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2014, 11(5): 1115-1137. doi: 10.3934/mbe.2014.11.1115

Transmission dynamics and control for a brucellosis model in Hinggan League of Inner Mongolia, China

1. 

Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China

2. 

Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030051, China, China

3. 

Department of mathematics, North University of China, Taiyuan 030051, PR

4. 

China Animal Health and Epidemiology Center, Qingdao, Shandong 266032, China, China, China

5. 

Hinggan League Animal Sanitation Supervision Stations, Ulanhot, Inner Mongolia, 137400, China

Received  July 2013 Revised  January 2014 Published  June 2014

Brucellosis is one of the major infectious and contagious bacterial diseases in Hinggan League of Inner Mongolia, China. The number of newly infected human brucellosis data in this area has increased dramatically in the last 10 years. In this study, in order to explore effective control and prevention measures we propose a deterministic model to investigate the transmission dynamics of brucellosis in Hinggan League. The model describes the spread of brucellosis among sheep and from sheep to humans. The model simulations agree with newly infected human brucellosis data from 2001 to 2011, and the trend of newly infected human brucellosis cases is given. We estimate that the control reproduction number $\mathcal{R}_{c}$ is about $1.9789$ for the brucellosis transmission in Hinggan League and compare the effect of existing mixed cross infection between basic ewes and other sheep or not for newly infected human brucellosis cases. Our study demonstrates that combination of prohibiting mixed feeding between basic ewes and other sheep, vaccination, detection and elimination are useful strategies in controlling human brucellosis in Hinggan League.
Citation: Mingtao Li, Guiquan Sun, Juan Zhang, Zhen Jin, Xiangdong Sun, Youming Wang, Baoxu Huang, Yaohui Zheng. Transmission dynamics and control for a brucellosis model in Hinggan League of Inner Mongolia, China. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1115-1137. doi: 10.3934/mbe.2014.11.1115
References:
[1]

B. Alnseba, B. Chahrazed and M. Pierre, A model for ovine brucellosis incorporating direct and indirect transmission,, J. Biol. Dyn., 4 (2010), 2.  doi: 10.1080/17513750903171688.  Google Scholar

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M. J. Corbel, Brucellosis: An overview,, Emerg. Infect. Dis., 3 (1997), 213.  doi: 10.3201/eid0302.970219.  Google Scholar

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O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R^{0}$ in models for infectious diseases in heterogeneous populations,, J. Math. Biol., 28 (1990), 365.  doi: 10.1007/BF00178324.  Google Scholar

[6]

O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models,, J. R. Soc. Interface, 7 (2010), 873.  doi: 10.1098/rsif.2009.0386.  Google Scholar

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V. Dobrean, A. Opris and S. Daraban, An epidemiological and surveillance overview of brucellosis in Romania,, Vet. Mic., 90 (2002), 157.  doi: 10.1016/S0378-1135(02)00251-1.  Google Scholar

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P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

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[11]

Q. Hou, X. D. Sun, J. Zhang, Y. J. Liu, Y. M. Wang and Z. Jin, Modeling the transmission dynamics of brucellosis in Inner Mongolia Autonomous Region, China,, Math. Biosci., 242 (2013), 51.  doi: 10.1016/j.mbs.2012.11.012.  Google Scholar

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Z. Huang, et al., A study on the prevalent type of human Brucellosis caused by $B.suis$ in Guangxi applying fuzzy fathematics and markov forecast,, End. Dise. Bul., 5 (1990), 101.   Google Scholar

[13]

M. T. Li, G. Q. Sun, Y. F. Wu, J. Zhang and Z. Jin, Transmission dynamics of a multi-group brucellosis model with mixed cross infection in public farm,, Appl. Math. Com., 237 (2014), 582.  doi: 10.1016/j.amc.2014.03.094.  Google Scholar

[14]

M. T. Li, G. Q. Sun, J. Zhang and Z. Jin, Global Dynamic Behavior of a Multigroup Cholera model with Indirect Transmission,, Discrete Dynamics in Nature and Society, (2013).   Google Scholar

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Z. Li, et al., Application of mathematical models to forecast for inspection district of brucellosis in China (II),, Chin. J. Ctrl. Endem. Dis., 15 (2000), 273.   Google Scholar

[16]

A. Lu, et al., Establishment of Brucellosis infection rate forcasting models and their accuracy comparison,, Chinese Journal of Animal Health Inspection, 17 (2000), 21.   Google Scholar

[17]

