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Effects of isolation and slaughter strategies in different species on emerging zoonoses
School of Science, Beijing University of Civil Engineering and Architecture, No. 1, Zhanlanguan Road, Xicheng District, Beijing 100044, China |
Zoonosis is the kind of infectious disease transmitting among different species by zoonotic pathogens. Different species play different roles in zoonoses. In this paper, we established a basic model to describe the zoonotic pathogen transmission from wildlife, to domestic animals, to humans. Then we put three strategies into the basic model to control the emerging zoonoses. Three strategies are corresponding to control measures of isolation, slaughter or similar in wildlife, domestic animals and humans respectively. We analyzed the effects of these three strategies on control reproductive numbers and equilibriums and we took avian influenza epidemic in China as an example to show the impacts of the strategies on emerging zoonoses in different areas at beginning.
References:
[1] |
L. J. S. Allen,
Mathematical Modeling of Viral Zoonoses in Wildlife, Natural Resource Modeling, 25 (2012), 5-51.
doi: 10.1111/j.1939-7445.2011.00104.x. |
[2] |
J. Arino, R. Jordan and P. V. D. Driessche,
Quarantine in a multi-species epidemic model with spatial dynamics, Mathematical Biosciences, 206 (2007), 46-60.
doi: 10.1016/j.mbs.2005.09.002. |
[3] |
R. M. Atlas and S. Maloy,
One Health: People, Animals, and the Environment, ASM Press, 2014. |
[4] |
R. G. Bengis, F. A. Leighton and J. R. Fischer,
The role of wildlife in emerging and re-emerging zoonoses, Revue Scientifique Et Technique, 23 (2004), 497-511.
|
[5] |
F. Brauer and C. Chavez,
Mathematical Models in Population Biology and Epidemiology 2$^{nd}$ edition, Springer, 2001.
doi: 10.1007/978-1-4757-3516-1. |
[6] |
N. Busquets, J. Segals and L. Crdoba,
Experimental infection with H1N1 European swine influenza virus protects pigs from an infection with the 2009 pandemic H1N1 human influenza virus, Veterinary Research, 41 (2010), 571-584.
doi: 10.1051/vetres/2010046. |
[7] |
China Agricultural Yearbook Editing Committee, ChinaAgriculture Yearbook, China Agriculture Press, China, 2012. |
[8] |
G. Chowell,
Model parameters and outbreak control for SARS, Emerging Infectious Diseases, 10 (2004), 1258-1263.
doi: 10.3201/eid1007.030647. |
[9] |
B. J. Coburn, B. G. Wagner and S. Blower, Modeling influenza epidemics and pandemics: Insights into the future of swine flu (H1N1) Bmc Medicine, 7 (2009), p30.
doi: 10.1186/1741-7015-7-30. |
[10] |
B. J. Coburn, C. Cosne and S. Ruan,
Emergence and dynamics of influenza super-strains, Bmc Public Health, 11 (2011), 597-615.
doi: 10.1186/1471-2458-11-S1-S6. |
[11] |
R. W. Compans and M. B. A. Oldstone,
Influenza Pathogenesis and Control -Volume I, Current Topics in Microbiology & Immunology, 2014.
doi: 10.1007/978-3-319-11155-1. |
[12] |
M. R. Conover,
Human Diseases from Wildlife, Boca Raton : CRC Press, Taylor & Francis Group, 2014.
doi: 10.1201/b17428. |
[13] |
M. Derouich and A. Boutayeb,
An avian influenza mathematical model, Applied Mathematical Sciences, 2 (2008), 1749-1760.
|
[14] |
K. Dietz, W. H. Wernsdorfer and I. Mcgregor,
Mathematical Models for Transmission and Control of Malaria, Malaria, 1988. |
[15] |
A. Dobson,
Population dynamics of pathogens with multiple host species, American Naturalist, 164 (2004), 64-78.
doi: 10.1086/424681. |
[16] |
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. |
[17] |
X. Fang,
The Role of Mammals in Epidemiology, Acta Theriologica Sinica, 2 (1981), 219-224.
|
[18] |
Z. Feng,
Final and peak epidemic sizes for SEIR models with quarantine and isolation, Mathematical Biosciences & Engineering, 4 (2007), 675-686.
doi: 10.3934/mbe.2007.4.675. |
[19] |
Z. Feng,
Applications of Epidemiological Models to Public Health Policymaking, World Scientific, 2014.
