
-
Previous Article
Modeling co-infection of Ixodes tick-borne pathogens
- MBE Home
- This Issue
-
Next Article
Modulation of first-passage time for bursty gene expression via random signals
A mathematical model for the seasonal transmission of schistosomiasis in the lake and marshland regions of China
a. | College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China |
b. | College of Mathematics and Physics, Xinjiang Agriculture University, Urumqi, Xinjiang 830052, China |
c. | Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA |
d. | Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, China |
e. | Department of Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China |
Schistosomiasis, a parasitic disease caused by Schistosoma Japonicum, is still one of the most serious parasitic diseases in China and remains endemic in seven provinces, including Hubei, Anhui, Hunan, Jiangsu, Jiangxi, Sichuan, and Yunnan. The monthly data of human schistosomiasis cases in Hubei, Hunan, and Anhui provinces (lake and marshland regions) released by the Chinese Center for Disease Control and Prevention (China CDC) display a periodic pattern with more cases in late summer and early autumn. Based on this observation, we construct a deterministic model with periodic transmission rates to study the seasonal transmission dynamics of schistosomiasis in these lake and marshland regions in China. We calculate the basic reproduction number $R_{0}$, discuss the dynamical behavior of solutions to the model, and use the model to fit the monthly data of human schistosomiasis cases in Hubei. We also perform some sensitivity analysis of the basic reproduction number $R_{0}$ in terms of model parameters. Our results indicate that treatment of at-risk population groups, improving sanitation, hygiene education, and snail control are effective measures in controlling human schistosomiasis in these lakes and marshland regions.
References:
[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.
doi: 10.1111/j.1461-0248.2005.00879.x. |
[2] |
J. Aron and I. Schwartz,
Seasonality and period-doubling bifurcations in an epidemic model, J. Theor. Biol., 110 (1984), 665-679.
doi: 10.1016/S0022-5193(84)80150-2. |
[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.
doi: 10.1007/s11538-006-9166-9. |
[4] |
N. Bacaër and S. Guernaoui,
The epdemic threshold of vector-borne sdiseas with seasonality, J. Math. Biol., 53 (2006), 421-436.
doi: 10.1007/s00285-006-0015-0. |
[5] |
C. Castillo-Chavez, Z. Feng and D. Xu,
A schistosomiasis model with mating structure and time delay, Math. Biolsci., 211 (2008), 333-341.
doi: 10.1016/j.mbs.2007.11.001. |
[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.
doi: 10.1016/j.actatropica.2010.02.012. |
[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.
doi: 10.1142/S0218339009002910. |
[12] |
D. Coon,
Schistosomiasis: overview of the history, biology, clinicopathology, and laboratory diagnosis, Clin. Microbiol. Newsl., 27 (2005), 163-168.
doi: 10.1016/j.clinmicnews.2005.10.001. |
[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.
doi: 10.4002/1543-8120-49.1.79. |
[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.
doi: 10.1016/j.amc.2014.08.061. |
[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.
doi: 10.1016/S0001-706X(02)00045-1. |
[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.
doi: 10.1016/j.aml.2004.02.002. |
[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.
doi: 10.1016/S0025-5564(01)00115-8. |
[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.
doi: 10.1007/s11071-010-9818-z. |
[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.
doi: 10.1016/j.mbs.2014.08.004. |
[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.
doi: 10.1371/journal.pone.0004058. |
[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.
doi: 10.1016/j.ijpara.2014.05.005. |
[22] |
J. Greenman, M. Kamo and M. Boots,
External forcing of ecological and epidemiological systems: A resonance approach, Physica D, 190 (2004), 136-151.
doi: 10.1016/j.physd.2003.08.008. |
[23] |
B. Gryseels, K. Polman, J. Clerinx and L. Kestens,
Human schistosomiasis, Lancet, 368 (2006), 1106-1118.
doi: 10.1016/S0140-6736(06)69440-3. |
[24] |
A. Guiro, S. Ouaro and A. Traore, Stability analysis of a schistosomiasis model with delays, Adv. Differ. Equ., 2013 (2013), 15pp.
doi: 10.1186/1687-1847-2013-303. |
[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.
doi: 10.1016/j.actatropica.2005.07.016. |
[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.
doi: 10.1016/j.sjbs.2010.04.010. |
[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.