J. C. Mi, Q. H. Zhang, L. T. Song and Z. Zheng, The epidemiological characteristics of human Brucellosis in Inner Mongolia,, Chin. J. Ctrl. Endem. Dis., 25 (2010), 34.   Google Scholar

[18]

Z. Mukandavire, S. Liao, J. Wang, H. Gaff, D. L. Smith and J. Glenn Morris, Jr., Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe,, Proc. Natl. Acad. Sci. USA, 108 (2011), 8767.   Google Scholar

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, National bureau of statistics of China (2012) China demographic yearbook of 2012,, , ().   Google Scholar

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S. Niu and R. Liu, Hinggan League 2001-2009 human brucellosis epidemiological analysis,, Med. Inform., 3 (2010), 473.   Google Scholar

[21]

G. Pappas, N. Akritidis, M. Bosilkovski and E. Tsianos, Brucellosis,, N. Engl. J. Med., 352 (2005), 2325.  doi: 10.1056/NEJMra050570.  Google Scholar

[22]

H. L. Ren, et al., The current research, prevention and control on brucellosis,, China Animal Husbandry Veterinary Medicine, 36 (2009), 139.   Google Scholar

[23]

E. J. Richey and C. Dix Harrell, Brucella Abortus Disease (Brucellosis) in Beef Cattle,, University of Florida, 100 (1997), 1.   Google Scholar

[24]

M. A. Sanchez and S. M. Blower, Uncertainty and sensitivity analysis of the basic reproductive rate: Tuberculosis as an example,, American Journal of Epidemiology, 145 (1997), 1127.  doi: 10.1093/oxfordjournals.aje.a009076.  Google Scholar

[25]

D. Q. Shang, D. L. Xiao and J. M. Yin, Epidemiology and control of brucellosis in China,, Vet. Microbiol., 69 (2002).   Google Scholar

[26]

K. J. Sharkey, R. G. Bowers, K. L. Morgan, S. E. Robinson and R. M. Christley, Epidemiological consequences of an incursion of highly pathogenic H5N1 avian influenza into the British poultry flock,, Proc. R. Soc. B, 275 (2008), 19.  doi: 10.1098/rspb.2007.1100.  Google Scholar

[27]

H. L. Smith and P. Waltman, The Theory of the Chemostat,, Cambridge University Press, (1995).  doi: 10.1017/CBO9780511530043.  Google Scholar

[28]

, The 2010 census bulletin of the main data of Hinggan League,, , ().   Google Scholar

[29]

H. R. Thieme, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations,, J. Math. Biol., 30 (1992), 755.  doi: 10.1007/BF00173267.  Google Scholar

[30]

H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model),, SIAM J. Math. Biosci., 24 (1993), 407.  doi: 10.1137/0524026.  Google Scholar

[31]

G. Wang, et al., China livestock brucellosis popular characteristics and cause analysis,, Chinese Journal of Animal Health Inspection, 27 (2010), 62.   Google Scholar

[32]

W. D. Wang, P. Fergola and C. Tenneriello, Innovation diffusion model in patch environment,, Appl. Math. Com., 134 (2003), 51.  doi: 10.1016/S0096-3003(01)00268-5.  Google Scholar

[33]

W. D. Wang and X. Q. Zhao, An epidemic model in a patchy environment,, Math. Biosci., 190 (2004), 97.  doi: 10.1016/j.mbs.2002.11.001.  Google Scholar

[34]

J. Zhang, Z. Jin, G. Sun, T. Zhou and S. Ruan, Analysis of rabies in China: Tranmission dynamics and control,, PLoS ONE, 6 (2011).  doi: 10.1371/journal.pone.0020891.  Google Scholar

[35]

J. Zhang, Z. Jin, G. Sun, X. Sun and S. Ruan, Modeling seasonal rabies epidemics in China,, Bull. Math. Biol., 74 (2012), 1226.  doi: 10.1007/s11538-012-9720-6.  Google Scholar

[36]

S. Y. Zhang and D. Zhu, In review of China brucellosis prevention to 50 years,, Chin. J. Ctrl. Endem. Dis., 18 (2003), 275.   Google Scholar

[37]

X. Q. Zhao, Uniform persistence and periodic coexistence states in infinite-dimensional periodic semiflows with applications,, Canad. Appl. Math. Quart., 3 (1995), 473.   Google Scholar

[38]

X. Q. Zhao and Z. J. Jing, Global asymptotic behavior in some cooperative systems of functional differential equations,, Canad. Appl. Math. Quart., 4 (1996), 421.   Google Scholar

[39]

