scholarly journals Dynamical Analysis and Design of Computational Methods for Nonlinear Stochastic Leprosy Epidemic Model

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Ali Raza ◽  
Muhammad Rafiq ◽  
Muhammad Mohsin
Keyword(s):  
Finite Difference ◽  
Computational Methods ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Cost Effective ◽  
Dynamical Analysis ◽  
Analysis And Design ◽  
Long Period ◽  
Runge Kutta ◽  
Positivity And Boundedness

Abstract In this article, we present the dynamical analysis of the stochastic leprosy epidemic model. Positivity and boundedness are the criteria used in the deterministic model. A primary technique known as the Euler Maruyama is employed in the solution of the said model. Standard and non-standard computational methods are applied in evaluating the design stability and efficiency based on the chosen criteria. The standard computational methods like the Stochastic Euler and the Stochastic Runge Kutta fail to restore the essential features of biological problems. However, our proposed approach, the stochastic non-standard finite difference (NSFD), is used and found to be efficient, cost-effective, and accommodates all the desired feasible properties. Our method achieves all-time convergence against the backdrop of other classical techniques that perform conditionally or fail over a long period. In the end, a comparison between this scheme and the existing ones reviews the novelty of our approach.

scholarly journals An epidemic model for the transmission dynamics of HIV and another pathogen

2003 ◽  
Vol 45 (2) ◽  
pp. 181-193 ◽  
Author(s):  
S. M. Moghadas ◽  
A. B. Gumel
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Linear Model ◽  
Difference Method ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Transmission Dynamics ◽  
Optimal Therapy ◽  
Existence And Stability ◽  
Disease Free

AbstractA five-dimensional deterministic model is proposed for the dynamics between HIV and another pathogen within a given population. The model exhibits four equilibria: a disease-free equilibrium, an HIV-free equilibrium, a pathogen-free equilibrium and a co-existence equilibrium. The existence and stability of these equilibria are investigated. A competitive finite-difference method is constructed for the solution of the non-linear model. The model predicts the optimal therapy level needed to eradicate both diseases.

scholarly journals Dynamical Analysis of a Parasite-Host Model within Fluctuating Environment

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Kun Xu ◽  
Ziang Zhou ◽  
Huitao Zhao
Keyword(s):  
Stochastic Model ◽  
Global Stability ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Deterministic Model ◽  
Dynamical Analysis ◽  
Boundedness Of Solutions ◽  
Fluctuating Environment ◽  
Global Positive Solution ◽  
Positivity And Boundedness

A parasite-host model within fluctuating environment is proposed. Firstly, the positivity and boundedness of solutions of the model within deterministic environment are discussed, and, then, the asymptotical stability and global stability of equilibria of deterministic model are investigated. Secondly, we show that the stochastic model has a unique global positive solution; furthermore, we show that the stochastic model has a stationary distribution under certain conditions. Finally, we give some numerical simulations to illustrate our analytical results.

scholarly journals Nonstandard Finite Difference Schemes for an SIR Epidemic Model

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3082
Author(s):  
Mohammad Mehdizadeh Khalsaraei ◽  
Ali Shokri ◽  
Samad Noeiaghdam ◽  
Maryam Molayi
Keyword(s):  
Finite Difference ◽  
Epidemic Model ◽  
Euler Method ◽  
Finite Difference Schemes ◽  
Sir Epidemic Model ◽  
Standard Methods ◽  
Sir Epidemic ◽  
Nonstandard Finite Difference ◽  
Better Than ◽  
Positivity And Boundedness

This paper aims to present two nonstandard finite difference (NFSD) methods to solve an SIR epidemic model. The proposed methods have important properties such as positivity and boundedness and they also preserve conservation law. Numerical comparisons confirm that the accuracy of our method is better than that of other existing standard methods such as the second-order Runge–Kutta (RK2) method, the Euler method and some ready-made MATLAB codes.

scholarly journals Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaodong Wang ◽  
Chunxia Wang ◽  
Kai Wang
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Media Coverage ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Stochastic Sir

AbstractIn this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $R_{0}$ R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

scholarly journals Improved Refractive Index Sensitivity Utilizing Long-Period Gratings with Periodic Corrugations on Cladding

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Anthony Lim ◽  
Wen Bin Ji ◽  
Swee Chuan Tjin
Keyword(s):  
Refractive Index ◽  
Cost Effective ◽  
Experimental Results ◽  
Refractive Index Sensitivity ◽  
Long Period ◽  
Specimen Collection ◽  
Long Period Gratings ◽  
Highly Sensitive ◽  
Index Sensitivity

A new structure of Long-Period Gratings (LPGs) sensor is introduced as a sensitive ambient RI sensor. This structure consists of creating periodic corrugations on the cladding of the LPG. The experimental results show that this LPG structure has good performances in terms of linearity and sensitivity and serves as a highly sensitive and cost-effective sensor. It also has the advantage of portability as the corrugation can also serve as the reservoir for the specimen collection to be tested.

A method for correcting acoustic finite-difference amplitudes for elastic effects

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. T243-T255 ◽  
Author(s):  
James W. D. Hobro ◽  
Chris H. Chapman ◽  
Johan O. A. Robertsson
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Effective Means ◽  
Cost Effective ◽  
P Wave ◽  
S Waves ◽  
Velocity Models ◽  
Acoustic Simulation ◽  
Wide Range ◽  
Elastic Simulation

We present a new method for correcting the amplitudes of arrivals in an acoustic finite-difference simulation for elastic effects. In this method, we selectively compute an estimate of the error incurred when the acoustic wave equation is used to approximate the behavior of the elastic wave equation. This error estimate is used to generate an effective source field in a second acoustic simulation. The result of this second simulation is then applied as a correction to the original acoustic simulation. The overall cost is approximately twice that of an acoustic simulation but substantially less than the cost of an elastic simulation. Because both simulations are acoustic, no S-waves are generated, so dispersed converted waves are avoided. We tested the characteristics of the method on a simple synthetic model designed to simulate propagation through a strong acoustic impedance contrast representative of sedimentary geology. It corrected amplitudes to high accuracy for reflected arrivals over a wide range of incidence angles. We also evaluated results from simulations on more complex models that demonstrated that the method was applicable in realistic sedimentary models containing a wide range of seismic contrasts. However, its accuracy was reduced for wide-angle reflections from very high impedance contrasts such as a shallow top-salt interface. We examined the influence of modeling at coarse grid resolutions, in which converted S-waves in the equivalent elastic simulation are dispersed. These results provide some validation for the accuracy of the method when applied using finite-difference grids designed for acoustic modeling. The method appears to offer a cost-effective means of modeling elastic amplitudes for P-wave arrivals in a useful range of velocity models. It has several potential applications in imaging and inversion.

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