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Multi-host transmission dynamics of schistosomiasis and its optimal control
1. | Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing, 210094, China |
2. | LAboratory of Mathematical Parallel Systems (LAMPS), Centre for Disease Modeling, Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3 |
References:
[1] |
A. Abdelrazec, S. Lenhart and H. Zhu, Transmission dynamics of West Nile virus in mosquitoes and corvids and non-corvids, Journal of Mathematical Biology, 68 (2014), 1553-1582.
doi: 10.1007/s00285-013-0677-3. |
[2] |
L. J. Abu-Raddad, A. S. Magaret, C. Celum, A. Wald, I. M. Longini Jr, S. G. Self and L. Corey, Genital herpes has played a more important role than any other sexually transmitted infection in driving HIV prevalence in Africa, PloS One, 3 (2008), e2230. http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0002230 |
[3] |
K. W. Blayneh, A. B. Gumel, S. Lenhart and C. Tim, Backward bifurcation and optimal control in transmission dynamics of West Nile virus, Bulletin of Mathematical Biology, 72 (2010), 1006-1028.
doi: 10.1007/s11538-009-9480-0. |
[4] |
C. Castillo-Chevez and H. R. Thieme, Asymptotically autonomous epidemic models, Mathematical Population Dynamics: Analysis of Heterogeneity, 1 (1995), 33-50. http://www.researchgate.net/publication/221674057_Asymptotically_autonomous_epidemic_models |
[5] |
Z. Feng, C. Li and F. A. Milner, Schistosomiasis models with density dependence and age of infection in snail dynamics, Mathematical Biosciences, 177 (2002), 271-286.
doi: 10.1016/S0025-5564(01)00115-8. |
[6] |
Z. Feng, Z. Qiu, Z. Sang, C. Lorenzo and J. Glasser, Modeling the synergy between HSV-2 and HIV and potential impact of HSV-2 therapy, Mathematical Biosciences, 245 (2013), 171-187.
doi: 10.1016/j.mbs.2013.07.003. |
[7] |
A. Fenton and A. B. Pedersen, Community epidemiology framework for classifying disease threats, Emerging Infectious Diseases, 11 (2005), 1815-1821. http://wwwnc.cdc.gov/eid/article/11/12/05-0306_article |
[8] |
W. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control, Springer, 1975. http://cds.cern.ch/record/1611958 |
[9] |
D. J. Gray, G. M. Williams, Y. Li and D. P. McManus, Transmission dynamics of Schistosoma japonicum in the lakes and marshlands of China, PLoS One, 3 (2008), e4058. http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0004058 |
[10] |
J. O. Lloyd-Smith, D. George, K. M. Pepin, V. E. Pitzer, J. R. Pulliam, A. P. Dobson, P. J. Hudson and B. T. Grenfell, Epidemic dynamics at the human-animal interface, Science, 326 (2009), 1362-1367, http://www.sciencemag.org/content/326/5958/1362.short |
[11] |
L. S. Pontryagin, Mathematical Theory of Optimal Processes, Interscience Publishers John Wiley and Sons, Inc., New York-London, 1962. |
[12] |
M. Rafikov, L. Bevilacqua and A. P. P. Wyse, Optimal control strategy of malaria vector using genetically modified mosquitoes, Journal of Theoretical Biology, 258 (2009), 418-425. http://www.sciencedirect.com/science/article/pii/S0022519308004190
doi: 10.1016/j.jtbi.2008.08.006. |
[13] |
S. Riley, H. Carabin, P. Bélisle, L. Joseph, V. Tallo, E. Balolong, A. L. Willingham III, T. J. Fernandez Jr., R. O. Gonzales, R. Olveda and S. T. McGarvey, Multi-host transmission dynamics of Schistosoma japonicum in Samar Province, the Philippines, PLoS Medicine, 5 (2008), e18. http://dx.plos.org/10.1371/journal.pmed.0050018 |
[14] |
J. W. Rudge, J. P. Webster, D. B. Lu, T. P. Wang, G. R. Fang and M. G. Basanez, Identifying host species driving transmission of schistosomiasis japonica, a multihost parasite system, in China, Proceedings of the National Academy of Sciences, 110 (2013), 11457-11462. http://www.pnas.org/content/110/28/11457.short |
[15] |
C. Shan, X. Zhou and H. Zhu, The Dynamics of Growing Islets and Transmission of Schistosomiasis Japonica in the Yangtze River, Bulletin of Mathematical Biology, 76 (2014), 1194-1217.
