`a`
Mathematical Biosciences and Engineering (MBE)
 

A mathematical model for the seasonal transmission of schistosomiasis in the lake and marshland regions of China
Pages: 1279 - 1299, Issue 5/6, October/December 2017

doi:10.3934/mbe.2017066      Abstract        References        Full text (699.1K)           Related Articles

Yingke Li - College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China (email)
Zhidong Teng - College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China (email)
Shigui Ruan - Department of Mathematics, University of Miami, Coral Gables, FL 33146, United States (email)
Mingtao Li - Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, China (email)
Xiaomei Feng - Department of Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China (email)

1 S. Altizer, A. Dobson, P. Hosseini, P. Hudson, M. Pascual and P. Rohani, Seasonality and the dynamics of infectious diseases, Ecol. Lett., 9 (2006), 467-484.
2 J. Aron and I. Schwartz, Seasonality and period-doubling bifurcations in an epidemic model, J. Theor. Biol., 110 (1984), 665-679.       
3 N. Bacaër, Approximation of the basic reprodution number $R_{0}$ for a vectir-borne diseases with a periodic vector population, Bull. Math. Biol., 69 (2007), 1067-1091.       
4 N. Bacaër and S. Guernaoui, The epdemic threshold of vector-borne sdiseas with seasonality, J. Math. Biol., 53 (2006), 421-436.       
5 C. Castillo-Chavez, Z. Feng and D. Xu, A schistosomiasis model with mating structure and time delay, Math. Biolsci., 211 (2008), 333-341.       
6 Centers for Disease Control and Prevention, Parasites - Schistosomiasis. Updated on November 7, 2012. Available from: http://www.cdc.gov/parasites/schistosomiasis/biology.html.
7 Centers for Disease Control and Prevention, Schistosomiasis Infection. Updated on May 3, 2016. Available from: http://www.cdc.gov/dpdx/schistosomiasis/index.html.
8 Z. Chen, L. Zou, D. Shen, W. Zhang and S. Ruan, Mathematical modelling and control of Schistosomiasis in Hubei Province, China, Acta Trop., 115 (2010), 119-125.
9 Chinese Center for Disease Control and Prevention, Schisosomiasis. Updated on November 11, 2012. Available from: http://www.ipd.org.cn/Article/xxjs/hzdw/201206/2431.html.
10 Chinese Center for Disease Control and Prevention/The Data-center of China Public Health Science, Schisosomiasis. Available from: http://www.phsciencedata.cn/Share/ky_sjml.jsp?id=5912cbb2-c84b-4bca-a554-7c234072a34c&show=0.
11 E. Chiyak and W. Garira, Mathematical analysis of the transmission dynamics of schistosomiasis in the humansnail hosts, J. Biol. Syst., 17 (2009), 397-423.
12 D. Coon, Schistosomiasis: overview of the history, biology, clinicopathology, and laboratory diagnosis, Clin. Microbiol. Newsl., 27 (2005), 163-168.
13 G. Davis, W. Wu, G. Williams, H. Liu, S. Lu, H. Chen, F. Zheng, D. Mcmanus and J. Guo, Schistosomiasis japonica intervention study on Poyang Lake, China: The snail's tale, Malacologia., 49 (2006), 79-105.
14 M. Diaby, A. Iggidr, M. Sy and A. Sène, Global analysis of a schistosomiasis infection model with biological control, Appl. Math. Comput., 246 (2014), 731-742.       
15 D. Engels, L. Chitsulo, A. Montresor and L. Savioli, The global epidemiological situation of schistosomiasis and new approaches to control and research, Acta Trop., 82 (2002), 139-146.
16 Z. Feng, A. Eppert, F. Milner and D. Minchella, Estimation of parameters governing the transmission dynamics of schistosomes, Appl. Math. Lett., 17 (2004), 1105-1112.       
17 Z. Feng, C. Li and F. Milner, Schistosomiasis models with density dependence and age of infection in snail dynamics, Math. Biosci., 177 (2002), 271-286.       
18 S. Gao, Y. Liu, Y. Luo and D. Xie, Control problems of mathematical model for schistosomiasis transmission dynamics, Nonlinear Dyn., 63 (2011), 503-512.       