Y. B. Zhou and X. L. Liu, The research progress in terms of prevalence, incidence reason and control strategies of brucellosis,, J. Liaoning Medical University, 1 (2010), 81.   Google Scholar

[40]

J. Zinsstag, F. Roth, D. Orkhon, G. Chimed-Ochir, M. Nansalmaa, J. Kolar and P. Vounatsou, A model of animal-human brucellosis transmission in Mongolia,, Prev. Vet. Med., 69 (2005), 77.  doi: 10.1016/j.prevetmed.2005.01.017.  Google Scholar

show all references

References:
[1]

B. Alnseba, B. Chahrazed and M. Pierre, A model for ovine brucellosis incorporating direct and indirect transmission,, J. Biol. Dyn., 4 (2010), 2.  doi: 10.1080/17513750903171688.  Google Scholar

[2]

S. M. Blower, A. R. McLean and T. C. Porco, et al., The intrinsic transmission dynamics of tuberculosis epidemics,, Nature Med., 1 (1995), 815.  doi: 10.1038/nm0895-815.  Google Scholar

[3]

S. M. Blower and H. Dowlatabadi, Sensitivity and uncertainty analysis of complex models of disease transmission: An HIV model as an example,, Int. Stat. Rev., 62 (1994), 229.  doi: 10.2307/1403510.  Google Scholar

[4]

M. J. Corbel, Brucellosis: An overview,, Emerg. Infect. Dis., 3 (1997), 213.  doi: 10.3201/eid0302.970219.  Google Scholar

[5]

O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R^{0}$ in models for infectious diseases in heterogeneous populations,, J. Math. Biol., 28 (1990), 365.  doi: 10.1007/BF00178324.  Google Scholar

[6]

O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models,, J. R. Soc. Interface, 7 (2010), 873.  doi: 10.1098/rsif.2009.0386.  Google Scholar

[7]

V. Dobrean, A. Opris and S. Daraban, An epidemiological and surveillance overview of brucellosis in Romania,, Vet. Mic., 90 (2002), 157.  doi: 10.1016/S0378-1135(02)00251-1.  Google Scholar

[8]

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[9]

, Hinggan League's annual statistical bulletin,, , ().   Google Scholar

[10]

Q. Hou, Z. Jin and S. Ruan, Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China,, J. Theoret. Biol., 300 (2012), 39.  doi: 10.1016/j.jtbi.2012.01.006.  Google Scholar

[11]

Q. Hou, X. D. Sun, J. Zhang, Y. J. Liu, Y. M. Wang and Z. Jin, Modeling the transmission dynamics of brucellosis in Inner Mongolia Autonomous Region, China,, Math. Biosci., 242 (2013), 51.  doi: 10.1016/j.mbs.2012.11.012.  Google Scholar

[12]

Z. Huang, et al., A study on the prevalent type of human Brucellosis caused by $B.suis$ in Guangxi applying fuzzy fathematics and markov forecast,, End. Dise. Bul., 5 (1990), 101.   Google Scholar

[13]

M. T. Li, G. Q. Sun, Y. F. Wu, J. Zhang and Z. Jin, Transmission dynamics of a multi-group brucellosis model with mixed cross infection in public farm,, Appl. Math. Com., 237 (2014), 582.  doi: 10.1016/j.amc.2014.03.094.  Google Scholar

[14]

M. T. Li, G. Q. Sun, J. Zhang and Z. Jin, Global Dynamic Behavior of a Multigroup Cholera model with Indirect Transmission,, Discrete Dynamics in Nature and Society, (2013).   Google Scholar

[15]

Z. Li, et al., Application of mathematical models to forecast for inspection district of brucellosis in China (II),, Chin. J. Ctrl. Endem. Dis., 15 (2000), 273.   Google Scholar

[16]

A. Lu, et al., Establishment of Brucellosis infection rate forcasting models and their accuracy comparison,, Chinese Journal of Animal Health Inspection, 17 (2000), 21.   Google Scholar

[17]

J. C. Mi, Q. H. Zhang, L. T. Song and Z. Zheng, The epidemiological characteristics of human Brucellosis in Inner Mongolia,, Chin. J. Ctrl. Endem. Dis., 25 (2010), 34.   Google Scholar

[18]

Z. Mukandavire, S. Liao, J. Wang, H. Gaff, D. L. Smith and J. Glenn Morris, Jr., Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe,, Proc. Natl. Acad. Sci. USA, 108 (2011), 8767.   Google Scholar

[19]

, National bureau of statistics of China (2012) China demographic yearbook of 2012,, , ().   Google Scholar

