Figure 1.
Schematic diagram for the knowledge dissemination model
-
Previous Article
Fractional Cauchy problems for infinite interval case
- DCDS-S Home
- This Issue
-
Next Article
Evolution fractional differential problems with impulses and nonlocal conditions
Global analysis of SIRI knowledge dissemination model with recalling rate
| 1. | Department of Mathematics, Xinzhou Teachers University, Xinzhou, Shan'xi 034000, China |
| 2. | Complex Systems Research Center, Shanxi University, Taiyuan Shan'xi 030006, China |
| 3. | Shanxi Key Laboratory of Mathematical Techniques and, Big Data Analysis on Disease Control and Prevention, Taiyuan, Shan'xi 030006, China |
In order to study the dissemination mechanism of knowledge, a SIRI dynamics model with the learning rate, the forgetting rate and the recalling rate is constructed in this paper. Stability of equilibria and global dynamics of the SIRI model are analyzed. Two thresholds that determine whether knowledge is disseminated are given. We describe the stability of the equilibria for the SIRI model in which there are an equilibrium and a line of equilibria. In particular, we find the dividing curve function which is used to partition invariant set in order to discuss the local stability, and obtain the equation of the wave peak value or wave trough value in the process of knowledge dissemination. Numerical simulations are provided to support the theoretical results. The complicated dynamics properties exhibit that the model is very sensitive to variation of parameters, which play an important role on controlling and administering the knowledge dissemination.
Keywords:
Knowledge dissemination model,
recalling rate,
global stability,
a line of equilibria,
thresholds.
Mathematics Subject Classification:
Primary: 34D23, 34D05; Secondary: 91E40, 91B52.
Citation:
Fang Liu, Zhen Jin, Cai-Yun Wang.
Global analysis of SIRI knowledge dissemination model with recalling rate. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020116
![]()
References:
| [1] |
M. T. Dora, H. Hussin and S. Sidek, Impacts of training on knowledge dissemination and application among academics in malaysian institutions of higher education, Asian Social Science, 8 (2012).
doi: 10.5539/ass.v8n1p146. |
| [2] |
B. van den Hooff and J. A. de Ridder,
Knowledge sharing in context: The influence of organizational commitment, communication climate and cmc use on knowledge sharing, Journal of Knowledge Management, 8 (2004), 117-130.
doi: 10.1108/13673270410567675. |
| [3] |
F. Llorens, J. J. Bayona, J. Gómez and F. Sanguino.,
The University of Alicante's institutional strategy to promote the open dissemination of knowledge, Online Information Review, 34 (2010), 565-582.
doi: 10.1108/14684521011072981. |
| [4] |
R. Monclar, A. Tecla, J. Oliveira and J. M. de Souza,
MEK: Using spatial-temporal information to improve social networks and knowledge dissemination, Information Sciences An International Journal, 179 (2009), 2524-2537.
doi: 10.1016/j.ins.2009.01.032. |
| [5] |
M. M. Parent, D. MacDonald and G. Goulet,
The theory and practice of knowledge management and transfer: The case of the Olympic Games, Sport Management Review, 17 (2014), 205-218.
doi: 10.1016/j.smr.2013.06.002. |
| [6] |
M. Song, H. Berends, H. van der Bij and M. Weggeman,
The effect of it and co-location on knowledge dissemination, Journal of Product Innovation Management, 24 (2007), 52-68.
doi: 10.1111/j.1540-5885.2006.00232.x. |
show all references
References:
| [1] |
M. T. Dora, H. Hussin and S. Sidek, Impacts of training on knowledge dissemination and application among academics in malaysian institutions of higher education, Asian Social Science, 8 (2012).
doi: 10.5539/ass.v8n1p146. |
| [2] |
B. van den Hooff and J. A. de Ridder,
Knowledge sharing in context: The influence of organizational commitment, communication climate and cmc use on knowledge sharing, Journal of Knowledge Management, 8 (2004), 117-130.
doi: 10.1108/13673270410567675. |
| [3] |
F. Llorens, J. J. Bayona, J. Gómez and F. Sanguino.,
The University of Alicante's institutional strategy to promote the open dissemination of knowledge, Online Information Review, 34 (2010), 565-582.
