Global Stability of Equilibrium Points of Typhoid Fever Model with Protection

2017 ◽  
Vol 21 (5) ◽  
pp. 1-6
Author(s):  
J Nthiiri
Keyword(s):  
Typhoid Fever ◽  
Global Stability ◽  
Equilibrium Points ◽  
Stability Of Equilibrium

scholarly journals Mathematical Modeling of Typhoid Fever Disease Incorporating Unprotected Humans in the Spread Dynamics

2019 ◽  
pp. 1-11
Author(s):  
Julia Wanjiku Karunditu ◽  
George Kimathi ◽  
Shaibu Osman
Keyword(s):  
Typhoid Fever ◽  
Global Stability ◽  
Equilibrium Point ◽  
Local Stability ◽  
Jacobian Matrix ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Spread Dynamics ◽  
Disease Free

A deterministic mathematical model of typhoid fever incorporating unprotected humans is formulated in this study and employed to study local and global stability of equilibrium points. The model incorporating Susceptible, unprotected, Infectious and Recovered humans which are analyzed mathematically and also result into a system of ordinary differential equations which are used for interpretations and comparison to the qualitative solutions in studying the spread dynamics of typhoid fever. Jacobian matrix was considered in the study of local stability of disease free equilibrium point and Castillo-Chavez approach used to determine global stability of disease free equilibrium point. Lyapunov function was used to study global stability of endemic equilibrium point. Both equilibrium points (DFE and EE) were found to be local and globally asymptotically stable. This means that the disease will be dependent on numbers of unprotected humans and other factors who contributes positively to the transmission dynamics.

scholarly journals Kestabilan Global Endemik Model Epidemi SEIR

2014 ◽  
Vol 9 (2) ◽  
pp. 52
Author(s):  
Roni Tri Putra ◽  
Sukatik - ◽  
Sri Nita ◽  
Yandraini Yunida
Keyword(s):  
Global Stability ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Seir Model ◽  
Stability Of Equilibrium ◽  
The Basic Reproduction Number

In this paper, it will be studied global stability endemic of equilibrium points of  a SEIR model with infectious force in latent, infected and immune period. From the model it will be found investigated the existence and its stability of points its equilibrium. The global stability of equilibrium points is depending on the value of the basic reproduction number  If   there is a unique endemic equilibrium which is globally asymptotically stable.

scholarly journals Global Stability of an Economic Model with a Continuous Delay of Kaldor Type Modified

2018 ◽  
Vol 2018 ◽  
pp. 1-18
Author(s):  
Aka Fulgence Nindjin ◽  
Tetchi Albin N’guessan ◽  
Sahoua Hypolithe Okou A Kpetihi ◽  
Kessé Tiban Tia
Keyword(s):  
Global Stability ◽  
Economic Model ◽  
Equilibrium Points ◽  
The Other ◽  
Boundedness Of Solutions ◽  
Economic Dynamics ◽  
Local And Global Stability ◽  
Stability Of Equilibrium ◽  
Continuous Delay ◽  
The One

This paper studies continuous nonlinear economic dynamics with a continuous delay of a Kaldor type modified in dimension two. The important results are, on the one hand, the boundedness of solutions, the existence of an attractive set, and the permanence of the system and, on the other hand, the local and global stability of equilibrium points.

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

scholarly journals “Stability Analysis of Three Species Ammensalism Model with Time Delay”

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3664-3670
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Time Delay ◽  
Global Stability ◽  
Analytical Study ◽  
Present Model ◽  
Ecological Model ◽  
Equilibrium Points

The present model is devoted to an analytical study of a three species syn-ecological model which the 1 st species ( ) N1 ammensal on the 2 nd species ( ) N2 and 2 nd species ( ) N2 ammensal on the 3 rd species ( ) N3 . Here 1 st species and 2 nd species are neutral to each other. A time delay is established between 1 st species and 2 nd species and 2 nd species and 3rd species. All attainable equilibrium points of the model are known and native stability for each case is mentioned and also the global stability of co-existing state is discussed by constructing appropriate Lyapunov operate. Further, precise solutions of perturbed equations are derived. The steadiness analysis is supported by numerical simulation victimization MatLab.

scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

scholarly journals A Stochastic Model for Three Species

2018 ◽  
Vol 7 (4.10) ◽  
pp. 497
Author(s):  
Y. Suresh Kumar ◽  
N. Seshagiri Rao ◽  
B. V AppaRao
Keyword(s):  
Stochastic Process ◽  
Stochastic Model ◽  
Global Stability ◽  
Numerical Simulations ◽  
Local Stability ◽  
Equilibrium Points ◽  
Limited Resources

The present work is related to a three species ecosystem including a mutualism interaction between two species and a predator, where the predator is depending on both the mutual species. All three species in this model are considered in limited resources. The sustainability of the system (local stability) is discussed through the perturbed technique at the possible existing each equilibrium points. Using Lyapunov's technique the global stability of the system is also described. Further the nature of the system is observed by introducing the stochastic process to the species and the numerical simulations are studied to know the interaction among the species. 

scholarly journals Modeling Dynamics of Prey-Predator Fishery Model with Harvesting: A Bioeconomic Model

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Charles Raymond ◽  
Alfred Hugo ◽  
Monica Kung’aro
Keyword(s):  
Global Stability ◽  
Lake Victoria ◽  
Equilibrium Points ◽  
Nile Perch ◽  
Type Ii ◽  
Bioeconomic Model ◽  
Eigenvalue Approach ◽  
Fishery Model ◽  
Predator System ◽  
Control Management

A mathematical model is proposed and analysed to study the dynamics of two-prey one predator system of fishery model with Holling type II function response. The effect of harvesting was incorporated to both populations and thoroughly analysed. We study the ecological dynamics of the Nile perch, cichlid, and tilapia fishes as prey-predator system of lake Victoria fishery in Tanzania. In both cases, by nondimensionalization of the system, the equilibrium points are computed and conditions for local and global stability of the system are obtained. Condition for local stability was obtained by eigenvalue approach and Routh-Hurwitz Criterion. Moreover, the global stability of the coexistence equilibrium point is proved by defining appropriate Lyapunov function. Bioeconomic equilibrium is analysed and numerical simulations are also carried out to verify the analytical results. The numerical results indicate that the three species would coexist if cichlid and tilapia fishes will not be overharvested as these populations contribute to the growth rates of Nile perch population. The fishery control management should be exercised to avoid overharvesting of cichlid and tilapia fishes.

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