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Modeling the intrinsic dynamics of foot-and-mouth disease
1. | Department of Mathematics, University of Zimbabwe, P.O. Box MP 167, Harare, Zimbabwe |
2. | NSF Center for Integrated Pest Management, NC State University, Raleigh, NC 27606, United States |
3. | Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States |
References:
[1] |
F. Aftosa, Foot and Mouth Disease, http://www.cfsph.iastate.edu/Factsheets/pdfs/foot_and_mouth_disease.pdf, (Accessed September 2014) |
[2] |
A. Alexandersen, Z. Zhang and I. A. Donaldson, Aspects of the persistence of foot-and -mouth disease virus in animals-the carrier problem, Microbes and Infection, 4 (2002), 1099-1110. |
[3] |
C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Mathematical Biosciences and Engineering, 1 (2004), 361-404.
doi: 10.3934/mbe.2004.1.361. |
[4] |
M. E. Chase-Topping, I. Handel, B. M. Bankowski, N. D. Juleff, D. Gibson, S. J. Cox, M. A. Windsor, E. Reid, C. Doel, R. Howey, P. V. Barnett, M. E. J. Woolhouse and B. Charleston, Understanding foot-and-mouth disease virus transmission biology: Identification of the indicators of infectiousness, Veterinary Research, 44 (2013), p46.
doi: 10.1186/1297-9716-44-46. |
[5] |
T. A. Dekker, H. Vernooij, A. Bouma and A. Stegeman, Rate of foot-and-mouth disease virus transmission by carriers quantified from experimental data, Risk Analysis, 28 (2008), 303-309.
doi: 10.1111/j.1539-6924.2008.01020.x. |
[6] |
O. Diekmann and J. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, 2000. |
[7] |
J. Gloster, H. Champion, J. Sorensen, T. Mikkelsen, D. Ryall, P. Astrup, S. Alexandersen and A. Donaldson, Airborne transmission of foot-and-mouth disease virus from Burnside Farm, Heddon-on-the-Wall, Northumberland, during the 2001 epidemic in the United Kingdom, The Veterinary Record, 152 (2003), 525-533. |
[8] |
R. R. Kao, L. Danon, D. M. Green and I. Z. Kiss, Demographic structure and pathogen dynamics on the network of livestock movements in Great Britain, Proceedings of the Royal Society B, 273 (2006), 1999-2007.
doi: 10.1098/rspb.2006.3505. |
[9] |
M. J. Keeling, M. E. J. Woolhouse, R. M. May, G. Davies and B. T. Grenfell, Modelling vaccination strategies against foot-and-mouth disease, Nature, 421 (2003), 136-142.
doi: 10.1038/nature01343. |
[10] |
R. P. Kitching, Identification of foot and mouth disease virus carrier and subclinically infected animals and differentiation from vaccinated animals, Revue scientifique et technique (International Office of Epizootics), 21 (2002), 531-538. |
[11] |
R. P. Kitching, A. M. Humber and M. V. Thrusfield, A review of foot-and-mouth disease with special consideration for the clinical and epidemiological factors relevant to predictive modelling of the disease, Veterinary Journal, 169 (2005), 197-209.
doi: 10.1016/j.tvjl.2004.06.001. |
[12] |
T. J. Knight-Jones, A. N. Bulut, K. D. Stark, D. U. Pfeiffer, K. J. Sumption and D. J. Paton, Retrospective evaluation of foot-and-mouth disease vaccine effectiveness in Turkey, Vaccine, 32 (2014), 1848-1855.
doi: 10.1016/j.vaccine.2014.01.071. |
[13] |
G. E. Lahodny Jr., R. Gautam and R. Ivanek, Estimating the probability of an extinction or major outbreak for an environmentally transmitted infectious disease, Journal of Biological Dynamics, 9 (2015), 128-155.
doi: 10.1080/17513758.2014.954763. |
[14] |
J. S. LaSalle, The stability of Dynamical Systems, SIAM: Philadelphia, 1976. |
[15] |
S. Mushayabasa, C. P. Bhunu and M. Dhlamini, Impact of vaccination and culling on controlling foot and mouth disease: a mathematical modeling approach, World Journal of Vaccines, 1 (2011), 156-161.
doi: 10.4236/wjv.2011.14016. |
[16] |
S. Parida, Vaccination against foot-and-mouth disease virus: Strategies and effectiveness, Expert Review of Vaccines, 8 (2009), 347-365.
doi: 10.1586/14760584.8.3.347. |
[17] |
D. Posny and J. Wang, Modelling cholera in periodic environments, Journal of Biological Dynamics, 8 (2014), 1-19.
doi: 10.1080/17513758.2014.896482. |
[18] |
D. Posny and J. Wang, Computing basic reproductive numbers for epidemiological models in nonhomogeneous environments, Applied Mathematics and Computation, 242 (2014), 473-490.
doi: 10.1016/j.amc.2014.05.079. |
[19] |
N. Ringa and C. T. Bauch, Impacts of constrained culling and vaccination on control of foot and mouth disease in near-endemic settings: A pair approximation model, Epidemics, 9 (2014), 18-30.
doi: 10.1016/j.epidem.2014.09.008. |
[20] |
Y. Sinkala, M. Simuunza, J. B. Muma, D. U. Pfeiffer, C. J. Kasanga and A. Mweene, Foot and mouth disease in Zambia: Spatial and temporal distributions of outbreaks, assessment of clusters and implications for control, Onderstepoort Journal of Veterinary Research, 81 (2014), 6pp.
doi: 10.4102/ojvr.v81i2.741. |
[21] |
P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[22] |
W. Wang and X. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, Journal of Dynamics and Differential Equations, 20 (2008), 699-717.
