Stability analysis of a schistosomiasis model with delays

Advances in Difference Equations

Volumn 2013, Issue , 2013, Pages

  Guiro, Aboudramane ^a   Ouaro, Stanislas ^b   Traore, Ali ^b  

^a Polytechnic University of Bobo Dioulasso   (Burkina Faso)

^b UNIVERSITÉ DE OUAGADOUGOU   (Burkina Faso)

Author keywords

Delays; Global stability; Lyapunov function; Mathematical model; Reproduction number; Schistosomiasis

Indexed keywords

EID: 84897888211     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2013-303     Document Type: Article

References (20)

1. World Health Organization. http://www.who.int/schistosomiasis/en/. Available on May, 2012
2. Allen, EJ, Victory, HD: Modelling and simulation of a schistosomiasis infection with biological control. Acta Trop. 87, 251-267 (2003)
3. Anderson, RM, May, RM: Prevalence of schistosome infections within molluscan populations: observed patterns and theoretical predictions. Parasitology 79, 63-94 (1979)
4. Anderson, RM, May, RM: Helminth infections of humans: mathematical models, population dynamics, and control. Adv. Parasitol. 24, 1-101 (1985)
5. Cohen, JE: Mathematical models of schistosomiasis. Annu. Rev. Ecol. Syst. 8, 209-233 (1977)
6. Feng, Z, Li, C, Milner, FA: Schistosomiasis models with density dependence and age of infection in snail dynamics. Math. Biosci. 177-178, 271-286 (2002)
7. Feng, Z, Li, C, Milner, FA: Schistosomiasis models with two migrating human groups. Math. Comput. Model. 41(11-12), 1213-1230 (2005)
8. Feng, Z, Milner, FA: A new mathematical model of schistosomiasis. In: Mathematical Models in Medical and Health Science (Nashville, TN, 1997). Innov. Appl. Math., pp. 117-128. Vanderbilt Univ. Press, Nashville (1998)
9. Macdonald, G: The dynamics of helminth infections, with special reference to schistosomiasis. Trans. R. Soc. Trop. Med. Hyg. 59, 489-506 (1965)
10. Nasell, I: A hybrid model of schistosomiasis with snail latency. Theor. Popul. Biol. 10, 47-69 (1976)
11. Yang, Y, Xiao, D: A mathematical model with delays for schistosomiasis. Chin. Ann. Math., Ser. B 31(4), 433-446 (2010)
12. Woolhouse, MEJ: On the application of mathematical models of schistosome transmission dynamics. I. Natural transmission. Acta Trop. 49, 1241-1270 (1991)
13. Woolhouse, MEJ: On the application of mathematical models of schistosome transmission dynamics. II. Control. Acta Trop. 50, 189-204 (1992)
14. Hale, JK, Verduyn Lunel, S: Introduction to Functional Differential Equations. Springer, Berlin (1993)
15. Bony, JM: Principe du maximum, inégalite de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés. Ann. Inst. Fourier (Grenoble) 19(1), 277-304 (1969)
16. Birkhoff, G, Rota, GC: Ordinary Differential Equations. Ginn, Boston (1982)
17. Van den Driesche, P, Watmough, J: Reproduction numbers and subthreshold endemic equilibria for the compartmental models of disease transmission. Math. Biosci. 180, 29-48 (2002)
18. Anderson, RM, May, RM: Infectious Disease of Human, pp. 17-19. Oxford University Press, Oxford (1991)
19. LaSalle, JP: The Stability of Dynamical Systems. SIAM, Philadelphia (1976)
20. Feng, Z, Milner, FA, Eppert, A, Minchella, DJ: Estimation of parameters governing the transmission dynamics of schistosomes. Appl. Math. Lett. 17(10), 1105-1112 (2004)