Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

In this paper, we discuss the Anthroponotic Cutaneous Leishmania transmission. In addition, we develop a mathematical model for the Anthroponotic Cutaneous Leishmania transmission and consider its qualitative behavior. We derive the threshold number $R_{0}$ R 0 of the model using the next generation method. In the disease-free case, we carry out the local and global stability under the condition $R_{0}<1$ R 0 < 1 . Moreover, we derive the global stability at the disease-free equilibrium point by utilizing the Castillo-Chavez method. On the other hand, at the endemic equilibrium point, we show the local and global stability to be held under specific conditions and $R_{0}>1$ R 0 > 1 . We also establish the global stability at the endemic equilibrium point with the help of a geometrical approach, which is a generalization of Lyapunov theory, by using a second additive compound matrix. Finally, we take into account the sensitivity analysis of the threshold number with other parameters. We also discuss several graphs of important parameters.

A Mathematical Study of a Generalized SEIR Model of COVID-19

In this work (Part I), we reinvestigate the study of the stability of the Covid-19 mathematical model constructed by Shah et al. (2020) [1]. In their paper, the transmission of the virus under different control strategies is modeled thanks to a generalized SEIR model. This model is characterized by a five dimensional nonlinear dynamical system, where the basic reproduction number can be established by using the next generation matrix method. In this work (Part I), it is established that the disease free equilibrium point is locally as well as globally asymptotically stable when . When , the local and global asymptotic stability of the equilibrium are determined employing the second additive compound matrix approach and the Li-Wang’s (1998) stability criterion for real matrices [2]. In the second paper (Part II), some control parameters with uncertainties will be added to stabilize the five-dimensional Covid-19 system studied here, in order to force the trajectories to go to the equilibria. The stability of the Covid-19 system with these new parameters will also be assessed in Intissar (2020) [3] applying the Li-Wang criterion and compound matrices theory. All sophisticated technical calculations including those in part I will be provided in appendices of the part II.

Characterization and sliding wear performance of PMMA reinforced with SiO2 nanoparticles

The characterization and wear sliding performance of the poly(methyl methacrylate) (PMMA) reinforced with hydrophilic and hydrophobic nanoparticles of silicon dioxide (SiO2) was studied. The final polymer matrix was treated in a water bath at a temperature of 100°C for 6 h. Steel balls were used to slide against the surface of PMMA specimens reinforced with SiO2 nanoparticles. Sliding wear tests were carried out in wet sliding conditions applying a drop of distilled water between the specimen and the ball. The tests were carried out up to 9000 cycles at room temperature. A frequency of 5 Hz, a stroke amplitude of 3 mm, and a maximum contact pressure of 1.087 GPa were selected. Fourier transform infrared spectroscopy spectrum, scanning electron microscopy, and microhardness and roughness of the pure PMMA and PMMA/SiO2 were obtained. The coefficient of friction and wear rates were calculated, and the main wear mechanisms found were adhesion wear, plastic deformation, ploughing, and pitting. The results showed that the addition of hydrophobic nanoparticles of SiO2 may be employed to enhance the wear resistance of external automotive parts made of polymeric compound matrix. Finally, the specimens showed a hydrophilic behavior (angular contact < 90°) due to the high polarity of the PMMA matrix and the incorporation of the SiO2 nanoparticles.

The Effect of Botanical Pesticide Extract Addition on the Nutrient Release of Fertilizer from Poultry Manure

Slow release fertilizer with pesticide (SRFP) has been formulated to provide nutrientenriched with pesticide using all natural compound. Matrix formulation is used with poultry manure(PM) as the nutrient source as well as the solid matrix for incorporating neem leave (Azadirachtaindica a.juss) and gendarussa leave (Justicia gendarussa burm) extract as the active compounds. Inthis study, the release of nutrient i.e. nitrogen by the addition of the two leave extracts during SRFPpreparation has been investigated using sand bed column leaching test. The leachate solution wasanalysed by Kjedahl method to measure total nitrogen amount released. Different volume of the leaveextract was investigated to study the effect of the extract addition on the release of the nitrogen. It isshown that the higher the volume of the leaves extract added during the granulation process, the fasterthe release of the nutrient.

Global Dynamics of an Avian Influenza A(H7N9) Epidemic Model with Latent Period and Nonlinear Recovery Rate

An SEIR type of compartmental model with nonlinear incidence and recovery rates was formulated to study the combined impacts of psychological effect and available resources of public health system especially the number of hospital beds on the transmission and control of A(H7N9) virus. Global stability of the disease-free and endemic equilibria is determined by the basic reproduction number as a threshold parameter and is obtained by constructing Lyapunov function and second additive compound matrix. The results obtained reveal that psychological effect and available resources do not change the stability of the steady states but can indeed diminish the peak and the final sizes of the infected. Our studies have practical implications for the transmission and control of A(H7N9) virus.

Microstructure Evolution and Hardness of AlCrFeNixMo0.2 High Entropy Alloy

The microstructures, phase composition and hardness of the AlCrFeNixMo0.2 high entropy alloy (x=0.5, 0.8, 1.2 and 1.5, the x values refer to molar ratio) were reported. When the value of x was smaller than 1.2, the alloys consisted of BCC and B2 structures. The BCC and B2 phases were identified to be (Cr, αFe) solid solution and NiAl intermetallic compound, respectively. With the increase of x from 0.5 to 1.2, the microstructure transformed from dendrite/inter-dendrite to eutectic microstructures. When the x was equal to 1.5, besides BCC and B2 phases, another CrFe2.32MoNi phases formed and Net-like (Cr, αFe) phases distributed in the NiAl intermetallic compound matrix. The hardness first decreased then increased with the increase of Ni content. Generally, Ni element is a FCC stabilizer. However, in AlCrFeNixMo0.2 alloys, Ni element promoted the formation of B2 and CrFe2.32MoNi phases. The influence mechanism of Ni element was discussed systematically.