A Mathematical Model for Schistosomiasis Japonicum with Harmless Delay

Huahua Cao, Shujing Gao, Xiangyu Zhang, Youquan Luo

College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China.

DOI: 10.4236/am.2014.517268                

Abstract

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

Stability, Schistosomiasis Japonicum, Time Delay

Conflicts of Interest

The authors declare no conflicts of interest.

References

[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.