doi: 10.1108/14684521011072981. |
| [4] |
R. Monclar, A. Tecla, J. Oliveira and J. M. de Souza,
MEK: Using spatial-temporal information to improve social networks and knowledge dissemination, Information Sciences An International Journal, 179 (2009), 2524-2537.
doi: 10.1016/j.ins.2009.01.032. |
| [5] |
M. M. Parent, D. MacDonald and G. Goulet,
The theory and practice of knowledge management and transfer: The case of the Olympic Games, Sport Management Review, 17 (2014), 205-218.
doi: 10.1016/j.smr.2013.06.002. |
| [6] |
M. Song, H. Berends, H. van der Bij and M. Weggeman,
The effect of it and co-location on knowledge dissemination, Journal of Product Innovation Management, 24 (2007), 52-68.
doi: 10.1111/j.1540-5885.2006.00232.x. |
Figure 2.
Transfer diagram for knowledge dissemination SIRI model
Figure 3.
When $ R_0 = 1 $ and keeping the fixed parameter $ \alpha = 0.72 $ , the phase portraits with different others parameters are given. (a) Parameters are $ \lambda = \beta = 0.0036 $ , $ K = 200 $ . (b) Parameters are $ \lambda = 0.0072 $ , $ \beta = 0.0172 $ , $ K = 100 $ . (c) Parameters are $ \lambda = 0.0072 $ , $ \beta = 0.0033 $ , $ K = 100 $
Figure 4.
When $ R_0<1 $ and keeping the fixed parameter $ \alpha = 0.72 $ , the phase portraits with different others parameters are given. (a) Parameters are $ \lambda = \beta = 0.0033 $ , $ K = 200 $ . (b1) Parameters are $ \lambda = 0.0033 $ , $ \beta = 0.005 $ , $ K = 200 $ . (b2) Parameters are $ \lambda = 0.0033 $ , $ \beta = 0.00357 $ , $ K = 200 $ . (c) Parameters are $ \lambda = 0.005 $ , $ \beta = 0.0033 $ , $ K = 130 $
Figure 5.
When $ R_0>1 $ and keeping the fixed parameter $ \alpha = 0.72 $ , the phase portraits with different others parameters are given. (a) Parameters are $ \lambda = \beta = 0.0032 $ , $ K = 300 $ . (b) Parameters are $ \lambda = 0.0033 $ , $ \beta = 0.005 $ , $ K = 250 $ . (c1) Parameters are $ \lambda = 0.004 $ , $ \beta = 0.0033 $ , $ K = 230 $ . (c2) Parameters are $ \lambda = 0.004 $ , $ \beta = 0.0033 $ , $ K = 200 $ . (c3) Parameters are $ \lambda = 0.005 $ , $ \beta = 0.0034 $ , $ K = 150 $
Figure 6.
The Numerical simulation for system(2) with $ K = 61 $ , $ \alpha = 0.4 $ , $ \beta = 0.01 $ . (a) Parameters are $ S(0) = 60 $ , $ I(0) = 1 $ , $ R(0) = 0 $ , $ \lambda = 0.004 $ . (b) Parameters are $ S(0) = 6 $ , $ I(0) = 55 $ , $ R(0) = 0 $ , $ \lambda = 0.04 $
Figure 7.
The Numerical simulation for system (2) with $ \beta = 0.01 $ , $ \lambda = 0.004 $ , $ \alpha_1 = 0.2 $ , $ \alpha_2 = 0.4 $ , $ \alpha_3 = 0.8 $
Figure 8.
The Numerical simulation for system (2) with $ \alpha = 0.4 $ , $ \lambda = 0.004 $ , $ \beta_1 = 0.005 $ , $ \beta_2 = 0.01 $ , $ \beta_3 = 0.02 $
Figure 9.
