scholarly journals Stability behaviour of mathematical model MERS corona virus spread in population

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3947-3960 ◽  
Author(s):  
Muhammad Tahir ◽  
Syed Shah ◽  
Gul Zaman ◽  
Tahir Khan
Keyword(s):  
Stability Analysis ◽  
Local Stability ◽  
Equilibrium Points ◽  
Reproductive Number ◽  
Virus Spread ◽  
Global Stability Analysis ◽  
Local Stability Analysis ◽  
Proposed Model ◽  
Disease Free ◽  
Model Existence

In this subsection, we first formulated the proposed model in there infectious classes and then we derived the basic key value reproductive number, R0 with the help of next generation approach. Then we obtained all the endemic equilibrium points, as well as, local stability analysis, at disease free equilibria and, at endemic equilibria of the related model and shown stable. Further the global stability analysis either, at disease free equilibria, and at endemic equilibria is discussed by constructing Lyapunov function which show the validity of the concern model exist. In the last part of the article numerical simulation is presented for the model which support the model existence with the help of RK-4 method.

scholarly journals A Mathematical Modeling of Tuberculosis Dynamics with Hygiene Consciousness as a Control Strategy

2020 ◽  
pp. 38-48
Author(s):  
Phineas Z. Mawira ◽  
David M. Malonza
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Control Strategy ◽  
Local Stability ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Linear Ordinary Differential Equations ◽  
Global Stability Analysis ◽  
Local Stability Analysis ◽  
Disease Free

Tuberculosis, an airborne infectious disease, remains a major threat to public health in Kenya. In this study, we derived a system of non-linear ordinary differential equations from the SLICR mathematical model of TB to study the effects of hygiene consciousness as a control strategy against TB in Kenya. The effective basic reproduction number (R0) of the model was determined by the next generation matrix approach. We established and analyzed the equilibrium points. Using the Routh-Hurwitz criterion for local stability analysis and comparison theorem for global stability analysis, the disease-free equilibrium (DFE) was found to be locally asymptotically stable given that R0 < 1.  Also by using the Routh-Hurwitz criterion for local stability analysis and Lyapunov function and LaSalle’s invariance principle for global stability analysis, the endemic equilibrium (EE) point was found to be locally asymptotically stable given that R0 > 1. Using MATLAB ode45 solver, we simulated the model numerically and the results suggest that hygiene consciousness can helpin controlling TB disease if incorporated effectively.

scholarly journals A Mathematical Model to Study the Effectiveness of Some of the Strategies Adopted in Curtailing the Spread of COVID-19

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Isa Abdullahi Baba ◽  
Bashir Abdullahi Baba ◽  
Parvaneh Esmaili
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Government Policy ◽  
Local Stability ◽  
Equilibrium Points ◽  
Compartmental Models ◽  
Effective Strategy ◽  
Local Stability Analysis ◽  
The Government

In this paper, we developed a model that suggests the use of robots in identifying COVID-19-positive patients and which studied the effectiveness of the government policy of prohibiting migration of individuals into their countries especially from those countries that were known to have COVID-19 epidemic. Two compartmental models consisting of two equations each were constructed. The models studied the use of robots for the identification of COVID-19-positive patients. The effect of migration ban strategy was also studied. Four biologically meaningful equilibrium points were found. Their local stability analysis was also carried out. Numerical simulations were carried out, and the most effective strategy to curtail the spread of the disease was shown.

Modelling the impacts of lockdown and isolation on the eradication of COVID-19

BIOMATH ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 2009107
Author(s):  
Joel N. Ndam
Keyword(s):  
Stability Analysis ◽  
Social Isolation ◽  
Local Stability ◽  
Effective Means ◽  
Asymptotically Stable ◽  
Effective Strategy ◽  
Local Stability Analysis ◽  
Strict Enforcement ◽  
Model Equations ◽  
Disease Free

A model describing the dynamics of COVID-19 is formulated and examined. The model is meant to address the impacts of lockdown and social isolation as strategies for the eradication of the pandemic. Local stability analysis indicate that the equilibria are locally-asymptotically stable for R0<1 and R_0>1 for the disease-free equilibrium and the endemic equilibrium respectively. Numerical simulations of the model equations show that lockdown is a more effective strategy in the eradication of the disease than social isolation. However, strict enforcement of both strategies is the most effective means that could end the disease within a shorter period of time.

scholarly journals Towards a quantitative comparison between global and local stability analysis

2017 ◽  
Vol 819 ◽  
pp. 147-164 ◽  
Author(s):  
L. Siconolfi ◽  
V. Citro ◽  
F. Giannetti ◽  
S. Camarri ◽  
P. Luchini
Keyword(s):  
Stability Analysis ◽  
Saddle Point ◽  
Global Stability ◽  
Local Stability ◽  
Correction Term ◽  
Three Dimensional ◽  
Higher Order ◽  
Order Correction ◽  
Global Stability Analysis ◽  
Local Stability Analysis