doi: 10.1007/s11538-014-9961-7. |
[16] |
H. L. Smith, Cooperative systems of differential equations with concave nonlinearities, Nonlinear Analysis: Theory, Methods and Applications, 10 (1986), 1037-1052. http://www.sciencedirect.com/science/article/pii/0362546X86900878 |
[17] |
H. L. Smith and P. Waltman, Perturbation of a globally stable steady state, Proceedings of the American Mathematical Society, 127 (1999), 447-453.
doi: 10.1090/S0002-9939-99-04768-1. |
[18] |
P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[19] |
W. Wang and X. Q. Zhao, An epidemic model in a patchy environment, Mathematical Biosciences, 190 (2004), 97-112.
doi: 10.1016/j.mbs.2002.11.001. |
[20] |
World Health Organization, http://www.who.int/features/factfiles/schistosomiasis/en/. |
[21] |
M. J. Woolhouse, On the application of mathematical models of schistosome transmission dynamics. II. Control, Acta Tropica, 50 (1992), 189-204. http://www.sciencedirect.com/science/article/pii/0001706X9290076A |
[22] |
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, Parasitology International, 62 (2013), 118-126. http://www.sciencedirect.com/science/article/pii/S1383576912001341 |
[23] |
P. Zhang, Z. Feng and F. Milner, A schistosomiasis model with an age-structure in human hosts and its application to treatment strategies, Mathematical Biosciences, 205 (2007), 83-107.
doi: 10.1016/j.mbs.2006.06.006. |
[24] |
R. Zhao and F. A. Milner, A mathematical model of Schistosoma mansoni in Biomphalaria glabrata with control strategies, Bulletin of Mathematical Biology, 70 (2008), 1886-1905.
doi: 10.1007/s11538-008-9330-5. |
[25] |
Y. B. Zhou, S. Liang and Q. W. Jiang, Factors impacting on progress towards elimination of transmission of schistosomiasis japonica in China, Parasit Vectors, 5 (2012), 257-275. http://www.biomedcentral.com/content/pdf/1756-3305-5-275.pdf |
show all references
References:
[1] |
A. Abdelrazec, S. Lenhart and H. Zhu, Transmission dynamics of West Nile virus in mosquitoes and corvids and non-corvids, Journal of Mathematical Biology, 68 (2014), 1553-1582.
doi: 10.1007/s00285-013-0677-3. |
[2] |
L. J. Abu-Raddad, A. S. Magaret, C. Celum, A. Wald, I. M. Longini Jr, S. G. Self and L. Corey, Genital herpes has played a more important role than any other sexually transmitted infection in driving HIV prevalence in Africa, PloS One, 3 (2008), e2230. http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0002230 |
[3] |
K. W. Blayneh, A. B. Gumel, S. Lenhart and C. Tim, Backward bifurcation and optimal control in transmission dynamics of West Nile virus, Bulletin of Mathematical Biology, 72 (2010), 1006-1028.
doi: 10.1007/s11538-009-9480-0. |
[4] |
C. Castillo-Chevez and H. R. Thieme, Asymptotically autonomous epidemic models, Mathematical Population Dynamics: Analysis of Heterogeneity, 1 (1995), 33-50. http://www.researchgate.net/publication/221674057_Asymptotically_autonomous_epidemic_models |
[5] |
Z. Feng, C. Li and F. A. Milner, Schistosomiasis models with density dependence and age of infection in snail dynamics, Mathematical Biosciences, 177 (2002), 271-286.
doi: 10.1016/S0025-5564(01)00115-8. |
[6] |
Z. Feng, Z. Qiu, Z. Sang, C. Lorenzo and J. Glasser, Modeling the synergy between HSV-2 and HIV and potential impact of HSV-2 therapy, Mathematical Biosciences, 245 (2013), 171-187.
