October  2017, 14(5&6): 1279-1299. doi: 10.3934/mbe.2017066

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

* Corresponding authorr: Zhidong Teng (E-mail: zhidong1960@163.com)

Received  April 05, 2016 Revised  October 30, 2016 Published  May 2017

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.

Citation: Yingke Li, Zhidong Teng, Shigui Ruan, Mingtao Li, Xiaomei Feng. A mathematical model for the seasonal transmission of schistosomiasis in the lake and marshland regions of China. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1279-1299. doi: 10.3934/mbe.2017066
References:
[1]

S. AltizerA. DobsonP. HosseiniP. HudsonM. 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

C. Castillo-ChavezZ. 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.  Google Scholar

[6]

Centers for Disease Control and Prevention, Parasites – Schistosomiasis. Updated on November 7,2012. Available from: http://www.cdc.gov/parasites/schistosomiasis/biology.html. Google Scholar

[7]

Centers for Disease Control and Prevention, Schistosomiasis Infection. Updated on May 3,2016. Available from: http://www.cdc.gov/dpdx/schistosomiasis/index.html. Google Scholar

[8]

Z. ChenL. ZouD. ShenW. 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.  Google Scholar

[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. Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[13]

G. DavisW. WuG. WilliamsH. LiuS. LuH. ChenF. ZhengD. 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.  Google Scholar

[14]

M. DiabyA. IggidrM. 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.  Google Scholar

[15]

D. EngelsL. ChitsuloA. 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.  Google Scholar

[16]

Z. FengA. EppertF. 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.  Google Scholar

[17]

Z. FengC. 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.  Google Scholar

[18]

S. GaoY. LiuY. 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.  Google Scholar

[19]

W. GariraD. 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.  Google Scholar

[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.  Google Scholar

[21]

D. GrayY. LiG. WilliamsZ. ZhaoD. HarnS. LiM. RenZ. FengF. GuoJ. GuoJ. ZhouY. DongY. LiA. 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.  Google Scholar

[22]

J. GreenmanM. 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.  Google Scholar

[23]

B. GryseelsK. PolmanJ. Clerinx and L. Kestens, Human schistosomiasis, Lancet, 368 (2006), 1106-1118.  doi: 10.1016/S0140-6736(06)69440-3.  Google Scholar

[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.  Google Scholar

[25]

N. Hairston, On the mathematical analysis of schistosome populations, Bull. WHO, 33 (1965), 45-62.   Google Scholar

[26]

G. HuJ. HuK. SongD. LinJ. ZhangC. CaoJ. XuD. 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.  Google Scholar

[27]

C. HuangJ. ZouS. 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.   Google Scholar

[28]

A. HusseinI. 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.  Google Scholar

[29]

R. J. Larsen and M. L. Marx, An Introduction to Mathematical Statistics and Its Applications, 4$^{nd}$ edition, Pearson Education, 2012. Google Scholar

[30]

S. LiangD. 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.  Google Scholar

[31]

J. LiuB. 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[34]

National Bureau of Statistics of China, China Demographic Yearbook of 2008. Available from: http://www.stats.gov.cn/tjsj/ndsj/2008/indexch.htm. Google Scholar

[35]

M. RiosJ. GarciaJ. 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.  Google Scholar

[36]

R. SpearA. HubbardS. 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.   Google Scholar

[37]

L. SunX. ZhouQ. HongG. YangY. HuangW. 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.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[40]

Z. TengY. 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.  Google Scholar

[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.  Google Scholar

[42]

World Health Organization, Media Centre: Schistosomiasis. Updated January 2017. Available from: http://www.who.int/mediacentre/factsheets/fs115/en/. Google Scholar

[43]

World Health Organization, Schistosomiasis. Available from: http://www.who.int/topics/schistosomiasis/en/. Google Scholar

[44]

World Health Organization, Global Health Observatory (GHO) Data: Schistosomiasis. Available from: http://www.who.int/gho/neglected_diseases/schistosomiasis/en/. Google Scholar

[45]

WHO Representative Office China, Schistosomiasis in China. Available from: http://www.wpro.who.int/china/mediacentre/factsheets/schistosomiasis/en/index.html. Google Scholar

[46]

L. WangH. ChenJ. GuoX. ZengX. HongJ. XiongX. WuX. WangL. WangG. XiaY. 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[49]

L. WangJ. Utzinger and X. Zhou, Schistosomiasis control: Experiences and lessons from China, Lancet, 372 (2008), 1793-1795.  doi: 10.1016/S0140-6736(08)61358-6.  Google Scholar

[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.  Google Scholar

[51]