A methodology is proposed here to estimate the stability characteristics of bluff-body wakes using local analysis under the assumption of weakly non-parallel flows. In this connection, a generalisation of the classic spatio-temporal stability analysis for fully three-dimensional flows is first described. Secondly, an additional higher-order correction term with respect to the common saddle-point global frequency estimation is included in the analysis. The proposed method is first validated for the case of the flow past a circular cylinder and then applied to two fully three-dimensional flows: the boundary layer flow over a wall-mounted hemispherical body and the wake flow past a fixed sphere. In all the cases considered, both the estimated unstable eigenvalue and the spatial shape of the associated eigenmode are determined by local stability analysis, and they are compared with the reference counterparts obtained at a definitely higher computational cost by a fully three-dimensional global stability analysis. It is shown that the results of local stability analysis, when the higher-order correction term is included, are in excellent agreement with those obtained by global stability analysis. It is also shown that the retained correction term is of crucial importance in this perspective, leading to a remarkable improvement in accuracy with respect to the classical saddle-point estimation.

scholarly journals Stability Analysis of Competing Insect Species for a Single Resource

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Sizah Mwalusepo ◽  
Henri E. Z. Tonnang ◽  
Estomih S. Massawe ◽  
Tino Johansson ◽  
Bruno Pierre Le Ru
Keyword(s):  
Stability Analysis ◽  
Local Stability ◽  
Equilibrium Points ◽  
Single Species ◽  
Insect Species ◽  
System Of Differential Equations ◽  
Competing Species ◽  
Local Study ◽  
Interior Equilibrium ◽  
Local Stability Analysis

The models explore the effects of resource and temperature on competition between insect species. A system of differential equations is proposed and analysed qualitatively using stability theory. A local study of the models is performed around axial, planar, and interior equilibrium points to successively estimate the effect of (i) one species interacting with a resource, (ii) two competing species for a single resource, and (iii) three competing species for a single resource. The local stability analysis of the equilibrium is discussed using Routh-Hurwitz criteria. Numerical simulation of the models is performed to investigate the sensitivity of certain key parameters. The models are used to predict population dynamics in the selected cases studied. The results show that when a single species interacts with a resource, the species will be able to establish and sustain a stable population. However, in competing situation, it is observed that the combinations of three parameters (half-saturation, growth rate, and mortality rate) determine which species wins for any given resource. Moreover, our results indicate that each species is the superior competitor for the resource for the range of temperature for which it has the lowest equilibrium resource.

scholarly journals Dynamics of a Cournot Duopoly Game with a Generalized Bounded Rationality

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
A. Al-khedhairi
Keyword(s):  
Stability Analysis ◽  
Bounded Rationality ◽  
Numerical Computation ◽  
Local Stability ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Cournot Duopoly ◽  
Local Stability Analysis

In this paper, the dynamics of Cournot duopoly game with a generalized bounded rationality is considered. The fractional bounded rationality of the Cournot duopoly game is introduced. The conditions of local stability analysis of equilibrium points of the game are derived. The effect of fractional marginal profit on the game is investigated. The complex dynamics behaviors of the game are discussed by numerical computation when parameters are varied.

scholarly journals Qualitative Stability Analysis of an Obesity Epidemic Model with Social Contagion

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Enrique Lozano-Ochoa ◽  
Jorge Fernando Camacho ◽  
Cruz Vargas-De-León
Keyword(s):  
Stability Analysis ◽  
Equilibrium Points ◽  
Social Contagion ◽  
The Other ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Feasible Region ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

We study an epidemiological mathematical model formulated in terms of an ODE system taking into account both social and nonsocial contagion risks of obesity. Analyzing first the case in which the model presents only the effect due to social contagion and using qualitative methods of the stability analysis, we prove that such system has at the most three equilibrium points, one disease-free equilibrium and two endemic equilibria, and also that it has no periodic orbits. Particularly, we found that when considering R0 (the basic reproductive number) as a parameter, the system exhibits a backward bifurcation: the disease-free equilibrium is stable when R0<1 and unstable when R0>1, whereas the two endemic equilibria appear from R0⁎ (a specific positive value reached by R0 and less than unity), one being asymptotically stable and the other unstable, but for R0>1 values, only the former remains inside the feasible region. On the other hand, considering social and nonsocial contagion and following the same methodology, we found that the dynamic of the model is simpler than that described above: it has a unique endemic equilibrium point that is globally asymptotically stable.

scholarly journals Local Stability Analysis of an SVIR Epidemic Model

CAUCHY ◽  
2017 ◽  
Vol 5 (1) ◽  
pp. 20
Author(s):  
Joko Harianto
Keyword(s):  
Stability Analysis ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Local Stability ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
System Disease ◽  
Local Stability Analysis ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, we present an SVIR epidemic model with deadly deseases. Initially the basic formulation of the model is presented. Two equilibrium point exists for the system; disease free and endemic equilibrium. The local stability of the disease free and endemic equilibrium exists when the basic reproduction number less or greater than unity, respectively. If the value of R0 less than one then the desease free equilibrium is locally stable, and if its exceeds, the endemic equilibrium is locally stable. The numerical results are presented for illustration.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

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