doi: 10.1016/S0001-706X(02)00018-9. |
[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.
doi: 10.1016/j.aml.2014.08.012. |
[32] |
G. Macdonald,
The dynamics of helminth infections, with special reference to schistosomes, Trans. R. Soci. Trop. Med. Hyg., 59 (1965), 489-506.
doi: 10.1016/0035-9203(65)90152-5. |
[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.
doi: 10.1371/journal.pone.0001438. |
[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.
doi: 10.1023/A:1007653329972. |
[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.
|
[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.
|
[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.
doi: 10.1016/S0898-1221(00)00069-9. |
[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.
doi: 10.1016/j.na.2007.08.036. |
[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.
doi: 10.1016/S0025-5564(02)00108-6. |
[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.
doi: 10.1056/NEJMoa0800135. |
[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.
doi: 10.1186/1756-3305-6-249. |
[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.
doi: 10.1016/j.actatropica.2014.01.005. |
[49] |
L. Wang, J. Utzinger and X. Zhou,
Schistosomiasis control: Experiences and lessons from China, Lancet, 372 (2008), 1793-1795.
doi: 10.1016/S0140-6736(08)61358-6. |
[50] |
W. Wang and X. Zhao,
Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Diff. Equat., 20 (2008), 699-717.
doi: 10.1007/s10884-008-9111-8. |
[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.
doi: 10.1016/S0001-706X(02)00017-7. |
[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.
doi: 10.1016/j.parint.2012.10.004. |
[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.
|
[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.
doi: 10.1007/s12190-013-0750-5. |
[55] |
J. Zhang, Z. Jin, G. Sun and S. Ruan,
Modeling seasonal rabies epidemic in China, Bull. Math. Biol., 74 (2012), 1226-1251.
doi: 10.1007/s11538-012-9720-6. |
[56] |
F. Zhang and X. Zhao,
A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516.
doi: 10.1016/j.jmaa.2006.01.085. |
[57] |
X. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
[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.
doi: 10.3201/eid1310.061423. |
[60] |
L. Zou and S. Ruan,
Schistosomiasis transmission and control in China, Acta Trop., 143 (2015), 51-57.
doi: 10.1016/j.actatropica.2014.12.004. |
show all references
References:
[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.
doi: 10.1111/j.1461-0248.2005.00879.x. |
[2] |
J. Aron and I. Schwartz,
Seasonality and period-doubling bifurcations in an epidemic model, J. Theor. Biol., 110 (1984), 665-679.
doi: 10.1016/S0022-5193(84)80150-2. |
[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.
doi: 10.1007/s11538-006-9166-9. |
[4] |
N. Bacaër and S. Guernaoui,
The epdemic threshold of vector-borne sdiseas with seasonality, J. Math. Biol., 53 (2006), 421-436.
doi: 10.1007/s00285-006-0015-0. |
[5] |
C. Castillo-Chavez, Z. Feng and D. Xu,
A schistosomiasis model with mating structure and time delay, Math. Biolsci., 211 (2008), 333-341.
doi: 10.1016/j.mbs.2007.11.001. |
[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.
doi: 10.1016/j.actatropica.2010.02.012. |
[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.
doi: 10.1142/S0218339009002910. |
[12] |
D. Coon,
Schistosomiasis: overview of the history, biology, clinicopathology, and laboratory diagnosis, Clin. Microbiol. Newsl., 27 (2005), 163-168.
doi: 10.1016/j.clinmicnews.2005.10.001. |
[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.
doi: 10.4002/1543-8120-49.1.79. |
[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.
doi: 10.1016/j.amc.2014.08.061. |
[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.
doi: 10.1016/S0001-706X(02)00045-1. |
[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.
doi: 10.1016/j.aml.2004.02.002. |
[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.
doi: 10.1016/S0025-5564(01)00115-8. |
[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.
doi: 10.1007/s11071-010-9818-z. |
[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.
doi: 10.1016/j.mbs.2014.08.004. |
[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.
doi: 10.1371/journal.pone.0004058. |
[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.
doi: 10.1016/j.ijpara.2014.05.005. |
[22] |
J. Greenman, M. Kamo and M. Boots,
External forcing of ecological and epidemiological systems: A resonance approach, Physica D, 190 (2004), 136-151.