doi: 10.1142/8884. |
[20] |
A. Fritsche, R. Engel and D. Buhl,
Mycobacterium bovis tuberculosis: From animal to man and back, International Journal of Tuberculosis & Lung Disease the Official Journal of the International Union Against Tuberculosis & Lung Disease, 8 (2004), 903-904.
|
[21] |
S. Iwami, Y. Takeuchi and X. Liu,
Avian-Chuman influenza epidemic model, Mathematical Biosciences, 207 (2007), 1-25.
doi: 10.1016/j.mbs.2006.08.001. |
[22] |
A. M. Kilpatrick and S. E. Randolph,
Drivers, dynamics, and control of emerging vector-borne zoonotic diseases, Lancet, 380 (2012), 1946-1955.
doi: 10.1016/S0140-6736(12)61151-9. |
[23] |
J. Lee, J. Kim and H. D. Kwon,
Optimal control of an influenza model with seasonal forcing and age-dependent transmission rates, Journal of Theoretical Biology, 317 (2013), 310-320.
doi: 10.1016/j.jtbi.2012.10.032. |
[24] |
J. S. Mackenzie,
One Health: The Human-Animal-Environment Interfaces in Emerging Infectious Diseases, Springer, Berlin, 2013. |
[25] |
A. Mubayi,
A cost-based comparison of quarantine strategies for new emerging diseases, Mathematical Biosciences & Engineering, 7 (2010), 687-717.
doi: 10.3934/mbe.2010.7.687. |
[26] |
R. A. Saenz, H. W. Hethcote and G. C. Gray,
Confined animal feeding operations as amplifiers of influenza, Vector Borne & Zoonotic Diseases, 6 (2006), 338-346.
doi: 10.1089/vbz.2006.6.338. |
[27] |
P. M. Sharp and B. H. Hahn,
Cross-species transmission and recombination of 'AIDS' viruses, Philosophical Transactions of the Royal Society B Biological Sciences, 349 (1995), 41-47.
doi: 10.1098/rstb.1995.0089. |
[28] |
A. Sing,
Zoonoses -Infections Affecting Humans and Animals, Springer Netherlands, Berlin, 2015.
doi: 10.1007/978-94-017-9457-2. |
[29] |
S. Towers and Z. Feng,
Pandemic H1N1 influenza: predicting the course of a pandemic and assessing the efficacy of the planned vaccination programme in the United States, European Communicable Disease Bulletin, 14 (2009), 6-8.
|
[30] |
Q. Xian, L. Cui and Y. Jiao,
Antigenic and genetic characterization of a European avian-like H1N1 swine influenza virus from a boy in China in 2011, Archives of Virology, 158 (2013), 39-53.
|
[31] |
W. D. Zhang,
Optimized strategy for the control and prevention of newly emerging influenza revealed by the spread dynamics model, Plos One, 91 (2014), 5-51.
|
[32] |
J. Zhang, Z. Jin and G. Q. Sun,
Modeling seasonal rabies epidemics in China, Bulletin of Mathematical Biology, 74 (2012), 1226-1251.
doi: 10.1007/s11538-012-9720-6. |
show all references
References:
[1] |
L. J. S. Allen,
Mathematical Modeling of Viral Zoonoses in Wildlife, Natural Resource Modeling, 25 (2012), 5-51.
doi: 10.1111/j.1939-7445.2011.00104.x. |
[2] |
J. Arino, R. Jordan and P. V. D. Driessche,
Quarantine in a multi-species epidemic model with spatial dynamics, Mathematical Biosciences, 206 (2007), 46-60.
doi: 10.1016/j.mbs.2005.09.002. |
[3] |
R. M. Atlas and S. Maloy,
One Health: People, Animals, and the Environment, ASM Press, 2014. |
[4] |
R. G. Bengis, F. A. Leighton and J. R. Fischer,
The role of wildlife in emerging and re-emerging zoonoses, Revue Scientifique Et Technique, 23 (2004), 497-511.
|
[5] |
F. Brauer and C. Chavez,
Mathematical Models in Population Biology and Epidemiology 2$^{nd}$ edition, Springer, 2001.
doi: 10.1007/978-1-4757-3516-1. |
[6] |
N. Busquets, J. Segals and L. Crdoba,
Experimental infection with H1N1 European swine influenza virus protects pigs from an infection with the 2009 pandemic H1N1 human influenza virus, Veterinary Research, 41 (2010), 571-584.
