Read full paper at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50913#.VFB-HlfHRK0
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50913#.VFB-HlfHRK0
Author(s)
From the lifecycle of schistosome, the phenomenon of
time delay is widespread. In this paper, a two-dimensional system is
studied that incorporates two time delays which are the incubation
period of human and snail, respectively. Our purpose is to demonstrate
that the time delays are harmless for stability of equilibria of the
system. Further, sufficient conditions of stability of equilibria are
obtained.
KEYWORDS
Cite this paper
Cao, H. , Gao, S. , Zhang, X. and Luo, Y. (2014) A
Mathematical Model for Schistosomiasis Japonicum with Harmless Delay. Applied Mathematics, 5, 2807-2814. doi: 10.4236/am.2014.517268.
| [1] |
Anderson, R.M. and May, R.M.
(1985) Helminth Infections of Humans Mathematical Models, Population
Dynamics, and Control. Advances in Parasitology, 24, 1-101. http://dx.doi.org/10.1016/S0065-308X(08)60561-8 |
| [2] | Barbour, A.D. (1996) Modeling the Transmission of Schistosomiasis: An Introductory View. The American Journal of Tropical Medicine and Hygiene, 55, 135-143. |
| [3] |
Woolhouse, M.E. (1991) On the
Application of Mathematical Models of Schistosome Transmission Dynamics.
I. Natural Transmission. Acta Tropica, 49, 241-270. http://dx.doi.org/10.1016/0001-706X(91)90077-W |
| [4] |
Yang, H.M. (2003) Comparison
between Schistosomiasis Transmission Modeling Considering Acquired
Immunity and Age-Structured Contact Pattern with Infested Water.
Mathematical Biosciences, 184, 1-26.
http://dx.doi.org/10.1016/S0025-5564(03)00045-2 |
| [5] |
Das, P., Mukherjee, D. and
Sarkar, A.K. (2006) A Study of Schistosome Transmission Dynamics and Its
Control. Journal of Biological Systems, 14, 295-302. http://dx.doi.org/10.1142/S0218339006001799 |
| [6] |
Chiyaka, E.T. and Garira, W.
(2009) Mathematical Analysis of the Transmission Dynamics of
Schistosomiasis in the Human-Snail Host. Journal of Biological Systems,
17, 397-423. http://dx.doi.org/10.1142/S0218339009002910 |
| [7] | Qi, L.X. and Cui, J. (2012) Modeling the Schistosomiasis on the Islets in Nanjing. International Journal of Biomathematics, 5, 189-205. |
| [8] |
Macdonald, G. (1965) The
Dynamics of Helminth Infections, with Special Reference to Schistosomes.
Transactions of the Royal Society of Tropical Medicine and Hygiene, 59,
489-506. http://dx.doi.org/10.1016/0035-9203(65)90152-5 |
| [9] | Hale, J.K. (1976) Theory of Functional Differential Equations. Springer, New York. eww141029lx |
评论
发表评论