Dynamic behavior of a parasite–host model with general incidence

AbstractIn this paper, we consider the global dynamics of a microparasite model with more general incidences. For the model with the bilinear incidence, Ebert et al. [D. Ebert, M. Lipsitch, K.L. Mangin, The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites, American Naturalist 156 (2000) 459–477] observed that parasites can reduce host density, but the extinction of both host population and parasite population occurs only under stochastic perturbations. Hwang and Kuang [T.W. Hwang, Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol. 46 (2003) 17–30] studied the model with the standard incidence and found that the host population may be extinct in the absence of random disturbance. We consider more general incidences that characterize transitions from the bilinear incidence to the standard incidence to simulate behavior changes of populations from random mobility in a fixed area to the mobility with a fixed population density. Using the techniques of Xiao and Ruan [D. Xiao, S. Ruan, Global dynamics of a ratio-dependent predator–prey system, J. Math. Biol. 43 (2001) 268–290], it is shown that parasites can drive the host to extinction only by the standard incidence. The complete classifications of dynamical behaviors of the model are obtained by a qualitative analysis

Dynamics of a Viral Infection Model with General Contact Rate between Susceptible Cells and Virus Particles

This paper investigates the dynamic behavior of a viral infection model with general contact rate between susceptible host cells and free virus particles. If the basic reproduction number of the virus is less than unity, by LaSalle’s invariance principle, the disease-free equilibrium is globally asymptotically stable. If the basic reproduction number of the virus is greater than unity, then the virus persists in the host and the endemic equilibrium is locally asymptotically stable

Demystifying Privacy Policy of Third-Party Libraries in Mobile Apps

The privacy of personal information has received significant attention in mobile software. Although previous researchers have designed some methods to identify the conflict between app behavior and privacy policies, little is known about investigating regulation requirements for third-party libraries (TPLs). The regulators enacted multiple regulations to regulate the usage of personal information for TPLs (e.g., the "California Consumer Privacy Act" requires businesses clearly notify consumers if they share consumers' data with third parties or not). However, it remains challenging to analyze the legality of TPLs due to three reasons: 1) TPLs are mainly published on public repositoriesinstead of app market (e.g., Google play). The public repositories do not perform privacy compliance analysis for each TPL. 2) TPLs only provide independent functions or function sequences. They cannot run independently, which limits the application of performing dynamic analysis. 3) Since not all the functions of TPLs are related to user privacy, we must locate the functions of TPLs that access/process personal information before performing privacy compliance analysis. To overcome the above challenges, in this paper, we propose an automated system named ATPChecker to analyze whether the Android TPLs meet privacy-related regulations or not. Our findings remind developers to be mindful of TPL usage when developing apps or writing privacy policies to avoid violating regulation

Long-Term Sphere Culture Cannot Maintain a High Ratio of Cancer Stem Cells: A Mathematical Model and Experiment

Acquiring abundant and high-purity cancer stem cells (CSCs) is an important prerequisite for CSC research. At present, researchers usually gain high-purity CSCs through flow cytometry sorting and expand them by short-term sphere culture. However, it is still uncertain whether we can amplify high-purity CSCs through long-term sphere culture. We have proposed a mathematical model using ordinary differential equations to derive the continuous variation of the CSC ratio in long-term sphere culture and estimated the model parameters based on a long-term sphere culture of MCF-7 stem cells. We found that the CSC ratio in long-term sphere culture presented as gradually decreased drift and might be stable at a lower level. Furthermore, we found that fitted model parameters could explain the main growth pattern of CSCs and differentiated cancer cells in long-term sphere culture

Timoshenko beam model for the vibration analysis of a cracked nanobeam with surface energy

Free vibration of a cracked nanobeam with consideration of surface energy and transverse shear deformation is studied. The cracked nanobeam is simplified to a system of two segments joined by a rotational spring located at the cracked section. Numerical examples demonstrate that the surface energy increases the natural frequency of the beam. However, the influence of surface energy on the natural frequency becomes smaller for the higher modes. In addition, the effect of transverse shear deformation on the frequency becomes more significant for the higher modes

Energy gathering performance of micro/nanoscale circular energy harvesters based on flexoelectric effect

At micro/nanoscale, flexoelectric energy harvesters (FEHs) are more effective than piezoelectric energy harvesters (PEHs). Calculating the voltage and efficiency of such small-scale FEHs is a challenge for their applications. Because of huge number of atoms, molecular dynamics simulation and first-principle theory are difficult to be used. It is essential to develop an analytical model that can provide a direct calculation of the voltage and the efficiency of FEHs. This paper develops an analytical model for micro/nanoscale circular FEHs which are a composite structure having a flexoelectric layer attached to an elastic substrate. Mechanical and electrical governing equations are derived based on the Hamiltonian principle and with consideration of the flexoelectric effect. Approximate closed-form solutions for voltage output, power output and optimal load resistance are obtained. The optimal values of the inner and outer radii of the flexoelectric layer for maximum voltage and power outputs are identified. The power output and the energy conversion efficiency of the present model are much larger than those of classical model which only includes piezoelectric effect. This research is helpful for materials scientists and mechanical engineers for designing high-performance micro/nanoscale energy harvesters