Energy-based model of forming subgroups on finite metric space

Local interactions between particles of a collection causes all particles to reorganize in new positions. The purpose of this paper is to construct an energy-based model of self-organizing subgroups, which describes the behavior of singular local moves of a particle. The present paper extends the Hegselmann-Krause model on consensus dynamics, where agents simultaneously move to the barycenter of all agents in an epsilon neighborhood. The Energy-based model presented here is analyzed and simulated on finite metric space. AMS Subject Classifications:81T80; 93A30; 37M05; 68U2

Condensing of self-organizing groups

Condensing phenomena for systems biology, ecology and sociology present in real life different complex behaviors. Based on local interaction between agents, we present another result of the Energy-based model presented by [20]. We involve an additional condition providing the total condensing (also called consensus) of a discrete positive measure. Key words: Condensing; consensus; random move; self-organizing groups; collective intelligence; stochastic modeling. AMS Subject Classifications: 81T80; 93A30; 37M05; 68U2

Condensing on metric spaces : modeling, analysis and simulation

In this work, we extend the Hegselmann and Krause (HK) model, presented in [16] to an arbitrary metric space. We also present some theoretical analysis and some numerical results of the condensing of particles in finite and continuous metric spaces. For simulations in a finite metric space, we introduce the notion "random metric" using the split metrics studies by Dress and al. [2, 11, 12]

Threshold dynamics of stochastic cholera epidemic model with direct transmission

This paper extends the cholera human-to-human direct transmission model from a deterministic to a stochastic framework. This is expressed as mixed system of stochastic and deterministic differential equations. A Lyapunov function is created to investigate the global stability of the stochastic cholera epidemic, which shows the existence of global positivity of the solution using the theory of stopping time. We then find the threshold quantity of the extended stochastic cholera epidemic model. We derive a parametric condition $\widetilde{R}_0$, and for additive white noise, we establish sufficient conditions for the extinction and the persistence of the cholera infection. Finally, for a suitable choice of the parameter of the system for $\widetilde{R}_0$, we perform numerical simulations for both scenarios of extinction and persistence of the dynamic of the cholera infection

Mathematical Modeling of a Class of Symmetrical Islamic Design

In this paper, we present a new model for simulating an interesting class of Islamic design. Based on periodic sequences on the one-dimensional manifolds, and from emerging numbers, we construct closed graphs with edges on the unit circle. These graphs build very nice shapes and lead to a symmetrical class of geometric patterns of so-called Islamic design. Moreover, we mathematically characterize and analyze some convergence properties of the used up-down sequences. Finally, four planar type of patterns are simulated

Optimal Decay Rate Estimates of a Nonlinear Viscoelastic Kirchhoff Plate

This paper is concerned with a nonlinear viscoelastic Kirchhoff plate uttt−σΔuttt+Δ2ut−∫0tgt−sΔ2usds=divF∇ut. By assuming the minimal conditions on the relaxation function g: g′t≤ξtGgt, where G is a convex function, we establish optimal explicit and general energy decay results to the system. Our result holds for Gt=tp with the range p∈1, 2, which improves earlier decay results with the range p∈1,3/2. At last, we give some numerical illustrations and related comparisons

Investigation of the effect of awareness and treatment on Tuberculosis infection via a novel epidemic model

We develop a novel deterministic epidemic model to investigate the effect of treatment ahdrence and awareness on the dynamics of tuberculosis (TB). To derive conditions for the stability of the local as well as the global behaviour of the proposed model, we determine the threshold ratio. Our considered model admits a positive disease endemic state, which shows global asymptotic stability for R0>1. To explore the robustness of the model to the parametric values, we perform sensitivity analysis. We use the normalised forward sensitivity index of a variable in a parameter approach. Finally, to verify the analytical findings, we perform numerical simulations to determine feasible parametric values for the proposed model. Our numerical simulations show that awareness and adherence to treatment play a vital role in the control of TB infection

Numerical analysis of MHD Casson Navier’s slip nanofluid flow yield by rigid rotating disk

An exertion is perform to report analysis on Casson liquid equipped above the rigid disk for z¯>0 as a semi-infinite region. The flow of Casson liquid is achieve through rotation of rigid disk with constant angular frequency Ω¯. Magnetic interaction is consider by applying uniform magnetic field normal to the axial direction. The nanosized particles are suspended in the Casson liquid and rotation of disk is manifested with Navier’s slip condition, heat generation/absorption and chemical reaction effects. The obtain flow narrating differential equations subject to MHD Casson nanofluid are transformed into ordinary differential system. For this purpose the Von Karman way of scheme is executed. To achieve accurate trends a computational algorithm is develop rather than to go on with usual build-in scheme. The effects logs of involved parameters, namely magnetic field parameter, Casson fluid parameter, slip parameter, thermophoresis and Brownian motion parameters on radial, tangential velocities, temperature, nanoparticles concentration, Nusselt and Sherwood numbers are provided by means of graphical and tabular structures. It is observed that both tangential and radial velocities are decreasing function of Casson fluid parameter. Keywords: Casson liquid, Nanoparticles, Rotating disk, Heat generation/absorption, Chemical reactio

Global behaviour of a tuberculosis model with difference in awareness and treatment adherence levels

The treatment adherence level of tuberculosis patients is critically related to their awareness level about tuberculosis and anti-tuberculosis therapy. Tuberculosis is always spreading if the community has low level of awareness. In this article a mathematical model describing the impact of treatment adherence and difference in awareness level on tuberculosis transmission dynamics is investigated. It is assumed that the detected infectious individuals with low level of awareness after treatment may enter either the recovered compartment due to treatment adherence or the latent compartment due to lack of adherence. We compute the epidemic threshold parameter, Rb, to study its role on the dynamics and stability of the proposed model. Mathematical analyses of this model reveal that treatment nonadherence of individuals with active tuberculosis may lead to relapse. Analysis of the epidemic threshold parameter shows that increase in awareness level, treatment and adherence to medication has a positive effect on tuberculosis control. Whereas, decrease in effective contact rate and endogenous reactivation rate help to reduce tuberculosis infection. The numerical simulations of the model illustrate the feasibility of our analytical conclusions

On both magnetized and non-magnetized dual stratified medium via stream lines topologies: A generalized formulation

Abstract The major concern of current pagination is to report the doubly stratified medium subject to both magnetized and non-magnetized flow fields. For this purpose both the Newtonian and non-Newtonian liquids are considered in a double stratified medium having magnetic field interaction. To be more specific, a generally accepted rheological liquid around a cylindrical surface having constant radius embedded in magnetized doubly stratified media is taken into account. Additionally, flow field is manifested with various pertinent physical effects. The flow problem statement is defended through generalized formulation via fundamental laws. A computational scheme is executed and stream lines topologies are constructed for the both magnetized and non-magnetized stratified medium to explore the interesting features. It is observed that the Casson fluid velocity towards cylindrical surface is higher in magnitude as compared to flat surface. Such observation is same for the both the magnetized and non-magnetized flow fields. Our general formulation yields some existing attempts in the literature. The variations in local skin friction coefficient (LSFC), local Nusselt number (LNN) and local Sherwood number (LSN) are provided with the aid of tabular forms. It is trusted that the obtain observations via stream lines topologies will serve a clear insight to the said flow problem