Global stability of an epidemic model for HIV–TB co-infection with infection-age

2014 ◽  
Vol 07 (04) ◽  
pp. 1450043 ◽  
Author(s):  
Xiao-Yan Wang ◽  
Yan-Ping Bai ◽  
Jun-Yuan Yang ◽  
Feng-Qin Zhang
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Semigroup Theory ◽  
Lyapunov Functionals ◽  
Local And Global Stability ◽  
Infection Age ◽  
Reproduction Numbers ◽  
Theoretical Results ◽  
Disease Free

A nonlinear mathematical HIV–TB model with infection-age is proposed in this paper. The basic reproduction numbers according to HIV and TB are respectively determined whether one of the diseases dies out or persists. The local and global stability of the disease-free and dominated equilibria are discussed by employing integral semigroup theory and Lyapunov functionals. The persistence of the system is also obtained by the persistence theories of the systems. The simulation illustrates the theoretical results.

Global stability of multi-group SEIRS epidemic models with vaccination

2018 ◽  
Vol 11 (01) ◽  
pp. 1850006
Author(s):  
Dejun Fan ◽  
Pengmiao Hao ◽  
Dongyan Sun ◽  
Junjie Wei
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Lyapunov Functionals ◽  
Group Model ◽  
Single Group ◽  
Connected Network ◽  
Reproduction Numbers ◽  
Seirs Epidemic Model ◽  
Strongly Connected ◽  
Strongly Connected Network

In this paper, a susceptible–exposed–infective–recovered–susceptible (SEIRS) epidemic model with vaccination has been formulated. We studied the global stability of the corresponding single-group model, multi-group model with strongly connected network and multi-group model without strongly connected network by means of analyzing their basic reproduction numbers and the application of Lyapunov functionals. Finally, we provide some numerical simulations to illustrate our analysis results.

scholarly journals Global Analysis of SIRS Epidemic Model With General Incidence Function and Incomplete Recovery Rates Stochastical Model

2020 ◽  
Vol 12 (6) ◽  
pp. 100
Author(s):  
Dramane Ouedraogo ◽  
Ali Traore ◽  
Aboudramane Guiro
Keyword(s):  
Stochastic Model ◽  
Global Stability ◽  
Stochastic Models ◽  
Epidemic Model ◽  
Global Analysis ◽  
Endemic Equilibrium ◽  
Epidemic Models ◽  
Local And Global Stability ◽  
Sirs Epidemic Model ◽  
Disease Free

In this paper, deterministic and stochastic models are developped for a class of SIRS epidemic models. Firstly, The conditions for the existence, local and global stability of the disease-free equilibrium and endemic equilibrium are obtained. Secondly, we built the stochastic model. The populations are computationally simulated under various conditions. Comparisons are made between the deterministic and stochastic model.

scholarly journals The Global Behavior of a Periodic Epidemic Model with Travel between Patches

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Luosheng Wen ◽  
Bin Long ◽  
Xin Liang ◽  
Fengling Zeng
Keyword(s):  
Epidemic Model ◽  
Transmission Rate ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Periodic Transmission ◽  
Theoretical Results ◽  
Disease Free

We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratioR0and two theorems on the global behavior: ifR0< 1 the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then it is unstable; ifR0> 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.

scholarly journals Analysis of COVID-19 based on SEIR epidemic models in a multi-patch environment

2021 ◽  
Author(s):  
Lan Meng ◽  
Wei Zhu
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behavior ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Migration Rate ◽  
Reproduction Number ◽  
Population Migration ◽  
Theoretical Results ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstract In this paper, an n-patch SEIR epidemic model for the coronavirus disease 2019 (COVID-19) is presented. It is shown that there is unique disease-free equilibrium for this model. Then, the dynamic behavior is studied by the basic reproduction number. Some numerical simulations with three patches are given to validate the effectiveness of the theoretical results. The influence of quarantined rate and population migration rate on the basic reproduction number is also discussed by simulation.

