Global Dynamics of a Water-Borne Disease Model with Multiple Transmission Pathways

We propose and analyze a water born disease model introducing water-to-person and person-toperson transmission and saturated incidence. The disease-free equilibrium and the existence criterion of endemic equilibrium are investigated. Trans critical bifurcation at the disease-free equilibrium is obtained when the basic reproductive number is one. The local stability of both the equilibria is shown and a Lyapunov functional approach is also applied to explore the global stability of the system around the equilibria. We display the effects of pathogen contaminated water and infection through contact on the system dynamics in the absence of person-to-person contact as well as in the presence of water-to-person contact. It is shown that in the presence of water-to-person transmission, the model system globally stable around both the disease-free and endemic equilibria. Lastly, some numerical simulations are provided to verify our analytical results

A Mathematical Study on the Dynamics of an Eco-Epidemiological Model in the Presence of Delay

In the present work a mathematical model of the prey-predator system with disease in the prey is proposed. The basic model is then modified by the introduction of time delay. The stability of the boundary and endemic equilibria are discussed. The stability and bifurcation analysis of the resulting delay differential equation model is studied and ranges of the delay inducing stability as well as the instability for the system are found. Using the normal form theory and center manifold argument, we derive the methodical formulae for determining the bifurcation direction and the stability of the bifurcating periodic solution. Some numerical simulations are carried out to explain our theoretical analysis

Quasi fuzzy delta compact spaces and a few related properties

In this paper, we introduce the concept of various types fuzzy delta $(\delta)$ compactness such as Quasi fuzzy delta compact, Quasi fuzzy countably delta compact, Weakly fuzzy delta compact, $a$-delta compact, Strong fuzzy delta compact, Ultra fuzzy delta compact and Fuzzy delta compact and characterize these types of fuzzy delta compactness using the notion of fuzzy upper limit of net of some types of delta $(\delta)$ closed sets

On the stability of a Pexiderized functional equation in intuitionistic fuzzy Banach spaces

During the last few decades several researchers have been devoted to establishing stability of different kinds of functional equations, differential equations, functional differential equations, fractional differential equations, etc. under different sufficient conditions in different spaces like Banach spaces, Banach modules, fuzzy Banach spaces etc. In this paper, we remain confined in the discussion of stability of functional equations in intuitionistic fuzzy Banach spaces. Ulam was the first person who introduced an open question concerning the stability of a group homomorphism in an international conference. Thereafter several researchers have replied and are still replying to this open question in different contexts. The objective of the present paper is to determine the Hyers-Ulam-Rassias type stability concerning the Pexiderized functional equation in intuitionistic fuzzy Banach spaces. Under a few sufficient conditions, Hyers-Ulam-Rassias type stability of a Pexiderized functional equation has been established in intuitionistic fuzzy Banach spaces

On Upward Drawings of Trees on a Given Grid

Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known for straight-line drawings of trees under various restrictions such as edge length or slope constraints. On the other hand, there exist polynomial-time algorithms for computing minimum-width (resp., minimum-height) upward drawings of trees, where the height (resp., width) is unbounded. In this paper we take a major step in understanding the complexity of the area minimization problem for strictly-upward drawings of trees, which is one of the most common styles for drawing rooted trees. We prove that given a rooted tree $T$ and a $W\times H$ grid, it is NP-hard to decide whether $T$ admits a strictly-upward (unordered) drawing in the given grid.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Phase Equilibrium Modeling in Gas Purification System

A thermodynamic model based on activity is proposed to correlate and predict the vapour-liquid equilibria of the aforesaid systems. The activity based models render an insight in to the molecular physics of the system; hence accurate speciation of the equilibriated liquid phase becomes a reality besides its prediction ability of solubility of the acid gases over alkanolamine solutions. The activity based model has been developed using extended Debye-Hückel theory of electrolytic solution with short range, non-electrostatic interactions. The vapor phase non-ideality has been taken care of in terms of fugacity coefficient calculated using Virial Equation of State. The equilibrium constants are taken from literature as functions of temperature only. The neutral and ionic species present in the equilibrated liquid phase have been estimated with zero interaction model and incorporated here. The interaction parameters in the activity models are estimated by minimizing the objective function, which is the summation of relative deviation between the experimental and model predicted CO2 partial pressures over a wide range. The parameter estimation for the phase equilibrium models have been formulated here as a multivariable optimization (minimization) problem with variable bounds. The MATLAB 7.6 optimization toolbox has been used extensively for the present work. ‘fmincon’ function, which is a constrained optimization function uses quasi-Newton and Sequential Quadratic Programming (SQP) methods, has been used here for minimization of the proposed objective functions with variable bounds for both approximate and rigorous modeling. There remains a necessity of refinement of the developed rigorous thermodynamic model in terms of the accurate speciation, i.e., exact determination of the species concentration in the equilibrated liquid phase and use of better optimization algorithm, may be non-traditional one, which will ensure global minima

Study of thickness dependent density in ultrathin water soluble polymer films

Density of the polyacrylamide ultrathin films has been studied using X-ray reflectivity technique. Two sources (one powder and another aqueous solution) of polyacrylamide were used to prepare spin coated films on silicon substrate. Light scattering measurements show that the polymer chains were unentangled in a concentrated (4 mg/ml) as well as in a dilute (2 mg/ml) solution prepared from the powder, whereas the solution (4 mg/ml) prepared by diluting the solution source shows entangled chain morphology. Three sets of films of different thicknesses were prepared using the three solutions by spin coating on silicon substrates. Comparison of X-ray reflectivity data for as prepared and dry films reveals that the shrinkage of the films decreases with increasing thickness. Average electron densities of the films were found to follow a trend of higher density for thinner films with a maximum increase of about 12% compared to the bulk. The densities of all the films irrespective of the nature of entanglement and concentration of their source were found to increase with spin speed of coating and attain saturation at higher speed. Absence of correlation between shrinkage and density data and the fact that the densities of all the films follow a master curve irrespective of their origin suggest that the higher density of the films result from the higher orientation of chains as a consequence of an interplay between stretching and stronger attractive interactions of polar nature.Comment: 6 figure