doi: 10.1051/vetres/2010046. |
[7] |
China Agricultural Yearbook Editing Committee, ChinaAgriculture Yearbook, China Agriculture Press, China, 2012. |
[8] |
G. Chowell,
Model parameters and outbreak control for SARS, Emerging Infectious Diseases, 10 (2004), 1258-1263.
doi: 10.3201/eid1007.030647. |
[9] |
B. J. Coburn, B. G. Wagner and S. Blower, Modeling influenza epidemics and pandemics: Insights into the future of swine flu (H1N1) Bmc Medicine, 7 (2009), p30.
doi: 10.1186/1741-7015-7-30. |
[10] |
B. J. Coburn, C. Cosne and S. Ruan,
Emergence and dynamics of influenza super-strains, Bmc Public Health, 11 (2011), 597-615.
doi: 10.1186/1471-2458-11-S1-S6. |
[11] |
R. W. Compans and M. B. A. Oldstone,
Influenza Pathogenesis and Control -Volume I, Current Topics in Microbiology & Immunology, 2014.
doi: 10.1007/978-3-319-11155-1. |
[12] |
M. R. Conover,
Human Diseases from Wildlife, Boca Raton : CRC Press, Taylor & Francis Group, 2014.
doi: 10.1201/b17428. |
[13] |
M. Derouich and A. Boutayeb,
An avian influenza mathematical model, Applied Mathematical Sciences, 2 (2008), 1749-1760.
|
[14] |
K. Dietz, W. H. Wernsdorfer and I. Mcgregor,
Mathematical Models for Transmission and Control of Malaria, Malaria, 1988. |
[15] |
A. Dobson,
Population dynamics of pathogens with multiple host species, American Naturalist, 164 (2004), 64-78.
doi: 10.1086/424681. |
[16] |
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. |
[17] |
X. Fang,
The Role of Mammals in Epidemiology, Acta Theriologica Sinica, 2 (1981), 219-224.
|
[18] |
Z. Feng,
Final and peak epidemic sizes for SEIR models with quarantine and isolation, Mathematical Biosciences & Engineering, 4 (2007), 675-686.
doi: 10.3934/mbe.2007.4.675. |
[19] |
Z. Feng,
Applications of Epidemiological Models to Public Health Policymaking, World Scientific, 2014.
doi: 10.1142/8884. |
[20] |
A. Fritsche, R. Engel and D. Buhl,
Mycobacterium bovis tuberculosis: From animal to man and back, International Journal of Tuberculosis & Lung Disease the Official Journal of the International Union Against Tuberculosis & Lung Disease, 8 (2004), 903-904.
|
[21] |
S. Iwami, Y. Takeuchi and X. Liu,
Avian-Chuman influenza epidemic model, Mathematical Biosciences, 207 (2007), 1-25.
doi: 10.1016/j.mbs.2006.08.001. |
[22] |
A. M. Kilpatrick and S. E. Randolph,
Drivers, dynamics, and control of emerging vector-borne zoonotic diseases, Lancet, 380 (2012), 1946-1955.
doi: 10.1016/S0140-6736(12)61151-9. |
[23] |
J. Lee, J. Kim and H. D. Kwon,
Optimal control of an influenza model with seasonal forcing and age-dependent transmission rates, Journal of Theoretical Biology, 317 (2013), 310-320.
doi: 10.1016/j.jtbi.2012.10.032. |
[24] |
J. S. Mackenzie,
One Health: The Human-Animal-Environment Interfaces in Emerging Infectious Diseases, Springer, Berlin, 2013. |
[25] |
A. Mubayi,
A cost-based comparison of quarantine strategies for new emerging diseases, Mathematical Biosciences & Engineering, 7 (2010), 687-717.
doi: 10.3934/mbe.2010.7.687. |
[26] |
R. A. Saenz, H. W. Hethcote and G. C. Gray,
Confined animal feeding operations as amplifiers of influenza, Vector Borne & Zoonotic Diseases, 6 (2006), 338-346.
doi: 10.1089/vbz.2006.6.338. |
[27] |
P. M. Sharp and B. H. Hahn,
Cross-species transmission and recombination of 'AIDS' viruses, Philosophical Transactions of the Royal Society B Biological Sciences, 349 (1995), 41-47.
doi: 10.1098/rstb.1995.0089. |
[28] |
A. Sing,
Zoonoses -Infections Affecting Humans and Animals, Springer Netherlands, Berlin, 2015.