doi: 10.1016/j.mbs.2013.07.003. |
[7] |
A. Fenton and A. B. Pedersen, Community epidemiology framework for classifying disease threats, Emerging Infectious Diseases, 11 (2005), 1815-1821. http://wwwnc.cdc.gov/eid/article/11/12/05-0306_article |
[8] |
W. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control, Springer, 1975. http://cds.cern.ch/record/1611958 |
[9] |
D. J. Gray, G. M. Williams, Y. Li and D. P. McManus, Transmission dynamics of Schistosoma japonicum in the lakes and marshlands of China, PLoS One, 3 (2008), e4058. http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0004058 |
[10] |
J. O. Lloyd-Smith, D. George, K. M. Pepin, V. E. Pitzer, J. R. Pulliam, A. P. Dobson, P. J. Hudson and B. T. Grenfell, Epidemic dynamics at the human-animal interface, Science, 326 (2009), 1362-1367, http://www.sciencemag.org/content/326/5958/1362.short |
[11] |
L. S. Pontryagin, Mathematical Theory of Optimal Processes, Interscience Publishers John Wiley and Sons, Inc., New York-London, 1962. |
[12] |
M. Rafikov, L. Bevilacqua and A. P. P. Wyse, Optimal control strategy of malaria vector using genetically modified mosquitoes, Journal of Theoretical Biology, 258 (2009), 418-425. http://www.sciencedirect.com/science/article/pii/S0022519308004190
doi: 10.1016/j.jtbi.2008.08.006. |
[13] |
S. Riley, H. Carabin, P. Bélisle, L. Joseph, V. Tallo, E. Balolong, A. L. Willingham III, T. J. Fernandez Jr., R. O. Gonzales, R. Olveda and S. T. McGarvey, Multi-host transmission dynamics of Schistosoma japonicum in Samar Province, the Philippines, PLoS Medicine, 5 (2008), e18. http://dx.plos.org/10.1371/journal.pmed.0050018 |
[14] |
J. W. Rudge, J. P. Webster, D. B. Lu, T. P. Wang, G. R. Fang and M. G. Basanez, Identifying host species driving transmission of schistosomiasis japonica, a multihost parasite system, in China, Proceedings of the National Academy of Sciences, 110 (2013), 11457-11462. http://www.pnas.org/content/110/28/11457.short |
[15] |
C. Shan, X. Zhou and H. Zhu, The Dynamics of Growing Islets and Transmission of Schistosomiasis Japonica in the Yangtze River, Bulletin of Mathematical Biology, 76 (2014), 1194-1217.
doi: 10.1007/s11538-014-9961-7. |
[16] |
H. L. Smith, Cooperative systems of differential equations with concave nonlinearities, Nonlinear Analysis: Theory, Methods and Applications, 10 (1986), 1037-1052. http://www.sciencedirect.com/science/article/pii/0362546X86900878 |
[17] |
H. L. Smith and P. Waltman, Perturbation of a globally stable steady state, Proceedings of the American Mathematical Society, 127 (1999), 447-453.
doi: 10.1090/S0002-9939-99-04768-1. |
[18] |
P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[19] |
W. Wang and X. Q. Zhao, An epidemic model in a patchy environment, Mathematical Biosciences, 190 (2004), 97-112.
doi: 10.1016/j.mbs.2002.11.001. |
[20] |
World Health Organization, http://www.who.int/features/factfiles/schistosomiasis/en/. |
[21] |
M. J. Woolhouse, On the application of mathematical models of schistosome transmission dynamics. II. Control, Acta Tropica, 50 (1992), 189-204. http://www.sciencedirect.com/science/article/pii/0001706X9290076A |
[22] |
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, Parasitology International, 62 (2013), 118-126. http://www.sciencedirect.com/science/article/pii/S1383576912001341 |
[23] |
P. Zhang, Z. Feng and F. Milner, A schistosomiasis model with an age-structure in human hosts and its application to treatment strategies, Mathematical Biosciences, 205 (2007), 83-107.
doi: 10.1016/j.mbs.2006.06.006. |
[24] |
R. Zhao and F. A. Milner, A mathematical model of Schistosoma mansoni in Biomphalaria glabrata with control strategies, Bulletin of Mathematical Biology, 70 (2008), 1886-1905.
doi: 10.1007/s11538-008-9330-5. |
[25] |
Y. B. Zhou, S. Liang and Q. W. Jiang, Factors impacting on progress towards elimination of transmission of schistosomiasis japonica in China, Parasit Vectors, 5 (2012), 257-275. http://www.biomedcentral.com/content/pdf/1756-3305-5-275.pdf |
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