19 W. Garira, D. Mathebula and R. Netshikweta, A mathematical modelling framework for linked within-host and between-host dynamics for infections pathogens in the environment, Math. Biosci., 256 (2014), 58-78.       
20 D. Gray, G. Williams, Y. Li and D. Mcmanus, Transmission dynamics of Schistosoma japonicum in the Lakes and Marshlands of China, PLoS One, 3 (2008), e4058.
21 D. Gray, Y. Li, G. Williams, Z. Zhao, D. Harn, S. Li, M. Ren, Z. Feng, F. Guo, J. Guo, J. Zhou, Y. Dong, Y. Li, A. Ross and D. McManus, A multi-component integrated approach for the elimination of schistosomiasis in the People's Republic of China: Design and baseline results of a 4-year cluster-randomised intervention trial, Int. J. Parasitol., 44 (2014), 659-668.
22 J. Greenman, M. Kamo and M.Boots, External forcing of ecological and epidemiological systems: A resonance approach, Physica D. 190 (2004), 136-151.
23 B. Gryseels, K. Polman, J. Clerinx and L. Kestens, Human schistosomiasis, Lancet, 368 (2006), 1106-1118.
24 A. Guiro, S. Ouaro and A. Traore, Stability analysis of a schistosomiasis model with delays, Adv. Differ. Equ., 2013 (2013), 15pp.       
25 N. Hairston, On the mathematical analysis of schistosome populations, Bull. WHO, 33 (1965), 45-62.
26 G. Hu, J. Hu , K. Song, D. Lin, J. Zhang, C. Cao, J. Xu, D. Li and W. Jiang, The role of health education and health promotionin the control of schistosomiasis: experiences from a 12-year intervention study in the Poyang Lake area, Acta Trop., 96 (2005), 232-241.
27 C. Huang, J. Zou, S. Li and X. Zhou, Survival and reproduction of Oncomelania hupensis robertsoni in water network regions in Hubei Province, China, Chin. J. Schisto. Control., 23 (2011), 173-177.
28 A. Hussein, I. Hassan and R. Khalifa, Development and hatching mechanism of Fasciola eggs, light and scanning electron microscopic studies, Saudi J. Biol. Sci., 17 (2010), 247-251.
29 R. J. Larsen and M. L. Marx, An Introduction to Mathematical Statistics and Its Applications, $4^{nd}$ edition, Pearson Education, 2012.
30 S. Liang, D. Maszle and R. Spear, A quantitative framework for a multi-group model of Schistosomiasis japonicum transmission dynamics and control in Sichuan China, Acta Trop., 82 (2002), 263-277.
31 J. Liu, B. Peng and T. Zhang, Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence, Appl Math Lett, 39 (2015), 60-66.       
32 G. Macdonald, The dynamics of helminth infections, with special reference to schistosomes, Trans. R. Soci. Trop. Med. Hyg., 59 (1965), 489-506.
33 T. Mangal, S. Paterson and A. Fenton, Predicting the impact of long-term temperature changes on the epidemiology and control of schistosomiasis: a mechanistic model, PLoSOne., 3 (2008), e1438.
34 National Bureau of Statistics of China, China Demographic Yearbook of 2008. Available from: http://www.stats.gov.cn/tjsj/ndsj/2008/indexch.htm.
35 M. Rios, J. Garcia, J. Sanchez and D. Perez, A statistical analysis of the seasonality in pulmonary tuberculosis, Eur. J. Epidemiol., 16 (2000), 483-488.
36 R. Spear, A. Hubbard, S. Liang and E. Seto, Disease transmission models for public health decision making: Toward an approach for designing intervention strategies for Schistosomiasis japonica, Environ. Health Perspect., 110 (2002), 907-915.
37 L. Sun, X. Zhou, Q. Hong, G. Yang, Y. Huang, W. Xi and Y. Jiang, Impact of global warming on transmission of schistosomiasis in China III. Relationship between snail infections rate and environmental temperature, Chin.J.Schist. Control, 15 (2003), 161-163 (in Chinese).
38 Z. Teng and L. Chen, The positive periodic solutions of periodic Kolmogorove type systems with delays, Acta Math. Appl. Sin., 22 (1999), 446-456 (in Chinese).       
