scholarly journals Analysis of a diffusive cholera model incorporating latency and bacterial hyperinfectivity

2021 ◽  
Vol 20 (11) ◽  
pp. 3921
Author(s):  
Wei Yang ◽  
Jinliang Wang
Keyword(s):  
Lyapunov Functional ◽  
Global Attractivity ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Flux Boundary Condition ◽  
Nonlocal Reaction ◽  
Theoretical Results ◽  
The Basic Reproduction Number

<p style='text-indent:20px;'>In this paper, we are concerned with the threshold dynamics of a diffusive cholera model incorporating latency and bacterial hyperinfectivity. Our model takes the form of spatially nonlocal reaction-diffusion system associated with zero-flux boundary condition and time delay. By studying the associated eigenvalue problem, we establish the threshold dynamics that determines whether or not cholera will spread. We also confirm that the threshold dynamics can be determined by the basic reproduction number. By constructing Lyapunov functional, we address the global attractivity of the unique positive equilibrium whenever it exists. The theoretical results are still hold for the case when the constant parameters are replaced by strictly positive and spatial dependent functions.</p>

scholarly journals Global proprieties of a delayed epidemic model with partial susceptible protection

2021 ◽  
Vol 19 (1) ◽  
pp. 209-224
Author(s):  
Abdelheq Mezouaghi ◽  
◽  
Salih Djillali ◽  
Anwar Zeb ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Isolation Rate ◽  
Globally Asymptotically Stable ◽  
The Government ◽  
The Basic Reproduction Number

<abstract><p>In the case of an epidemic, the government (or population itself) can use protection for reducing the epidemic. This research investigates the global dynamics of a delayed epidemic model with partial susceptible protection. A threshold dynamics is obtained in terms of the basic reproduction number, where for $ R_0 &lt; 1 $ the infection will extinct from the population. But, for $ R_0 &gt; 1 $ it has been shown that the disease will persist, and the unique positive equilibrium is globally asymptotically stable. The principal purpose of this research is to determine a relation between the isolation rate and the basic reproduction number in such a way we can eliminate the infection from the population. Moreover, we will determine the minimal protection force to eliminate the infection for the population. A comparative analysis with the classical SIR model is provided. The results are supported by some numerical illustrations with their epidemiological relevance.</p></abstract>

scholarly journals Threshold Dynamics of a Diffusive Herpes Model Incorporating Fixed Relapse Period in a Spatial Heterogeneous Environment

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Yueming Lu ◽  
Wei Yang ◽  
Desheng Ji
Keyword(s):  
Eigenvalue Problem ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Principal Eigenvalue ◽  
Threshold Dynamics ◽  
Heterogeneous Environment ◽  
Homogeneous Case ◽  
Operator Approach ◽  
Theoretical Results ◽  
The Basic Reproduction Number

In this paper, we aim to establish the threshold-type dynamics of a diffusive herpes model that assumes a fixed relapse period and nonlinear recovery rate. It turns out that when considering diseases with a fixed relapse period, the diffusion of recovered individuals will lead to nonlocal recovery term. We characterize the basic reproduction number, ℜ 0 , for the model through the next generation operator approach. Moreover, in a homogeneous case, we calculate the ℜ 0 explicitly. By utilizing the principal eigenvalue of the associated eigenvalue problem or equivalently by ℜ 0 , we establish the threshold-type dynamics of the model in the sense that the herpes is either extinct or close to the epidemic value. Numerical simulations are performed to verify the theoretical results and the effects of the spatial heterogeneity on disease transmission.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

scholarly journals Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jianping Wang ◽  
Shujing Gao ◽  
Yueli Luo ◽  
Dehui Xie
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Logistic Growth ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction numberR0which is defined through the spectral radius of a linear integral operator. IfR0< 1, then the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given.

scholarly journals Modeling Cell-to-Cell Spread of HIV-1 with Nonlocal Infections

