Annals of Operations Research

, Volume 219, Issue 1, pp 25–47 | Cite as

Mathematical formulation and validation of the Be-FAST model for Classical Swine Fever Virus spread between and within farms

  • Benjamin IvorraEmail author
  • Beatriz Martínez-López
  • José M. Sánchez-Vizcaíno
  • Ángel M. Ramos


Classical Swine Fever is a viral disease of pigs that causes severe restrictions on the movement of pigs and pig products in the affected areas. The knowledge of its spread patterns and risk factors would help to implement specific measures for controlling future outbreaks. In this article, we describe in detail a spatial hybrid model, called Be-FAST, based on the combination of a stochastic Individual-Based model (modeling the interactions between the farms, considered as individuals) for between-farm spread with a Susceptible-Infected model for within-farm spread, to simulate the spread of this disease and identify risk zones in a given region. First, we focus on the mathematical formulation of each component of the model. Then, in order to validate Be-FAST, we perform various numerical experiments considering the Spanish province of Segovia. Obtained results are compared with the ones given by two other Individual-Based models and real outbreaks data from Segovia and The Netherlands.


Epidemiological modeling Individual-Based model Susceptible-Infected model Model validation Classical Swine Fever 



This work was carried out thanks to the financial support of the Spanish Ministry of Science and Innovation under projects MTM2008-04621 and MTM2011-22658; the project CONS-C6-0356 of the I-MATH Proyecto Ingenio Mathematica; the Research Group MOMAT supported by the “Banco Santander” and the “Universidad Complutense de Madrid” (Ref. 910480); and the “Comunidad de Madrid” and “European Social Fund” through project S2009/PPQ-1551. We gratefully acknowledge the assistance of Olga Minguez, her team, the Regional Government of Castilla and Leon Region and the Spanish Ministry of the Environment and Rural and Marine Affairs for providing us data and technical assistance. A.M. Ramos has also been Funded by Fundación Caja Madrid.