39 Z. Teng and Z. Li, Permanence and asymptotic behavior of the N-species nonautonomous Lotka-Volterra competitive systems, Comp. Math. Appl., 39 (2000), 107-116.       
40 Z. Teng, Y. Liu and L. Zhang, Persistence and extinction of disease in non-autonomous SIRS epidemic models with disease-induced mortality, Nonlinear Anal., 69 (2008), 2599-2614.       
41 P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.       
42 World Health Organization, Media Centre: Schistosomiasis. Updated January 2017. Available from: http://www.who.int/mediacentre/factsheets/fs115/en/.
43 World Health Organization, Schistosomiasis. Available from: http://www.who.int/topics/schistosomiasis/en/.
44 World Health Organization, Global Health Observatory (GHO) Data: Schistosomiasis. Available from: http://www.who.int/gho/neglected_diseases/schistosomiasis/en/.
45 WHO Representative Office China, Schistosomiasis in China. Available from: http://www.wpro.who.int/china/mediacentre/factsheets/schistosomiasis/en/index.html.
46 L. Wang, H. Chen, J. Guo, X. Zeng, X. Hong, J. Xiong, X. Wu, X. Wang, L. Wang, G. Xia, Y. Hao and X. Zhou, A strategy to control transmission of Schistosoma japonicum in China, N. Engl. J. Med., 360 (2009), 121-128.
47 W. Wang, Y. Liang, Q. Hong and J. Dai, African schistosomiasis in mainland China: Risk of transmission and countermeasures to tackle the risk, Parasites Vectors, 6 (2013), 249.
48 S. Wang and R. Spear, Exploring the impact of infection-induced immunity on the transmission of Schistosoma japonicum in hilly and mountainous environments in China, Acta Trop., 133 (2014), 8-14.
49 L. Wang, J. Utzinger and X. Zhou, Schistosomiasis control: Experiences and lessons from China, Lancet, 372 (2008), 1793-1795.
50 W. Wang and X. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Diff. Equat., 20 (2008), 699-717.       
51 G. Williams, A. Sleigh and Y. Li, Mathematical modelling of schistosomiasis japonica: Comparison of control strategies in the People's Republic of China, Acta Trop., 82 (2002), 253-262.
52 J. Xiang, H. Chen and H. Ishikawa, A mathematical model for the transmission of Schistosoma japonicum in consideration of seasonal water level fluctuations of Poyang Lake in Jiangxi, China, Parasitol. Int., 62 (2013), 118-126.
53 J. Xu, D. Lin, X. Wu, R. Zhu, Q. Wang, S. Lv, G. Yang, Y. Han, Y. Xiao, Y. Zhang, W. Chen, M. Xiong, R. Lin, L. Zhang, J. Xu, S. Zhang, T. Wang, L. Wen and X. Zhou, Retrospective investigation on national endemic situation of schistosomiasis $II$ Analysis of changes of endemic situation in transmission controlled counties, Chin. J. Schisto. Control., 23 (2011), 237-242 (in Chinese).
54 X. Zhang, S. Gao and H. Cao, Threshold dynamics for a nonautonomous schistosomiasis model in a periodic environment, J. Appl. Math. Comput., 46 (2014), 305-319.       
55 J. Zhang, Z. Jin, G. Sun and S. Ruan, Modeling seasonal rabies epidemic in China, Bull. Math. Biol., 74 (2012), 1226-1251.       
56 F. Zhang and X. Zhao, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516.       
57 X. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.       
58 X. Zhou, L. Cai, X. Zhang, H. Sheng, X. Ma, Y. Jin, X. Wu, X. Wang, L. Wang, T. Lin, W. Shen, J. Lu and Q. Dai, Potential risks for transmission of Schistosomiasis caused by mobile population in Shanghai, Chin. J. Parasitol. Parasit. Dis., 25 (2007), 180-184.
59 X. Zhou, J. Guo, X. Wu, Q. Jiang, J. Zheng, H. Dang, X. Wang, J. Xu,H. Zhu, G. Wu, Y. Li, X. Xu, H. Chen, T. Wang, Y. Zhu, D. Qiu, X. Dong, G. Zhao, S. Zhang, N. Zhao, G. Xia, L. Wang, S. Zhang, D. Lin, M. Chen and Y. Hao, Epidemiology of Schistosomiasis in the People's Republic of China, Emerg. Infect. Dis., 13 (2007), 1470-1476.
60 L. Zou and S. Ruan, Schistosomiasis transmission and control in China, Acta Trop., 143 (2015), 51-57.

Go to top