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoting Fan ◽  
Yi Song ◽  
Wencai Zhao
Keyword(s):  
Reproduction Number ◽  
Reaction Diffusion ◽  
Threshold Dynamics ◽  
Delayed Reaction ◽  
Heterogeneous Model ◽  
Host Environment ◽  
Reaction Diffusion Model ◽  
Globally Attractive ◽  
Cell Spread ◽  
Hiv 1

This paper is devoted to develop a nonlocal and time-delayed reaction-diffusion model for HIV infection within host cell-to-cell viral transmissions. In a bounded spatial domain, we study threshold dynamics in terms of basic reproduction number R0 for the heterogeneous model. Our results show that if R0<1, the infection-free steady state is globally attractive, implying infection becomes extinct, while if R0>1, virus will persist in the host environment.

scholarly journals Global dynamics of a Huanglongbing model with a periodic latent period

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yan Hong ◽  
Xiuxiang Liu ◽  
Xiao Yu
Keyword(s):  
Reproduction Number ◽  
Threshold Value ◽  
Transmission Model ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Temperature Dependent ◽  
Candidatus Liberibacter ◽  
Effects Of Temperature ◽  
Disease Free ◽  
The Basic Reproduction Number

<p style='text-indent:20px;'>Huanglongbing (HLB) is a disease of citrus that caused by phloem-restricted bacteria of the Candidatus Liberibacter group. In this paper, we present a HLB transmission model to investigate the effects of temperature-dependent latent periods and seasonality on the spread of HLB. We first establish disease free dynamics in terms of a threshold value <inline-formula><tex-math id="M1">\begin{document}$ R^p_0 $\end{document}</tex-math></inline-formula>, and then introduce the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> and show the threshold dynamics of HLB with respect to <inline-formula><tex-math id="M3">\begin{document}$ R^p $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>. Numerical simulations are further provided to illustrate our analytic results.</p>

scholarly journals Analysis of the Mathematical Model for the Spread of Pine Wilt Disease

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiangyun Shi ◽  
Guohua Song
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Pine Wilt Disease ◽  
Wilt Disease ◽  
Endemic Equilibrium ◽  
Feasible Region ◽  
Global Dynamics ◽  
Pine Wilt ◽  
Theoretical Results ◽  
The Basic Reproduction Number

This paper formulates and analyzes a pine wilt disease model. Mathematical analyses of the model with regard to invariance of nonnegativity, boundedness of the solutions, existence of nonnegative equilibria, permanence, and global stability are presented. It is proved that the global dynamics are determined by the basic reproduction numberℛ0and the other valueℛcwhich is larger thanℛ0. Ifℛ0andℛcare both less than one, the disease-free equilibrium is asymptotically stable and the pine wilt disease always dies out. If one is between the two values, though the pine wilt disease could occur, the outbreak will stop. If the basic reproduction number is greater than one, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at the endemic equilibrium state if it initially exists. Numerical simulations are carried out to illustrate the theoretical results, and some disease control measures are especially presented by these theoretical results.

Dynamical Analysis of Multipathways and Multidelays of General Virus Dynamics Model

2019 ◽  
Vol 29 (03) ◽  
pp. 1950031 ◽  
Author(s):  
Ángel G. Cervantes-Pérez ◽  
Eric Ávila-Vales
Keyword(s):  
Immune Response ◽  
Time Delays ◽  
Reproduction Number ◽  
Dynamical Analysis ◽  
Multiple Time Scales ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Virus Dynamics ◽  
Multiple Time ◽  
Dynamics Model

This paper considers a general virus dynamics model with cell-mediated immune response and direct cell-to-cell infection modes. The model incorporates two types of intracellular distributed time delays and a discrete delay in the CTL immune response. Under certain conditions, the model exhibits a global threshold dynamics with respect to two parameters: the basic reproduction number and the reproduction number of immune response. We use suitable Lyapunov functionals and apply Lasalle’s invariance principle to establish the global asymptotic stability of the two boundary equilibria. We also perform a bifurcation analysis for the positive equilibrium to show that the time delays may lead to sustained oscillations. To determine the direction of the Hopf bifurcation and the stability of the periodic solutions, the method of multiple time scales is applied. Finally, we carry out numerical simulations to illustrate our results.

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