doi: 10.1007/s10884-008-9111-8. |
[23] |
X.-Q. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
show all references
References:
[1] |
F. Aftosa, Foot and Mouth Disease, http://www.cfsph.iastate.edu/Factsheets/pdfs/foot_and_mouth_disease.pdf, (Accessed September 2014) |
[2] |
A. Alexandersen, Z. Zhang and I. A. Donaldson, Aspects of the persistence of foot-and -mouth disease virus in animals-the carrier problem, Microbes and Infection, 4 (2002), 1099-1110. |
[3] |
C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Mathematical Biosciences and Engineering, 1 (2004), 361-404.
doi: 10.3934/mbe.2004.1.361. |
[4] |
M. E. Chase-Topping, I. Handel, B. M. Bankowski, N. D. Juleff, D. Gibson, S. J. Cox, M. A. Windsor, E. Reid, C. Doel, R. Howey, P. V. Barnett, M. E. J. Woolhouse and B. Charleston, Understanding foot-and-mouth disease virus transmission biology: Identification of the indicators of infectiousness, Veterinary Research, 44 (2013), p46.
doi: 10.1186/1297-9716-44-46. |
[5] |
T. A. Dekker, H. Vernooij, A. Bouma and A. Stegeman, Rate of foot-and-mouth disease virus transmission by carriers quantified from experimental data, Risk Analysis, 28 (2008), 303-309.
doi: 10.1111/j.1539-6924.2008.01020.x. |
[6] |
O. Diekmann and J. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, 2000. |
[7] |
J. Gloster, H. Champion, J. Sorensen, T. Mikkelsen, D. Ryall, P. Astrup, S. Alexandersen and A. Donaldson, Airborne transmission of foot-and-mouth disease virus from Burnside Farm, Heddon-on-the-Wall, Northumberland, during the 2001 epidemic in the United Kingdom, The Veterinary Record, 152 (2003), 525-533. |
[8] |
R. R. Kao, L. Danon, D. M. Green and I. Z. Kiss, Demographic structure and pathogen dynamics on the network of livestock movements in Great Britain, Proceedings of the Royal Society B, 273 (2006), 1999-2007.
doi: 10.1098/rspb.2006.3505. |
[9] |
M. J. Keeling, M. E. J. Woolhouse, R. M. May, G. Davies and B. T. Grenfell, Modelling vaccination strategies against foot-and-mouth disease, Nature, 421 (2003), 136-142.
doi: 10.1038/nature01343. |
[10] |
R. P. Kitching, Identification of foot and mouth disease virus carrier and subclinically infected animals and differentiation from vaccinated animals, Revue scientifique et technique (International Office of Epizootics), 21 (2002), 531-538. |
[11] |
R. P. Kitching, A. M. Humber and M. V. Thrusfield, A review of foot-and-mouth disease with special consideration for the clinical and epidemiological factors relevant to predictive modelling of the disease, Veterinary Journal, 169 (2005), 197-209.
doi: 10.1016/j.tvjl.2004.06.001. |
[12] |
T. J. Knight-Jones, A. N. Bulut, K. D. Stark, D. U. Pfeiffer, K. J. Sumption and D. J. Paton, Retrospective evaluation of foot-and-mouth disease vaccine effectiveness in Turkey, Vaccine, 32 (2014), 1848-1855.
doi: 10.1016/j.vaccine.2014.01.071. |
[13] |
G. E. Lahodny Jr., R. Gautam and R. Ivanek, Estimating the probability of an extinction or major outbreak for an environmentally transmitted infectious disease, Journal of Biological Dynamics, 9 (2015), 128-155.
doi: 10.1080/17513758.2014.954763. |
[14] |
J. S. LaSalle, The stability of Dynamical Systems, SIAM: Philadelphia, 1976. |
[15] |
S. Mushayabasa, C. P. Bhunu and M. Dhlamini, Impact of vaccination and culling on controlling foot and mouth disease: a mathematical modeling approach, World Journal of Vaccines, 1 (2011), 156-161.
doi: 10.4236/wjv.2011.14016. |
[16] |
S. Parida, Vaccination against foot-and-mouth disease virus: Strategies and effectiveness, Expert Review of Vaccines, 8 (2009), 347-365.
doi: 10.1586/14760584.8.3.347. |
[17] |
D. Posny and J. Wang, Modelling cholera in periodic environments, Journal of Biological Dynamics, 8 (2014), 1-19.
doi: 10.1080/17513758.2014.896482. |
[18] |
D. Posny and J. Wang, Computing basic reproductive numbers for epidemiological models in nonhomogeneous environments, Applied Mathematics and Computation, 242 (2014), 473-490.
doi: 10.1016/j.amc.2014.05.079. |
[19] |
N. Ringa and C. T. Bauch, Impacts of constrained culling and vaccination on control of foot and mouth disease in near-endemic settings: A pair approximation model, Epidemics, 9 (2014), 18-30.
doi: 10.1016/j.epidem.2014.09.008. |
[20] |
Y. Sinkala, M. Simuunza, J. B. Muma, D. U. Pfeiffer, C. J. Kasanga and A. Mweene, Foot and mouth disease in Zambia: Spatial and temporal distributions of outbreaks, assessment of clusters and implications for control, Onderstepoort Journal of Veterinary Research, 81 (2014), 6pp.
doi: 10.4102/ojvr.v81i2.741. |
[21] |
P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[22] |
W. Wang and X. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, Journal of Dynamics and Differential Equations, 20 (2008), 699-717.
doi: 10.1007/s10884-008-9111-8. |
[23] |
X.-Q. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
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