  1. Anderson, R., & May, R. (1979). Population biology of infectious diseases: Part 1. Nature, 280, 361–367. CrossRefGoogle Scholar
  2. Brauer, F., & Castillo-Chavez, C. (2001). Mathematical models in population biology and epidemiology. Berlin: Springer. CrossRefGoogle Scholar
  3. DeAngelis, D., & Gross, L. (1991). Individual-based models and approaches in ecology. New York: Chapman and Hall. Google Scholar
  4. DeRose, L., & Padua, D. (1999). Techniques for the translation of Matlab programs into Fortran 90. ACM Trans. Program. Lang. Syst., 21(2), 285–322. Google Scholar
  5. Edwards, S., Fukusho, A., Lefevre, P., Lipowski, A., Pejsak, Z., Roehe, P., & Westergaard, J. (2000). Classical Swine Fever: the global situation. Vet. Microbiol., 27(3), 103–109. CrossRefGoogle Scholar
  6. E.S.R.I. (2012). ArcGIS.
  7. Elbers, A., Stegeman, A., Moser, H., Ekker, H., Smak, J., & Pluimers, H. (1999). The CSF epidemic 1997–1998 in The Netherlands: descriptive epidemiology. Prev. Vet. Med., 4, 157–184. CrossRefGoogle Scholar
  8. Fernández, E., Ivorra, B., Ramos, A., Martínez-Lopez, B., & Sánchez-Vizcaíno, J. (2011). Diseño de un modelo económico y de planes de control para una epidemia de Peste Porcina Clásica. Preprint de la Universidad Complutense de Madrid.
  9. Jalvingh, A., Nielen, M., Maurice, H., Stegeman, A., Elbers, A.R., & Dijkhuizen, A. (1999). Spatial and stochastic simulation to evaluate the impact of events and control measures on the 1997–1998 CSF epidemic in The Netherlands. Prev. Vet. Med., 42, 271–295. CrossRefGoogle Scholar
  10. J.C.L. (2008). Junta de Castilla y Leon—Agricultura y Ganadería, expert opinion elicitation performed for FMD and CSF.
  11. Kartsen, S., Rave, G., & Krieter, J. (2005a). Monte Carlo simulation of CSF epidemics and control I. General concepts and description of the model. Vet. Microbiol., 108, 187–198. CrossRefGoogle Scholar
  12. Kartsen, S., Rave, G., & Krieter, J. (2005b). Monte Carlo simulation of CSF epidemics and control II. Validation of the model. Vet. Microbiol., 108, 199–205. CrossRefGoogle Scholar
  13. Kartsen, S., Rave, G., Teuffert, J., & Krieter, J. (2007). Evaluation of measures for the control of CSF using a simulation model. Arch. Tierz., 50, 92–104. Google Scholar
  14. Klinkenberg, D., DeBree, J., Laevens, H., & DeJong, M. C. M. (2002). Within- and between-pen transmission of Classical Swine Fever Virus: a new method to estimate the basic reproduction ratio from transmission experiments. Epidemiol. Infect., 128, 293–299. CrossRefGoogle Scholar
  15. Koenen, F., Van Caenegem, G., Vermeersch, J., Vandenheede, J., & Deluyker, H. (1996). Epidemiological characteristics of an outbreak of Classical Swine Fever in an area of high pig density. Vet. Rec., 139(15), 367–371. CrossRefGoogle Scholar
  16. Lyytikäinen, T., Niemi, J., Sahlström, L., Virtanen, T., & Lehtonen, H. (2011). The spread of Foot-and-Mouth Disease (FMD) within Finland and emergency vaccination in case of an epidemic outbreak. Finnish Food Safety Authority Evira, Helsinki. Research Reports, 1/2011.
  17. Mangen, M., Nielen, M., & Burrell, A. (2002). Simulated effect of pig-population density on epidemic size and choice of control strategy for Classical Swine Fever epidemics in The Netherlands. Prev. Vet. Med., 56(2), 141–163. CrossRefGoogle Scholar
  18. M.A.P.A. (2006). Ministerio de Agricultura, Pesca y Alimentación, Manual práctico de actuaciones contra la PPC.
  19. Martínez-López, B. (2009). Desarrollo de modelos epidemiológicos cuantitativos para el análisis del riesgo de introducción y difusión potencial de los virus de la Fiebre Aftosa y de la Peste Porcina Clásica en España. PhD thesis, Univ. Complutense de Madrid, Spain. Google Scholar
  20. Martínez-López, B., Ivorra, B., Ramos, A. M., & Sánchez-Vizcaíno, J. (2011). A novel spatial and stochastic model to evaluate the within and between farm transmission of CSF Virus: 1. General concepts and description of the model. Vet. Microbiol., 147(3), 300–309. CrossRefGoogle Scholar
  21. Martínez-López, B., Ivorra, B., Ramos, A. M., & Sánchez-Vizcaíno, J. (2012). A novel spatial and stochastic model to evaluate the within and between farm transmission of CSF Virus: 2. Model sensitivity analysis. Vet. Microbiol., 155(1), 21–30. CrossRefGoogle Scholar
  22. Martínez-López, B., Pérez, A., & Sánchez-Vizcaíno, J. (2009). A stochastic model to quantify the risk for Classical Swine Fever Virus introduction through import of domestic and wild boars into Spain. Epidemiol. Infect., 137(10), 1505–1515. CrossRefGoogle Scholar
  23. Massey Univ. (2012). InterSpread Plus.
  24. MathWorks (2012). Matlab.
  25. Mintiens, K., Laevens, H., Dewulf, J., Boelaert, F., Verloo, D., & Koenen, F. (2003). Risk analysis of the spread of CSF virus through neighborhood infections for different regions in Belgium. Prev. Vet. Med., 60(1), 27–36. CrossRefGoogle Scholar
  26. Moennig, V. (2000). Introduction to Classical Swine Fever: virus, disease and control policy. Vet. Microbiol., 73(2), 93–102. CrossRefGoogle Scholar
  27. Niemi, J., Lehtonen, H., Pietola, K., Lyytikäinen, T., & Raulo, S. (2008). Economic implications of potential Classical Swine Fever outbreaks for Finnish pig production sector. Prev. Vet. Med., 84, 194–212. CrossRefGoogle Scholar
  28. Ribbens, S., Dewulf, J., Koenen, F., Laevens, H., & de Kruif, A. (2004). Transmission of Classical Swine Fever. A review. Vet. Q., 26, 146–155. CrossRefGoogle Scholar
  29. Sanson, R. (1993). The development of a decision support system for an animal disease emergency. PhD thesis, Massey University, New Zealand. Google Scholar
  30. Stegeman, A., Elbers, A., Bouma, A., & DeJong, M. (2002). Rate of inter-farm transmission of Classical Swine Fever Virus by different types of contact during the 1997–1998 epidemic in The Netherlands. Epidemiol. Infect., 128, 285–291. CrossRefGoogle Scholar
  31. Stegeman, A., Elbers, A., Smak, J., & DeJong, M. (1999). Quantification of the transmission of Classical Swine Fever Virus between farms during the 1997–1998 epidemic in The Netherlands. Prev. Vet. Med., 42, 219–234. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Benjamin Ivorra
    • 1
    Email author
  • Beatriz Martínez-López
    • 2
  • José M. Sánchez-Vizcaíno
    • 2
  • Ángel M. Ramos
    • 1
  1. 1.Departamento de Matemática Aplicada, Fac. de C.C. Matemáticas & Instituto de Matemática InterdisciplinarUniversidad Complutense de MadridMadridSpain
  2. 2.Departamento de Sanidad Animal, Fac. de C.C. VeterinariaUniversidad Complutense de MadridMadridSpain

Personalised recommendations