scholarly journals Global Stability of Vector-Host Disease with Variable Population Size

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Saeed Islam ◽  
Sher Afzal Khan ◽  
Gul Zaman
Keyword(s):  
Global Stability ◽  
Population Size ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Host Disease ◽  
Variable Population ◽  
Globally Stable ◽  
Disease Free ◽  
Disease Persistence ◽  
Variable Population Size

The paper presents the vector-host disease with a variability in population. We assume, the disease is fatal and for some cases the infected individuals become susceptible. We first show the local and global stability of the disease-free equilibrium, for the case when, the disease free-equilibrium of the model is both locally as well as globally stable. For , the disease persistence occurs. The endemic equilibrium is locally as well as globally asymptotically stable for . Numerical results are presented for the justifications of theoratical results.

ON THE GLOBAL STABILITY OF CHOLERA MODEL WITH PREVENTION AND CONTROL

2018 ◽  
Vol 3 (1) ◽  
pp. 28
Author(s):  
M O Ibrahim ◽  
A A Ayoade ◽  
O J Peter ◽  
F A Oguntolu
Keyword(s):  
Global Stability ◽  
Prevention And Control ◽  
Control Measures ◽  
Extended Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
First Order ◽  
Prevention And Control Measures ◽  
And Control ◽  
Disease Free

In this study, a system of first order ordinary differential equations is used to analyse the dynamics of cholera disease via a mathematical model extended from Fung (2014) cholera model. The global stability analysis is conducted for the extended model by suitable Lyapunov function and LaSalle’s invariance principle. It is shown that the disease free equilibrium (DFE) for the extended model is globally asymptotically stable if 𝑅0 𝑞 < 1 and the disease eventually disappears in the population with time while there exists a unique endemic equilibrium that is globally asymptotically stable whenever 𝑅0 𝑞 > 1 for the extended model or 𝑅0 > 1 for the original model and the disease persists at a positive level though with mild waves (i.e few cases of cholera) in the case of𝑅0 𝑞 > 1. Numerical simulations for strong, weak, and no prevention and control measures are carried out to verify the analytical results and Maple 18 is used to carry out the computations.

Analysis of a sex-structured HIV/AIDS model with the effect of screening of infectives

2014 ◽  
Vol 07 (05) ◽  
pp. 1450054 ◽  
Author(s):  
S. Athithan ◽  
Mini Ghosh
Keyword(s):  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Epidemic Threshold ◽  
Heterosexual Contact ◽  
Globally Asymptotically Stable ◽  
Transmission Of Disease ◽  
Globally Stable ◽  
Disease Free ◽  
Hiv Aids

This paper presents a nonlinear sex-structured mathematical model to study the spread of HIV/AIDS by considering transmission of disease by heterosexual contact. The epidemic threshold and equilibria for the model are determined, local stability and global stability of both the "Disease-Free Equilibrium" (DFE) and "Endemic Equilibrium" (EE) are discussed in detail. The DFE is shown to be locally and globally stable when the basic reproductive number ℛ0 is less than unity. We also prove that the EE is locally and globally asymptotically stable under some conditions. Finally, numerical simulations are reported to support the analytical findings.

scholarly journals Global Stability of a HIV-1 Model with General Nonlinear Incidence and Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yaping Wang ◽  
Fuqin Sun
Keyword(s):  
Global Stability ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Threshold Behavior ◽  
Globally Asymptotically Stable ◽  
Incidence Functions ◽  
The Given ◽  
Disease Free ◽  
Hiv 1 ◽  
Intracellular Delays

A HIV-1 model with two distributed intracellular delays and general incidence function is studied. Conditions are given under which the system exhibits the threshold behavior: the disease-free equilibriumE0is globally asymptotically stable ifR0≤1; ifR0>1, then the unique endemic equilibriumE1is globally asymptotically stable. Finally, it is shown that the given conditions are satisfied by several common forms of the incidence functions.