doi: 10.1016/j.physd.2003.08.008. |
[23] |
B. Gryseels, K. Polman, J. Clerinx and L. Kestens,
Human schistosomiasis, Lancet, 368 (2006), 1106-1118.
doi: 10.1016/S0140-6736(06)69440-3. |
[24] |
A. Guiro, S. Ouaro and A. Traore, Stability analysis of a schistosomiasis model with delays, Adv. Differ. Equ., 2013 (2013), 15pp.
doi: 10.1186/1687-1847-2013-303. |
[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.
doi: 10.1016/j.actatropica.2005.07.016. |
[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.
doi: 10.1016/j.sjbs.2010.04.010. |
[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.
doi: 10.1016/S0001-706X(02)00018-9. |
[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.
doi: 10.1016/j.aml.2014.08.012. |
[32] |
G. Macdonald,
The dynamics of helminth infections, with special reference to schistosomes, Trans. R. Soci. Trop. Med. Hyg., 59 (1965), 489-506.
doi: 10.1016/0035-9203(65)90152-5. |
[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.
doi: 10.1371/journal.pone.0001438. |
[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.
doi: 10.1023/A:1007653329972. |
[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.
|
[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.
|
[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.
doi: 10.1016/S0898-1221(00)00069-9. |
[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.
doi: 10.1016/j.na.2007.08.036. |
[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.
doi: 10.1016/S0025-5564(02)00108-6. |
[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.
doi: 10.1056/NEJMoa0800135. |
[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.
doi: 10.1186/1756-3305-6-249. |
[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.
doi: 10.1016/j.actatropica.2014.01.005. |
[49] |
L. Wang, J. Utzinger and X. Zhou,
Schistosomiasis control: Experiences and lessons from China, Lancet, 372 (2008), 1793-1795.
doi: 10.1016/S0140-6736(08)61358-6. |
[50] |
W. Wang and X. Zhao,
Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Diff. Equat., 20 (2008), 699-717.
doi: 10.1007/s10884-008-9111-8. |
[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.
doi: 10.1016/S0001-706X(02)00017-7. |
[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.
doi: 10.1016/j.parint.2012.10.004. |
[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.
|
[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.
doi: 10.1007/s12190-013-0750-5. |
[55] |
J. Zhang, Z. Jin, G. Sun and S. Ruan,
Modeling seasonal rabies epidemic in China, Bull. Math. Biol., 74 (2012), 1226-1251.
doi: 10.1007/s11538-012-9720-6. |
[56] |
F. Zhang and X. Zhao,
A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516.
doi: 10.1016/j.jmaa.2006.01.085. |
[57] |
X. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
[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.
doi: 10.3201/eid1310.061423. |
[60] |
L. Zou and S. Ruan,
Schistosomiasis transmission and control in China, Acta Trop., 143 (2015), 51-57.
doi: 10.1016/j.actatropica.2014.12.004. |





Parameter | Interpretation | Value | Unit | Source |
| Recruiting of susceptible humans | | month | [34] |
| Natural death rate of humans | | month | [34] |
| The baseline transmission rate | | month | Estimated |
| The magnitude of forcing | 0.6 | none | [54] |
| The initial phase | | none | Estimated |
| Cure rate | 0.131 | month | [44] |
| Migration rate | 209 | month | [5], [33] |
| Natural death rate of miracidia | 27 | month | [18], [36] |
| Recruiting of susceptible snails | | month | [8], [27], [53] |
| Natural death rate of snails | | month | [33] |
| Disease induced death rate of snails | 0.012 | month | [18], [33] |
| The baseline transmission rate | | month | Estimated |
| The magnitude of forcing | 0.6 | none | [54] |
| The initial phase | | none | Estimated |
| Migration rate | 78 | month | [18], [33] |
| Natural death rate of cercariae | 0.12 | month | [18], [36] |
Parameter | Interpretation | Value | Unit | Source |
| Recruiting of susceptible humans | | month | [34] |
| Natural death rate of humans | | month | [34] |
| The baseline transmission rate | | month | Estimated |
| The magnitude of forcing | 0.6 | none | [54] |
| The initial phase | | none | Estimated |
| Cure rate | 0.131 | month | [44] |
| Migration rate | 209 | month | [5], [33] |