doi: 10.1007/978-94-017-9457-2. |
[29] |
S. Towers and Z. Feng,
Pandemic H1N1 influenza: predicting the course of a pandemic and assessing the efficacy of the planned vaccination programme in the United States, European Communicable Disease Bulletin, 14 (2009), 6-8.
|
[30] |
Q. Xian, L. Cui and Y. Jiao,
Antigenic and genetic characterization of a European avian-like H1N1 swine influenza virus from a boy in China in 2011, Archives of Virology, 158 (2013), 39-53.
|
[31] |
W. D. Zhang,
Optimized strategy for the control and prevention of newly emerging influenza revealed by the spread dynamics model, Plos One, 91 (2014), 5-51.
|
[32] |
J. Zhang, Z. Jin and G. Q. Sun,
Modeling seasonal rabies epidemics in China, Bulletin of Mathematical Biology, 74 (2012), 1226-1251.
doi: 10.1007/s11538-012-9720-6. |






Strategies | no strategy | Strategy 1 | Strategy 2 | Strategy 3 |
Reproductive number in wildlife | | |||
Reproductive number in domestic animals | | | ||
Reproductive number in humans | | | ||
Strategies | no strategy | Strategy 1 | Strategy 2 | Strategy 3 |
Reproductive number in wildlife | | |||
Reproductive number in domestic animals | | | ||
Reproductive number in humans | | | ||
Parameter | Definitions | Values | Sources |
birth or immigration rate of wild aquatic birds | 0.137 birds/day | Est. | |
| natural mortality rate of wild aquatic birds | 0.000137/day | [33] |
| recovery rate of wild aquatic birds | 0.25/day | Est. |
| disease-induced mortality rate of wild aquatic birds | 0.0025/day | Est. |
| birth or immigration rate of domestic birds | 48.72 birds/day | [33] |
| natural mortality rate of domestic birds | 0.0058/day | [33] |
| recovery rate of domestic birds | 0.25/day | [26] |
| disease-induced mortality rate of domestic birds | 0.0025/day | Est. |
| birth or immigration rate of humans | 0.07people/day | [23] |
| natural mortality rate of humans | 0.000035/day | [23] |
| recovery rate of humans | 0.33/day | [26, 31] |
| remove rate from isolation compartment to susceptible compartment. | 0.5/day | Est. |
| remove rate from isolation compartment to recovery individual compartment. | 0.5/day | Est. |
| disease-induced mortality rate of humans | 0.0033/day | Est. |
| basic reproductive number of wild aquatic birds | 2 | Est. |
| basic reproductive number of domestic birds | 2 | Est. |
| basic reproductive number of humans | 1.2 | [26] |
| per capita incidence rate from wild aquatic birds to domestic birds | Est. | |
| per capita incidence rate from wild aquatic birds to humans | Est. | |
| per capita incidence rate from domestic birds to humans | Est. |
Parameter | Definitions | Values | Sources |
birth or immigration rate of wild aquatic birds | 0.137 birds/day | Est. | |
| natural mortality rate of wild aquatic birds | 0.000137/day | [33] |
| recovery rate of wild aquatic birds | 0.25/day | Est. |
| disease-induced mortality rate of wild aquatic birds | 0.0025/day | Est. |
| birth or immigration rate of domestic birds | 48.72 birds/day | [33] |
| natural mortality rate of domestic birds | 0.0058/day | [33] |
| recovery rate of domestic birds | 0.25/day | [26] |
| disease-induced mortality rate of domestic birds | 0.0025/day | Est. |
| birth or immigration rate of humans | 0.07people/day | [23] |
| natural mortality rate of humans | 0.000035/day | [23] |
| recovery rate of humans | 0.33/day | [26, 31] |
| remove rate from isolation compartment to susceptible compartment. | 0.5/day | Est. |
| remove rate from isolation compartment to recovery individual compartment. | 0.5/day | Est. |
| disease-induced mortality rate of humans | 0.0033/day | Est. |
| basic reproductive number of wild aquatic birds | 2 | Est. |
| basic reproductive number of domestic birds | 2 | Est. |
| basic reproductive number of humans | 1.2 | [26] |
| per capita incidence rate from wild aquatic birds to domestic birds | Est. | |
| per capita incidence rate from wild aquatic birds to humans | Est. | |
| per capita incidence rate from domestic birds to humans | Est. |
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