-powered sensors.