G. WilliamsA. 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.  Google Scholar

[52]

J. XiangH. 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.  Google Scholar

[53]

J. XuD. LinX. WuR. ZhuQ. WangS. LvG. YangY. HanY. XiaoY. ZhangW. ChenM. XiongR. LinL. ZhangJ. XuS. ZhangT. WangL. 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.   Google Scholar

[54]

X. ZhangS. 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.  Google Scholar

[55]

J. ZhangZ. JinG. Sun and S. Ruan, Modeling seasonal rabies epidemic in China, Bull. Math. Biol., 74 (2012), 1226-1251.  doi: 10.1007/s11538-012-9720-6.  Google Scholar

[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.  Google Scholar

[57]

X. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003. doi: 10.1007/978-0-387-21761-1.  Google Scholar

[58]

X. ZhouL. CaiX. ZhangH. ShengX. MaY. JinX. WuX. WangL. WangT. LinW. ShenJ. 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.   Google Scholar

[59]

X. ZhouJ. GuoX. WuQ. JiangJ. ZhengH. DangX. WangJ. XuH. ZhuG. WuY. LiX. XuH. ChenT. WangY. ZhuD. QiuX. DongG. ZhaoS. ZhangN. ZhaoG. XiaL. WangS. ZhangD. LinM. 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.  Google Scholar

[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.  Google Scholar

show all references

References:
[1]

S. AltizerA. DobsonP. HosseiniP. HudsonM. 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

C. Castillo-ChavezZ. 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.  Google Scholar

[6]

Centers for Disease Control and Prevention, Parasites – Schistosomiasis. Updated on November 7,2012. Available from: http://www.cdc.gov/parasites/schistosomiasis/biology.html. Google Scholar

[7]

Centers for Disease Control and Prevention, Schistosomiasis Infection. Updated on May 3,2016. Available from: http://www.cdc.gov/dpdx/schistosomiasis/index.html. Google Scholar

[8]

Z. ChenL. ZouD. ShenW. 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.  Google Scholar

[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. Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[13]

G. DavisW. WuG. WilliamsH. LiuS. LuH. ChenF. ZhengD. 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.  Google Scholar

[14]

M. DiabyA. IggidrM. 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.  Google Scholar

[15]

D. EngelsL. ChitsuloA. 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.  Google Scholar

[16]

Z. FengA. EppertF. 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.  Google Scholar

[17]

Z. FengC. 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.  Google Scholar

[18]

S. GaoY. LiuY. 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.  Google Scholar

[19]

W. GariraD. 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.  Google Scholar

[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.  Google Scholar

[21]

D. GrayY. LiG. WilliamsZ. ZhaoD. HarnS. LiM. RenZ. FengF. GuoJ. GuoJ. ZhouY. DongY. LiA. 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.  Google Scholar

[22]

J. GreenmanM. 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.  Google Scholar

[23]

B. GryseelsK. PolmanJ. Clerinx and L. Kestens, Human schistosomiasis, Lancet, 368 (2006), 1106-1118.  doi: 10.1016/S0140-6736(06)69440-3.  Google Scholar

[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.  Google Scholar

[25]

N. Hairston, On the mathematical analysis of schistosome populations, Bull. WHO, 33 (1965), 45-62.   Google Scholar

[26]

G. HuJ. HuK. SongD. LinJ. ZhangC. CaoJ. XuD. 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.  Google Scholar

[27]

C. HuangJ. ZouS. 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.   Google Scholar

[28]

A. HusseinI. 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.  Google Scholar

[29]

R. J. Larsen and M. L. Marx, An Introduction to Mathematical Statistics and Its Applications, 4$^{nd}$ edition, Pearson Education, 2012. Google Scholar

[30]

S. LiangD. 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.  Google Scholar

[31]

J. LiuB. 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[34]

National Bureau of Statistics of China, China Demographic Yearbook of 2008. Available from: http://www.stats.gov.cn/tjsj/ndsj/2008/indexch.htm. Google Scholar

[35]

M. RiosJ. GarciaJ. 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.  Google Scholar

[36]

R. SpearA. HubbardS. 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.   Google Scholar

[37]

L. SunX. ZhouQ. HongG. YangY. HuangW. 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.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[40]

Z. TengY. 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.  Google Scholar

[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.  Google Scholar

[42]

World Health Organization, Media Centre: Schistosomiasis. Updated January 2017. Available from: http://www.who.int/mediacentre/factsheets/fs115/en/. Google Scholar

[43]

World Health Organization, Schistosomiasis. Available from: http://www.who.int/topics/schistosomiasis/en/. Google Scholar

[44]