| Natural death rate of miracidia | 27 | month | [18], [36] |
| Recruiting of susceptible snails | | month | [8], [27], [53] |
| Natural death rate of snails | | month | [33] |
| Disease induced death rate of snails | 0.012 | month | [18], [33] |
| The baseline transmission rate | | month | Estimated |
| The magnitude of forcing | 0.6 | none | [54] |
| The initial phase | | none | Estimated |
| Migration rate | 78 | month | [18], [33] |
| Natural death rate of cercariae | 0.12 | month | [18], [36] |
[1] |
Keng Deng, Yixiang Wu. Extinction and uniform strong persistence of a size-structured population model. Discrete and Continuous Dynamical Systems - B, 2017, 22 (3) : 831-840. doi: 10.3934/dcdsb.2017041 |
[2] |
Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 37-56. doi: 10.3934/dcdsb.2013.18.37 |
[3] |
Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595 |
[4] |
Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh, Rana Parshad. Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2021170 |
[5] |
Ling Xue, Caterina Scoglio. Network-level reproduction number and extinction threshold for vector-borne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565-584. doi: 10.3934/mbe.2015.12.565 |
[6] |
Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman. The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1455-1474. doi: 10.3934/mbe.2013.10.1455 |
[7] |
Tianhui Yang, Ammar Qarariyah, Qigui Yang. The effect of spatial variables on the basic reproduction ratio for a reaction-diffusion epidemic model. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 3005-3017. doi: 10.3934/dcdsb.2021170 |
[8] |
Gabriela Marinoschi. Identification of transmission rates and reproduction number in a SARS-CoV-2 epidemic model. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022128 |
[9] |
Kaifa Wang, Aijun Fan. Uniform persistence and periodic solution of chemostat-type model with antibiotic. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 789-795. doi: 10.3934/dcdsb.2004.4.789 |
[10] |
Shangzhi Li, Shangjiang Guo. Persistence and extinction of a stochastic SIS epidemic model with regime switching and Lévy jumps. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 5101-5134. doi: 10.3934/dcdsb.2020335 |
[11] |
Tianhui Yang, Lei Zhang. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (12) : 6771-6782. doi: 10.3934/dcdsb.2019166 |
[12] |
Fabio Augusto Milner, Ruijun Zhao. A deterministic model of schistosomiasis with spatial structure. Mathematical Biosciences & Engineering, 2008, 5 (3) : 505-522. doi: 10.3934/mbe.2008.5.505 |
[13] |
Attila Dénes, Gergely Röst. Single species population dynamics in seasonal environment with short reproduction period. Communications on Pure and Applied Analysis, 2021, 20 (2) : 755-762. doi: 10.3934/cpaa.2020288 |
[14] |
Sebastian J. Schreiber. On persistence and extinction for randomly perturbed dynamical systems. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 457-463. doi: 10.3934/dcdsb.2007.7.457 |
[15] |
Scott W. Hansen. Controllability of a basic cochlea model. Evolution Equations and Control Theory, 2016, 5 (4) : 475-487. doi: 10.3934/eect.2016015 |
[16] |
Chunhua Shan, Hongjun Gao, Huaiping Zhu. Dynamics of a delay Schistosomiasis model in snail infections. Mathematical Biosciences & Engineering, 2011, 8 (4) : 1099-1115. doi: 10.3934/mbe.2011.8.1099 |
[17] |
Antoine Perasso. Global stability and uniform persistence for an infection load-structured SI model with exponential growth velocity. Communications on Pure and Applied Analysis, 2019, 18 (1) : 15-32. doi: 10.3934/cpaa.2019002 |
[18] |
Kazuo Yamazaki, Xueying Wang. Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model. Mathematical Biosciences & Engineering, 2017, 14 (2) : 559-579. doi: 10.3934/mbe.2017033 |
[19] |
Tom Burr, Gerardo Chowell. The reproduction number $R_t$ in structured and nonstructured populations. Mathematical Biosciences & Engineering, 2009, 6 (2) : 239-259. doi: 10.3934/mbe.2009.6.239 |
[20] |
Naveen K. Vaidya, Feng-Bin Wang. Persistence of mosquito vector and dengue: Impact of seasonal and diurnal temperature variations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 393-420. doi: 10.3934/dcdsb.2021048 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]