# American Institute of Mathematical Sciences

2007, 4(3): 373-402. doi: 10.3934/mbe.2007.4.373

## Stochastic and deterministic models for agricultural production networks

 1 Department of Statistics, University of North Carolina, Hill, NC, United States 2 Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC, United States, United States, United States, United States, United States, United States 3 National Institute of Statistical Sciences, Research Triangle Park, NC, United States 4 Department of Mathematics and Statistics, University of Louisville, KY, United States 5 Department of Population Health and Pathobiology, College of Veterinary Medicine, North Carolina State University, Raleigh, NC, United States

Received  February 2007 Revised  March 2007 Published  May 2007

An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.
Citation: P. Bai, H.T. Banks, S. Dediu, A.Y. Govan, M. Last, A.L. Lloyd, H.K. Nguyen, M.S. Olufsen, G. Rempala, B.D. Slenning. Stochastic and deterministic models for agricultural production networks. Mathematical Biosciences & Engineering, 2007, 4 (3) : 373-402. doi: 10.3934/mbe.2007.4.373
 [1] Steady Mushayabasa, Drew Posny, Jin Wang. Modeling the intrinsic dynamics of foot-and-mouth disease. Mathematical Biosciences & Engineering, 2016, 13 (2) : 425-442. doi: 10.3934/mbe.2015010 [2] Hongxiao Hu, Liguang Xu, Kai Wang. A comparison of deterministic and stochastic predator-prey models with disease in the predator. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2837-2863. doi: 10.3934/dcdsb.2018289 [3] H.Thomas Banks, Danielle Robbins, Karyn L. Sutton. Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1301-1333. doi: 10.3934/mbe.2013.10.1301 [4] Qi Wang, Jingyue Yang, Feng Yu. Boundedness in logistic Keller-Segel models with nonlinear diffusion and sensitivity functions. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 5021-5036. doi: 10.3934/dcds.2017216 [5] Caglar S. Aksezer. On the sensitivity of desirability functions for multiresponse optimization. Journal of Industrial and Management Optimization, 2008, 4 (4) : 685-696. doi: 10.3934/jimo.2008.4.685 [6] Uwe Helmke, Michael Schönlein. Minimum sensitivity realizations of networks of linear systems. Numerical Algebra, Control and Optimization, 2016, 6 (3) : 241-262. doi: 10.3934/naco.2016010 [7] Jaroslaw Smieja, Malgorzata Kardynska, Arkadiusz Jamroz. The meaning of sensitivity functions in signaling pathways analysis. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2697-2707. doi: 10.3934/dcdsb.2014.19.2697 [8] Guoqiang Ren, Heping Ma. Global existence in a chemotaxis system with singular sensitivity and signal production. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 343-360. doi: 10.3934/dcdsb.2021045 [9] Connell McCluskey. Lyapunov functions for disease models with immigration of infected hosts. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4479-4491. doi: 10.3934/dcdsb.2020296 [10] Alireza Ghaffari Hadigheh, Tamás Terlaky. Generalized support set invariancy sensitivity analysis in linear optimization. Journal of Industrial and Management Optimization, 2006, 2 (1) : 1-18. doi: 10.3934/jimo.2006.2.1 [11] Behrouz Kheirfam, Kamal mirnia. Comments on ''Generalized support set invariancy sensitivity analysis in linear optimization''. Journal of Industrial and Management Optimization, 2008, 4 (3) : 611-616. doi: 10.3934/jimo.2008.4.611 [12] Wei Wang, Kai Liu, Xiulian Wang. Sensitivity to small delays of mean square stability for stochastic neutral evolution equations. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2403-2418. doi: 10.3934/cpaa.2020105 [13] Azmy S. Ackleh, Shuhua Hu. Comparison between stochastic and deterministic selection-mutation models. Mathematical Biosciences & Engineering, 2007, 4 (2) : 133-157. doi: 10.3934/mbe.2007.4.133 [14] Xiaoming Yan, Ping Cao, Minghui Zhang, Ke Liu. The optimal production and sales policy for a new product with negative word-of-mouth. Journal of Industrial and Management Optimization, 2011, 7 (1) : 117-137. doi: 10.3934/jimo.2011.7.117 [15] Tobias Black. Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 119-137. doi: 10.3934/dcdss.2020007 [16] Wenji Zhang. Global generalized solvability in the Keller-Segel system with singular sensitivity and arbitrary superlinear degradation. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022121 [17] Marzena Dolbniak, Malgorzata Kardynska, Jaroslaw Smieja. Sensitivity of combined chemo-and antiangiogenic therapy results in different models describing cancer growth. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 145-160. doi: 10.3934/dcdsb.2018009 [18] Xin Zhao, Tao Feng, Liang Wang, Zhipeng Qiu. Threshold dynamics and sensitivity analysis of a stochastic semi-Markov switched SIRS epidemic model with nonlinear incidence and vaccination. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6131-6154. doi: 10.3934/dcdsb.2021010 [19] Tao Yu. Measurable sensitivity via Furstenberg families. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4543-4563. doi: 10.3934/dcds.2017194 [20] H. Thomas Banks, Kidist Bekele-Maxwell, Lorena Bociu, Marcella Noorman, Giovanna Guidoboni. Local sensitivity via the complex-step derivative approximation for 1D Poro-Elastic and Poro-Visco-Elastic models. Mathematical Control and Related Fields, 2019, 9 (4) : 623-642. doi: 10.3934/mcrf.2019044

2018 Impact Factor: 1.313