Dynamical analysis for delayed virus infection models with cell-to-cell transmission and density-dependent diffusion

2020 ◽  
Vol 13 (07) ◽  
pp. 2050060
Author(s):  
Shaoli Wang ◽  
Achun Zhang ◽  
Fei Xu
Keyword(s):  
Neumann Boundary ◽  
Basic Reproductive Number ◽  
Dynamical Analysis ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Cell Infection ◽  
Globally Asymptotically Stable ◽  
Single Strain ◽  
Density Dependent ◽  
Number Formula

In this paper, certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion are investigated. For the viral model with a single strain, we have proved the well-posedness and studied the global stabilities of equilibria by defining the basic reproductive number [Formula: see text] and structuring proper Lyapunov functional. Moreover, we found that the infection-free equilibrium is globally asymptotically stable if [Formula: see text], and the infection equilibrium is globally asymptotically stable if [Formula: see text]. For the multi-strain model, we found that all viral strains coexist if the corresponding basic reproductive number [Formula: see text], while virus will extinct if [Formula: see text]. As a result, we found that delay and the density-dependent diffusion does not influence the global stability of the model with cell-to-cell infection and homogeneous Neumann boundary conditions.

scholarly journals Global Dynamics of an HTLV-1 Model with Cell-to-Cell Infection and Mitosis

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Sumei Li ◽  
Yicang Zhou
Keyword(s):  
Chronic Infection ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Cell Infection ◽  
Globally Asymptotically Stable ◽  
Human T Cell

A mathematical model of human T-cell lymphotropic virus type 1 in vivo with cell-to-cell infection and mitosis is formulated and studied. The basic reproductive numberR0is derived. It is proved that the dynamics of the model can be determined completely by the magnitude ofR0. The infection-free equilibrium is globally asymptotically stable (unstable) ifR0<1  (R0>1). There exists a chronic infection equilibrium and it is globally asymptotically stable ifR0>1.

scholarly journals Dynamics of a Reaction Diusion Brucellosis Model

2021 ◽  
pp. 52-69
Author(s):  
Paride O. Lolika ◽  
Steady Mushayabasa
Keyword(s):  
Disease Transmission ◽  
Animal Movement ◽  
Travelling Waves ◽  
Neumann Boundary ◽  
Turing Instability ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Spatial Movement

To understand the effects of animal movement on transmission and control of brucellosis infection, a reaction diffusion partial differential equation (PDE) brucellosis model that incorporates wild and domesticated animals under homogeneous Neumann boundary conditions is proposed and analysed. We computed the reproductive number for the brucellosis model in the absence of spatial movement and we established that, the associated model has a globally asymptotically stable disease-free equilibrium whenever the reproductive number is less or equal to unity. However, if the reproductive number is greater than unity an endemic equilibrium point which is globally asymptotically stable exists. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. For the model with spatial movement the disease threshold is studied by using the basic reproductive number. Additionally we investigate the existence of a Turing stability and travelling waves. Our results shows that incorporating diffusive spatial spread does not produce a Turing instability when the reproductive number R0ODE  associated with the ODE model is less than unity. Finally the results suggest that minimizing interaction between buffalo and cattle population can be essential to manage brucellosis spillover between domesticated and wildlife animals. Numerical simulations are carried out to support analytical findings.

Global properties for an age-structured within-host model with Crowley–Martin functional response

2017 ◽  
Vol 10 (02) ◽  
pp. 1750030 ◽  
Author(s):  
Shaoli Wang ◽  
Xinyu Song
Keyword(s):  
Functional Response ◽  
Viral Infections ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Multi Scale ◽  
Global Properties ◽  
Age Structured

Based on a multi-scale view, in this paper, we study an age-structured within-host model with Crowley–Martin functional response for the control of viral infections. By means of semigroup and Lyapunov function, the global asymptotical property of infected steady state of the model is obtained. The results show that when the basic reproductive number falls below unity, the infection dies out. However, when the basic reproductive number exceeds unity, there exists a unique positive equilibrium which is globally asymptotically stable. This model can be deduced to different viral models with or without time delay.

scholarly journals Global Stability of an SEIS Epidemic Model with General Saturation Incidence

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hui Zhang ◽  
Li Yingqi ◽  
Wenxiong Xu
Keyword(s):  
Latent Period ◽  
Epidemic Model ◽  
Convergence Theorem ◽  
Incidence Rates ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

We present an SEIS epidemic model with infective force in both latent period and infected period, which has different general saturation incidence rates. It is shown that the global dynamics are completely determined by the basic reproductive number R0. If R0≤1, the disease-free equilibrium is globally asymptotically stable in T by LaSalle’s Invariance Principle, and the disease dies out. Moreover, using the method of autonomous convergence theorem, we obtain that the unique epidemic equilibrium is globally asymptotically stable in T0, and the disease spreads to be endemic.