THE IMPACT OF MEDIA COVERAGE ON THE DYNAMICS OF INFECTIOUS DISEASE

2008 ◽  
Vol 01 (01) ◽  
pp. 65-74 ◽  
Author(s):  
YIPING LIU ◽  
JING-AN CUI
Keyword(s):  
Infectious Disease ◽  
Media Coverage ◽  
Compartment Model ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Impact ◽  
Globally Stable ◽  
Disease Free

In this paper, we give a compartment model to discuss the influence of media coverage to the spreading and controlling of infectious disease in a given region. The model exhibits two equilibria: a disease-free and a unique endemic equilibrium. Stability analysis of the models shows that the disease-free equilibrium is globally asymptotically stable if the reproduction number (ℝ0), which depends on parameters, is less than unity. But if ℝ0 > 1, it is shown that a unique endemic equilibrium appears, which is asymptotically stable. On a special case, the endemic equilibrium is globally stable. We discuss the role of media coverage on the spreading based on the theory results.

scholarly journals Global Stability of an Epidemic Model with Incomplete Treatment and Vaccination

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hai-Feng Huo ◽  
Li-Xiang Feng
Keyword(s):  
Global Stability ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Incomplete Treatment ◽  
Disease Free ◽  
The Basic Reproduction Number

An epidemic model with incomplete treatment and vaccination for the newborns and susceptibles is constructed. We establish that the global dynamics are completely determined by the basic reproduction numberR0. IfR0≤1, then the disease-free equilibrium is globally asymptotically stable. IfR0>1, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also given to explain our conclusions.

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 Mathematical study for the phase-based transmissibility of a novel COVID-19 Coronavirus

2020 ◽  
Author(s):  
Miled EL HAJJI ◽  
Sayed SAYARI ◽  
Abdelhamid ZAGHDANI
Keyword(s):  
Disease Transmission ◽  
System Modeling ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Mathematical Study ◽  
Infectious Disease Transmission ◽  
Globally Asymptotically Stable ◽  
Dynamical System Modeling ◽  
Disease Free ◽  
Disease Persistence

Abstract In this paper, a mathematical dynamical system modeling a SEIRW model of infectious disease transmission for a transmissibility of a novel COVID-19 Coronavirus is studied. A qualitative analysis such as the local and global stability of equilibrium points is carried out.It is proved that if $\R \leq 1$, then the disease-free equilibrium is globally asymptotically stable and if $\R > 1$, then the disease-persistence equilibrium is globally asymptotically stable.

scholarly journals Analysis of an SEIS Epidemic Model with a Changing Delitescence

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Jinghai Wang
Keyword(s):  
Epidemic Model ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Globally Stable ◽  
Disease Free

An SEIS epidemic model with a changing delitescence is studied. The disease-free equilibrium and the endemic equilibrium of the model are studied as well. It is shown that the disease-free equilibrium is globally stable under suitable conditions. Moreover, we also show that the unique endemic equilibrium of the system is globally asymptotically stable under certain conditions.

scholarly journals Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Kwang Sung Lee ◽  
Abid Ali Lashari
Keyword(s):  
Global Stability ◽  
Pine Wilt Disease ◽  
Geometric Approach ◽  
Wilt Disease ◽  
Endemic Equilibrium ◽  
Vector Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Pine Wilt ◽  
Disease Free

Based on classical epidemic models, this paper considers a deterministic epidemic model for the spread of the pine wilt disease which has vector mediated transmission. The analysis of the model shows that its dynamics are completely determined by the basic reproduction numberR0. Using a Lyapunov function and a LaSalle's invariant set theorem, we proved the global asymptotical stability of the disease-free equilibrium. We find that ifR0≤1, the disease free equilibrium is globally asymptotically stable, and the disease will be eliminated. IfR0>1, a unique endemic equilibrium exists and is shown to be globally asymptotically stable, under certain restrictions on the parameter values, using the geometric approach method for global stability, due to Li and Muldowney and the disease persists at the endemic equilibrium state if it initially exists.

Sign in / Sign up

Export Citation Format

Share Document