American Institute of Mathematical Sciences

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

Stochastic and deterministic models for agricultural production networks

P. Bai 1, , H.T. Banks 2, , S. Dediu 2, , A.Y. Govan 2, , M. Last 3, , A.L. Lloyd 2, , H.K. Nguyen 2, , M.S. Olufsen 2, , G. Rempala 4, and  B.D. Slenning 5,

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.
Keywords: stochastic and deterministic models, sensitivity and generalized sensitivity functions, foot-and-mouth disease., agricultural production networks.
Mathematics Subject Classification: 60J20, 34A34, 49Q12, 92D3.
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
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