In this paper, we established a mathematical model of an SI1I2R epidemic disease with saturated incidence and general recovery functions of the first disease I1. Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that supported our theoretical findings
Compaction curves are widely used in civil engineering especially for road constructions, embankments, etc. Obtaining the precise amount of Optimum Moisture Content (OMC) that gives the Maximum Dry Unit weight gdmax. is very important, where the desired soil strength can be achieved in addition to economic aspects.
In this paper, three peak functions were used to obtain the OMC and gdmax. through curve fitting for the values obtained from Standard Proctor Test. Another surface fitting was also used to model the Ohio’s compaction curves that represent the very large variation of compacted soil types.
The results showed very good correlation between the values obtained from some publ
... Show MoreThis paper presents a nonlinear finite element modeling and analysis of steel fiber reinforced concrete (SFRC) deep beams with and without openings in web subjected to two- point loading. In this study, the beams were modeled using ANSYS nonlinear finite element
software. The percentage of steel fiber was varied from 0 to 1.0%.The influence of fiber content in the concrete deep beams has been studied by measuring the deflection of the deep beams at mid- span and marking the cracking patterns, compute the failure loads for each deep beam, and also study the shearing and first principal stresses for the deep beams with and without openings and with different steel fiber ratios. The above study indicates that the location of openings an
In this paper, a discrete SIS epidemic model with immigrant and treatment effects is proposed. Stability analysis of the endemic equilibria and disease-free is presented. Numerical simulations are conformed the theoretical results, and it is illustrated how the immigrants, as well as treatment effects, change current model behavior
The interplay of predation, competition between species and harvesting is one of the most critical aspects of the environment. This paper involves exploring the dynamics of four species' interactions. The system includes two competitive prey and two predators; the first prey is preyed on by the first predator, with the former representing an additional food source for the latter. While the second prey is not exposed to predation but rather is exposed to the harvest. The existence of possible equilibria is found. Conditions of local and global stability for the equilibria are derived. To corroborate our findings, we constructed time series to illustrate the existence and the stability of equilibria numerically by varying the different values
... Show MoreThis paper presents the non-linear finite element method to study the behavior of four reinforced rectangular concrete MD beams with web circular openings tested under two-point load. The numerical finite elements methods have been used in a much more practical way to achieve approximate solutions for more complex problems. The ABAQUS /CAE is chosen to explore the behavior of MD beams. This paper also studies, the effect of both size and shape of the circular apertures of MD beams. The strengthening technique that used in this paper is externally strengthening using CFRP around the opening in the MD beams. The numerical results were compared to the experimental results in terms of ultimate load failure and displace
... Show MoreIn this work, the occurrence conditions of both local Bifurcation and persistence were studied, Saddle-node bifurcation appears near fourth point, near the first point, the second point and the third point a transcritical bifurcation occurred but no pitchfork bifurcation happened near any of the four equilibrium points. In addition to study conditions for Hopf-bifurcation near positive stable point that is the fourth point. Besides discuss persistence occurrence as globally property of the food chain of three species include prey, first predator and top predator with impact of toxin in all species and harvesting effect on the predator’s only. Numerical results for the set of hypothe