World Health Organization, Global Health Observatory (GHO) Data: Schistosomiasis. Available from: http://www.who.int/gho/neglected_diseases/schistosomiasis/en/. Google Scholar

[45]

WHO Representative Office China, Schistosomiasis in China. Available from: http://www.wpro.who.int/china/mediacentre/factsheets/schistosomiasis/en/index.html. Google Scholar

[46]

L. WangH. ChenJ. GuoX. ZengX. HongJ. XiongX. WuX. WangL. WangG. XiaY. 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[49]

L. WangJ. Utzinger and X. Zhou, Schistosomiasis control: Experiences and lessons from China, Lancet, 372 (2008), 1793-1795.  doi: 10.1016/S0140-6736(08)61358-6.  Google Scholar

[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.  Google Scholar

[51]

G. WilliamsA. 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.  Google Scholar

[52]

J. XiangH. 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.  Google Scholar

[53]

J. XuD. LinX. WuR. ZhuQ. WangS. LvG. YangY. HanY. XiaoY. ZhangW. ChenM. XiongR. LinL. ZhangJ. XuS. ZhangT. WangL. 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.   Google Scholar

[54]

X. ZhangS. 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.  Google Scholar

[55]

J. ZhangZ. JinG. Sun and S. Ruan, Modeling seasonal rabies epidemic in China, Bull. Math. Biol., 74 (2012), 1226-1251.  doi: 10.1007/s11538-012-9720-6.  Google Scholar

[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.  Google Scholar

[57]

X. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003. doi: 10.1007/978-0-387-21761-1.  Google Scholar

[58]

X. ZhouL. CaiX. ZhangH. ShengX. MaY. JinX. WuX. WangL. WangT. LinW. ShenJ. 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.   Google Scholar

[59]

X. ZhouJ. GuoX. WuQ. JiangJ. ZhengH. DangX. WangJ. XuH. ZhuG. WuY. LiX. XuH. ChenT. WangY. ZhuD. QiuX. DongG. ZhaoS. ZhangN. ZhaoG. XiaL. WangS. ZhangD. LinM. 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.  Google Scholar

[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.  Google Scholar

Figure 1.  The human cases in Hunan, Anhui and Hubei from January 2008 to December 2011
Figure 2.  Simplified life cycle of human schistosomiasis
Figure 3.  Transmission diagram of schistosomiasis among human, snail, and miracidia and cercariae in water
Figure 4.  The $12$-periodic solutions in Example 5.3 when $R_{0}=1.8048>1.$
Figure 5.  Comparison between the reported human schistosomiasis cases in Hubei from January 2008 to December 2014 and the simulation of $I_{H}(t)$ from model (1)
Figure 6.  Disease development trend by forecasting model (1). The parameter and initial values are the same as in Figure 5
Figure 7.  Tendency of human schistosomiasis cases with different $R_{0}$: (a) $\gamma_{H}=0.131$, $R_{0}=1.2387$; (b) $\gamma_{H}=0.207$, $R_{0}=0.9971$. All other parameter values are the same as in Table 1
Figure 8.  The influence of parameters on $R_{0}$: (a) versus $\Lambda_{V}$, (b) versus $\lambda_{M}$, (c) versus $\lambda_{P}$, (d) versus $\gamma_{H}$. Other parameter values are unchanged as in Table 1
Figure 9.  The influence of different values on $I_{H}(t)$: (a) different values of $\Lambda_V$, (b) different values of $\mu_V$, (c) different values of $\lambda_M$, (d) different values of $\lambda_P$, (e) different values of $a_H$, (f) different values of $\gamma_H$. Interval $t\in[0, 84]$ represents the period from June 2008 to December 2014
Table 1.  Descriptions and values of parameters in model (1)
ParameterInterpretationValueUnitSource
$\Lambda_{H}$Recruiting of susceptible humans $2.431\times10^{4}$month$^{-1}$[34]
$\mu_{H}$Natural death rate of humans $1.126\times10^{-3}$month$^{-1}$[34]
$a_{H}$The baseline transmission rate $8.00\times10^{-14}$month$^{-1}$Estimated
$b_{H}$The magnitude of forcing0.6none[54]
$\varphi_{H}$The initial phase $ 4.978$noneEstimated
$\gamma_{H}$Cure rate0.131month$^{-1}$[44]
$\lambda_{M}$Migration rate209month$^{-1}$[5], [33]
$\mu_{M}$Natural death rate of miracidia27month$^{-1}$[18], [36]
$\Lambda_{V}$Recruiting of susceptible snails $5.660\times10^{5}$month$^{-1}$[8], [27], [53]
$\mu_{V}$Natural death rate of snails $ 1.788\times10^{-2}$month$^{-1}$[33]
$\alpha_{V}$Disease induced death rate of snails0.012month$^{-1}$[18], [33]
$a_{V}$The baseline transmission rate $1.974\times10^{-8}$month$^{-1}$Estimated
$b_{V}$The magnitude of forcing0.6none[54]
$\varphi_{V}$The initial phase $4.407$noneEstimated
$\lambda_{P}$Migration rate78month$^{-1}$[18], [33]
$\mu_{P}$Natural death rate of cercariae0.12month$^{-1}$[18], [36]
ParameterInterpretationValueUnitSource
$\Lambda_{H}$Recruiting of susceptible humans $2.431\times10^{4}$month$^{-1}$[34]
$\mu_{H}$Natural death rate of humans $1.126\times10^{-3}$month$^{-1}$[34]
$a_{H}$The baseline transmission rate $8.00\times10^{-14}$month$^{-1}$Estimated
$b_{H}$The magnitude of forcing0.6none[54]
$\varphi_{H}$The initial phase $ 4.978$noneEstimated
$\gamma_{H}$Cure rate0.131month$^{-1}$[44]
$\lambda_{M}$Migration rate209month$^{-1}$[5], [33]
$\mu_{M}$Natural death rate of miracidia27month$^{-1}$[18], [36]
$\Lambda_{V}$Recruiting of susceptible snails $5.660\times10^{5}$month$^{-1}$[8], [27], [53]
$\mu_{V}$Natural death rate of snails $ 1.788\times10^{-2}$month$^{-1}$[33]
$\alpha_{V}$Disease induced death rate of snails0.012month$^{-1}$[18], [33]
$a_{V}$The baseline transmission rate $1.974\times10^{-8}$month$^{-1}$Estimated
$b_{V}$The magnitude of forcing0.6none[54]
$\varphi_{V}$The initial phase $4.407$noneEstimated
$\lambda_{P}$Migration rate78month$^{-1}$[18], [33]
$\mu_{P}$Natural death rate of cercariae0.12month$^{-1}$[18], [36]
[1]

Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020276

[2]

Laurence Cherfils, Stefania Gatti, Alain Miranville, Rémy Guillevin. Analysis of a model for tumor growth and lactate exchanges in a glioma. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020457

[3]

Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020316

[4]

Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020317

[5]

Yining Cao, Chuck Jia, Roger Temam, Joseph Tribbia. Mathematical analysis of a cloud resolving model including the ice microphysics. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 131-167. doi: 10.3934/dcds.2020219

[6]

Zhouchao Wei, Wei Zhang, Irene Moroz, Nikolay V. Kuznetsov. Codimension one and two bifurcations in Cattaneo-Christov heat flux model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020344

[7]

Shuang Chen, Jinqiao Duan, Ji Li. Effective reduction of a three-dimensional circadian oscillator model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020349

[8]

Barbora Benešová, Miroslav Frost, Lukáš Kadeřávek, Tomáš Roubíček, Petr Sedlák. An experimentally-fitted thermodynamical constitutive model for polycrystalline shape memory alloys. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020459

[9]

Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. The threshold dynamics of a discrete-time echinococcosis transmission model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020339

[10]

Yolanda Guerrero–Sánchez, Muhammad Umar, Zulqurnain Sabir, Juan L. G. Guirao, Muhammad Asif Zahoor Raja. Solving a class of biological HIV infection model of latently infected cells using heuristic approach. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020431

[11]

Chao Xing, Jiaojiao Pan, Hong Luo. Stability and dynamic transition of a toxin-producing phytoplankton-zooplankton model with additional food. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020275

[12]

H. M. Srivastava, H. I. Abdel-Gawad, Khaled Mohammed Saad. Oscillatory states and patterns formation in a two-cell cubic autocatalytic reaction-diffusion model subjected to the Dirichlet conditions. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020433

[13]

Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020347

[14]

A. M. Elaiw, N. H. AlShamrani, A. Abdel-Aty, H. Dutta. Stability analysis of a general HIV dynamics model with multi-stages of infected cells and two routes of infection. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020441

[15]

Hai-Feng Huo, Shi-Ke Hu, Hong Xiang. Traveling wave solution for a diffusion SEIR epidemic model with self-protection and treatment. Electronic Research Archive, , () : -. doi: 10.3934/era.2020118

[16]

Bernard Bonnard, Jérémy Rouot. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model. Journal of Geometric Mechanics, 2020  doi: 10.3934/jgm.2020032

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (173)
  • HTML views (130)
  • Cited by (3)

[Back to Top]