The Numerical simulation for system (2) with $ \alpha = 0.4 $ , $ \beta = 0.01 $ , $ \lambda_1 = 0.002 $ , $ \lambda_2 = 0.004 $ , $ \lambda_3 = 0.008 $
| [1] |
Shangbing Ai. Global stability of equilibria in a tick-borne disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 567-572. doi: 10.3934/mbe.2007.4.567 |
| [2] |
Zigen Ouyang, Chunhua Ou. Global stability and convergence rate of traveling waves for a nonlocal model in periodic media. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 993-1007. doi: 10.3934/dcdsb.2012.17.993 |
| [3] |
Paul Georgescu, Hong Zhang, Daniel Maxin. The global stability of coexisting equilibria for three models of mutualism. Mathematical Biosciences & Engineering, 2016, 13 (1) : 101-118. doi: 10.3934/mbe.2016.13.101 |
| [4] |
Shouying Huang, Jifa Jiang. Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate. Mathematical Biosciences & Engineering, 2016, 13 (4) : 723-739. doi: 10.3934/mbe.2016016 |
| [5] |
Yu Ji. Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences & Engineering, 2015, 12 (3) : 525-536. doi: 10.3934/mbe.2015.12.525 |
| [6] |
Yu Ji, Lan Liu. Global stability of a delayed viral infection model with nonlinear immune response and general incidence rate. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 133-149. doi: 10.3934/dcdsb.2016.21.133 |
| [7] |
Ting Guo, Haihong Liu, Chenglin Xu, Fang Yan. Global stability of a diffusive and delayed HBV infection model with HBV DNA-containing capsids and general incidence rate. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4223-4242. doi: 10.3934/dcdsb.2018134 |
| [8] |
Sílvia Cuadrado. Stability of equilibria of a predator-prey model of phenotype evolution. Mathematical Biosciences & Engineering, 2009, 6 (4) : 701-718. doi: 10.3934/mbe.2009.6.701 |
| [9] |
Cruz Vargas-De-León, Alberto d'Onofrio. Global stability of infectious disease models with contact rate as a function of prevalence index. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1019-1033. doi: 10.3934/mbe.2017053 |
| [10] |
Haibo Cui, Zhensheng Gao, Haiyan Yin, Peixing Zhang. Stationary waves to the two-fluid non-isentropic Navier-Stokes-Poisson system in a half line: Existence, stability and convergence rate. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4839-4870. doi: 10.3934/dcds.2016009 |
| [11] |
Tong Li, Sunčica Čanić. Critical thresholds in a quasilinear hyperbolic model of blood flow. Networks & Heterogeneous Media, 2009, 4 (3) : 527-536. doi: 10.3934/nhm.2009.4.527 |
| [12] |
Henri Berestycki, Jean-Pierre Nadal, Nancy Rodíguez. A model of riots dynamics: Shocks, diffusion and thresholds. Networks & Heterogeneous Media, 2015, 10 (3) : 443-475. doi: 10.3934/nhm.2015.10.443 |
| [13] |
Haiyan Yin, Changjiang Zhu. Convergence rate of solutions toward stationary solutions to a viscous liquid-gas two-phase flow model in a half line. Communications on Pure & Applied Analysis, 2015, 14 (5) : 2021-2042. doi: 10.3934/cpaa.2015.14.2021 |
| [14] |
Shengqin Xu, Chuncheng Wang, Dejun Fan. Stability and bifurcation in an age-structured model with stocking rate and time delays. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2535-2549. doi: 10.3934/dcdsb.2018264 |
| [15] |
Hong Yang, Junjie Wei. Global behaviour of a delayed viral kinetic model with general incidence rate. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1573-1582. doi: 10.3934/dcdsb.2015.20.1573 |
| [16] |
Yongming Liu, Lei Yao. Global solution and decay rate for a reduced gravity two and a half layer model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2613-2638. doi: 10.3934/dcdsb.2018267 |
| [17] |
PaweŁ Hitczenko, Georgi S. Medvedev. Stability of equilibria of randomly perturbed maps. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 369-381. doi: 10.3934/dcdsb.2017017 |
| [18] |
Frederik Riis Mikkelsen. A model based rule for selecting spiking thresholds in neuron models. Mathematical Biosciences & Engineering, 2016, 13 (3) : 569-578. doi: 10.3934/mbe.2016008 |
| [19] |
Jianxin Yang, Zhipeng Qiu, Xue-Zhi Li. Global stability of an age-structured cholera model. Mathematical Biosciences & Engineering, 2014, 11 (3) : 641-665. doi: 10.3934/mbe.2014.11.641 |
| [20] |
Yukihiko Nakata, Yoichi Enatsu, Yoshiaki Muroya. On the global stability of an SIRS epidemic model with distributed delays. Conference Publications, 2011, 2011 (Special) : 1119-1128. doi: 10.3934/proc.2011.2011.1119 |
2018 Impact Factor: 0.545
Tools
Metrics
Other articles
by authors
[Back to Top]