SVIR epidemic model with age structure in susceptibility, vaccination effects and relapse

2017 ◽  
Vol 82 (5) ◽  
pp. 945-970 ◽  
Author(s):  
Jinliang Wang ◽  
Min Guo ◽  
Shengqiang Liu
Keyword(s):  
Age Structure ◽  
Epidemic Model ◽  
Lyapunov Functional ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Combined Effects ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Disease Free

Abstract An SVIR epidemic model with continuous age structure in the susceptibility, vaccination effects and relapse is proposed. The asymptotic smoothness, existence of a global attractor, the stability of equilibria and persistence are addressed. It is shown that if the basic reproductive number $\Re_0&lt;1$, then the disease-free equilibrium is globally asymptotically stable. If $\Re_0&gt;1$, the disease is uniformly persistent, and a Lyapunov functional is used to show that the unique endemic equilibrium is globally asymptotically stable. Combined effects of susceptibility age, vaccination age and relapse age on the basic reproductive number are discussed.

scholarly journals Dynamical Behavior of a New Epidemiological Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zizi Wang ◽  
Zhiming Guo
Keyword(s):  
Time Delay ◽  
Dynamical Behavior ◽  
Endemic Equilibrium ◽  
Epidemiological Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain timeτ. The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive numberR0is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease-free equilibrium is globally asymptotically stable provided thatR0≤1; ifR0>1, then there exists a unique endemic equilibrium, and it is globally asymptotically stable. For the model with time delay, a sufficient condition is given to ensure that the disease-free equilibrium is locally asymptotically stable. Hopf bifurcation in endemic equilibrium with respect to the timeτis also addressed.

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 Analysis of a HBV Model with Diffusion and Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Noé Chan Chí ◽  
Eric ÁvilaVales ◽  
Gerardo García Almeida
Keyword(s):  
Reproduction Number ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Spatial Diffusion ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
B Virus ◽  
Comparison Arguments ◽  
Hbv Model ◽  
Iteration Technique

This paper discussed a hepatitis B virus infection with delay, spatial diffusion, and standard incidence function. The local stability of equilibrium is obtained via characteristic equations. By using comparison arguments, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproductive number is greater than unity, by means of an iteration technique, sufficiently conditions are obtained for the global asymptotic stability of the infected steady state. Numerical simulations are carried out to illustrate our findings.

scholarly journals Modeling and Analysis of the Spread of Malware with the Influence of User Awareness

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Qingyi Zhu ◽  
Xuhang Luo ◽  
Yuhang Liu
Keyword(s):  
Propagation Model ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Sis Model ◽  
Globally Asymptotically Stable ◽  
Modeling And Analysis ◽  
Malware Propagation ◽  
User Awareness

By incorporating the security awareness of computer users into the susceptible-infected-susceptible (SIS) model, this study proposes a new malware propagation model, named the SID model, where D compartment denotes the group of nodes with user awareness. Through qualitative analysis, the basic reproductive number R 0 is given. Furthermore, it is proved that the virus-free equilibrium is globally asymptotically stable if R 0 is less than one, whereas the viral equilibrium is globally asymptotically stable if R 0 is greater than one. Then, some numerical examples are given to demonstrate the analytical results. Finally, we put forward some efficient control measures according to the theoretical and experimental analysis.

Global Stability of a HBV Infection Model with Saturated Infection Rates and Time Delay

2013 ◽  
Vol 791-793 ◽  
pp. 1314-1317
Author(s):  
Wei Juan Pang ◽  
Zhi Xing Hu ◽  
Fu Cheng Liao
Keyword(s):  
Global Stability ◽  
Sufficient Conditions ◽  
Hbv Infection ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Infection Rates ◽  
Globally Asymptotically Stable ◽  
Viral Infection Model

This paper investigates the global stability of a viral infection model of HBV infection of hepatocytes with saturated infection rate and intracellular delay. we obtain if the basic reproductive number is less than or equal to one, the infection-free equilibrium is globally asymptotically stable. If its greater than one, we obtain the sufficient conditions for the global stability of the infected equilibrium.

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