[20]

S. Niu and R. Liu, Hinggan League 2001-2009 human brucellosis epidemiological analysis,, Med. Inform., 3 (2010), 473.   Google Scholar

[21]

G. Pappas, N. Akritidis, M. Bosilkovski and E. Tsianos, Brucellosis,, N. Engl. J. Med., 352 (2005), 2325.  doi: 10.1056/NEJMra050570.  Google Scholar

[22]

H. L. Ren, et al., The current research, prevention and control on brucellosis,, China Animal Husbandry Veterinary Medicine, 36 (2009), 139.   Google Scholar

[23]

E. J. Richey and C. Dix Harrell, Brucella Abortus Disease (Brucellosis) in Beef Cattle,, University of Florida, 100 (1997), 1.   Google Scholar

[24]

M. A. Sanchez and S. M. Blower, Uncertainty and sensitivity analysis of the basic reproductive rate: Tuberculosis as an example,, American Journal of Epidemiology, 145 (1997), 1127.  doi: 10.1093/oxfordjournals.aje.a009076.  Google Scholar

[25]

D. Q. Shang, D. L. Xiao and J. M. Yin, Epidemiology and control of brucellosis in China,, Vet. Microbiol., 69 (2002).   Google Scholar

[26]

K. J. Sharkey, R. G. Bowers, K. L. Morgan, S. E. Robinson and R. M. Christley, Epidemiological consequences of an incursion of highly pathogenic H5N1 avian influenza into the British poultry flock,, Proc. R. Soc. B, 275 (2008), 19.  doi: 10.1098/rspb.2007.1100.  Google Scholar

[27]

H. L. Smith and P. Waltman, The Theory of the Chemostat,, Cambridge University Press, (1995).  doi: 10.1017/CBO9780511530043.  Google Scholar

[28]

, The 2010 census bulletin of the main data of Hinggan League,, , ().   Google Scholar

[29]

H. R. Thieme, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations,, J. Math. Biol., 30 (1992), 755.  doi: 10.1007/BF00173267.  Google Scholar

[30]

H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model),, SIAM J. Math. Biosci., 24 (1993), 407.  doi: 10.1137/0524026.  Google Scholar

[31]

G. Wang, et al., China livestock brucellosis popular characteristics and cause analysis,, Chinese Journal of Animal Health Inspection, 27 (2010), 62.   Google Scholar

[32]

W. D. Wang, P. Fergola and C. Tenneriello, Innovation diffusion model in patch environment,, Appl. Math. Com., 134 (2003), 51.  doi: 10.1016/S0096-3003(01)00268-5.  Google Scholar

[33]

W. D. Wang and X. Q. Zhao, An epidemic model in a patchy environment,, Math. Biosci., 190 (2004), 97.  doi: 10.1016/j.mbs.2002.11.001.  Google Scholar

[34]

J. Zhang, Z. Jin, G. Sun, T. Zhou and S. Ruan, Analysis of rabies in China: Tranmission dynamics and control,, PLoS ONE, 6 (2011).  doi: 10.1371/journal.pone.0020891.  Google Scholar

[35]

J. Zhang, Z. Jin, G. Sun, X. Sun and S. Ruan, Modeling seasonal rabies epidemics in China,, Bull. Math. Biol., 74 (2012), 1226.  doi: 10.1007/s11538-012-9720-6.  Google Scholar

[36]

S. Y. Zhang and D. Zhu, In review of China brucellosis prevention to 50 years,, Chin. J. Ctrl. Endem. Dis., 18 (2003), 275.   Google Scholar

[37]

X. Q. Zhao, Uniform persistence and periodic coexistence states in infinite-dimensional periodic semiflows with applications,, Canad. Appl. Math. Quart., 3 (1995), 473.   Google Scholar

[38]

X. Q. Zhao and Z. J. Jing, Global asymptotic behavior in some cooperative systems of functional differential equations,, Canad. Appl. Math. Quart., 4 (1996), 421.   Google Scholar

[39]

Y. B. Zhou and X. L. Liu, The research progress in terms of prevalence, incidence reason and control strategies of brucellosis,, J. Liaoning Medical University, 1 (2010), 81.   Google Scholar

[40]

J. Zinsstag, F. Roth, D. Orkhon, G. Chimed-Ochir, M. Nansalmaa, J. Kolar and P. Vounatsou, A model of animal-human brucellosis transmission in Mongolia,, Prev. Vet. Med., 69 (2005), 77.  doi: 10.1016/j.prevetmed.2005.01.017.  Google Scholar

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