Media effects on the dynamics of a stochastic SIRI epidemic model with relapse and Lévy noise perturbation

2019 ◽  
Vol 12 (03) ◽  
pp. 1950037 ◽  
Author(s):  
Badr-Eddine Berrhazi ◽  
Mohamed El Fatini ◽  
Roger Pettersson ◽  
Aziz Laaribi
Keyword(s):  
Epidemic Model ◽  
Media Coverage ◽  
Deterministic Model ◽  
Dynamic Properties ◽  
Lévy Noise ◽  
Noise Perturbation ◽  
Global Positive Solution ◽  
Levy Noise ◽  
Theoretical Results ◽  
Disease Free

In this paper, we study the dynamic properties of an SIRI epidemic model incorporating media coverage, and stochastically perturbed by a Lévy noise. We establish the existence of a unique global positive solution. We investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model depending on the basic reproduction number under some noise excitation. Furthermore, we present some numerical simulations to support the theoretical results.

scholarly journals Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Karim Khan ◽  
Rahat Zarin ◽  
Amir Khan ◽  
Abdullahi Yusuf ◽  
Mohammed Al-Shomrani ◽  
...  
Keyword(s):  
Global Stability ◽  
Equilibrium Point ◽  
Lyapunov Theory ◽  
Endemic Equilibrium ◽  
Qualitative Behavior ◽  
Geometrical Approach ◽  
Local And Global Stability ◽  
Free Case ◽  
Compound Matrix ◽  
Disease Free

AbstractIn this paper, we discuss the Anthroponotic Cutaneous Leishmania transmission. In addition, we develop a mathematical model for the Anthroponotic Cutaneous Leishmania transmission and consider its qualitative behavior. We derive the threshold number $R_{0}$ R 0 of the model using the next generation method. In the disease-free case, we carry out the local and global stability under the condition $R_{0}<1$ R 0 < 1 . Moreover, we derive the global stability at the disease-free equilibrium point by utilizing the Castillo-Chavez method. On the other hand, at the endemic equilibrium point, we show the local and global stability to be held under specific conditions and $R_{0}>1$ R 0 > 1 . We also establish the global stability at the endemic equilibrium point with the help of a geometrical approach, which is a generalization of Lyapunov theory, by using a second additive compound matrix. Finally, we take into account the sensitivity analysis of the threshold number with other parameters. We also discuss several graphs of important parameters.

Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate

2016 ◽  
Vol 09 (05) ◽  
pp. 1650068 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Yasir Khan ◽  
Sehra Khan ◽  
Saeed Islam
Keyword(s):  
Global Stability ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Disease Free ◽  
The Basic Reproduction Number

This study considers SEIVR epidemic model with generalized nonlinear saturated incidence rate in the host population horizontally to estimate local and global equilibriums. By using the Routh–Hurwitz criteria, it is shown that if the basic reproduction number [Formula: see text], the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if [Formula: see text]. The geometric approach is used to present the global stability of the endemic equilibrium. For [Formula: see text], the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.

An infection age-space-structured SIR epidemic model with Dirichlet boundary condition

2019 ◽  
Vol 14 (5) ◽  
pp. 505 ◽  
Author(s):  
Abdennasser Chekroun ◽  
Toshikazu Kuniya
Keyword(s):  
Boundary Condition ◽  
Steady State ◽  
Dirichlet Boundary Condition ◽  
Epidemic Model ◽  
Dirichlet Boundary ◽  
Upper And Lower Solutions ◽  
Sir Epidemic Model ◽  
Infection Age ◽  
Sir Epidemic ◽  
Disease Free

In this paper, we are concerned with the global asymptotic behavior of an SIR epidemic model with infection age-space structure. Under the homogeneous Dirichlet boundary condition, we first reformulate the model into the coupled reaction-diffusion and difference system by using the method of characteristics. We then obtain the spatially heterogeneous disease-free steady state and define the basic reproduction number ℛ0 by the spectral radius of the next generation operator. We then show the existence and uniqueness of the global classical solution by constructing suitable upper and lower solutions. As a threshold result, we establish that the disease-free steady state is globally attractive if ℛ0 < 1, whereas the system is uniformly weakly persistent in norm if ℛ0 > 1. Finally, numerical simulations are exhibited to illustrate our theoretical results together with how to compute ℛ0.

Global stability and Hopf bifurcation of an eco-epidemiological model with time delay

2019 ◽  
Vol 12 (06) ◽  
pp. 1950062
Author(s):  
Jinna Lu ◽  
Xiaoguang Zhang ◽  
Rui Xu
Keyword(s):  
Time Delay ◽  
Global Stability ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Epidemiological Model ◽  
Hopf Bifurcations ◽  
Lyapunov Functionals ◽  
Predator Population ◽  
Disease Free ◽  
Transmissible Disease

In this paper, an eco-epidemiological model with time delay representing the gestation period of the predator is investigated. In the model, it is assumed that the predator population suffers a transmissible disease and the infected predators may recover from the disease and become susceptible again. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease-free and coexistence equilibria are established, respectively. By means of Lyapunov functionals and LaSalle’s invariance principle, sufficient conditions are obtained for the global stability of the coexistence equilibrium, the disease-free equilibrium and the predator-extinct equilibrium of the system, respectively.

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