Mathematical assessment of the role of non-linear birth and maturation delay in the population dynamics of the malaria vector

Applied Mathematics and Computation

Volumn 217, Issue 7, 2010, Pages 3286-3313

  Ngwa, Gideon A ^a   Niger, Ashrafi M ^b   Gumel, Abba B ^b  

^a UNIVERSITY OF BUEA   (Cameroon)

^b UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Birth rate function; Hopf bifurcation; Maturation delay; Vector population dynamics

Indexed keywords

ASYMPTOTICALLY STABLE; BIRTH RATES; DIFFERENTIAL EQUATION MODEL; ECOLOGICAL FEATURES; LIMIT CYCLE; LOGISTIC GROWTH; LOGISTIC GROWTH MODEL; MATURATION DELAY; NON-LINEAR; NON-TRIVIAL EQUILIBRIUM; NUMERICAL SIMULATION; OSCILLATING SOLUTIONS; SUSTAINED OSCILLATIONS; TRIVIAL EQUILIBRIUM; VERHULST;

ASYMPTOTIC ANALYSIS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; DYNAMICS; ECOLOGY; FRUITS; HOPF BIFURCATION; POPULATION DYNAMICS; VECTORS;

POPULATION STATISTICS;

EID: 78049242009     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.08.062     Document Type: Article

References (20)

1. Brännström, and D.J.T. Sumpter The role of competition and clustering in population dynamics Proc. R. Soc. B. 272 2005 2065 2072
2. C. Celik The stability and Hopf bifurcation for a predator-prey system with time delay Chaos. Soliton. Fract. 37 2008 87 99
3. K. Cooke, P. van den Driessche, and X. Zou Interaction of maturation delay and nonlinear birth in population and epidemic models J. Math. Biol. 39 1999 332 352
4. + T-cells Math. Biosci. 165 2000 27 39
5. J. Dieuonné Foundations of Modern Analysis 1969 Academic Press London
6. J. Forde, and P. Nelson Applications of Strum sequences to bifurcation analysis of delay differential equation models J. Math. Anal. Appl. 300 2004 273 284
7. J.K. Hale Ordinary Differential Equations 1969 John Wiley and Sons New York
8. H.M. Giles, and D.A. Warrel Bruce-Chwatt's Essential Malariology third ed 1993 Heinemann Medical Books Portsmouth, NH
9. W.M. Hirsch, H. Hanisch, and J.P. Gabriel Differential equation models for some parasitic infections; methods for the study of asymptotic behaviour, Comm. Pure Appl. Math. Vector fields vol. 38 1985 Springer-Verlag New York pp. 733-753
10. S.R.-J. Jang Contest and scramble competition with a dynamic resource Nonlinear Anal. 63 2005 109 118
11. Y. Kuang Delay Differential Equations with Applications in Population Dynamics 1993 Academic Press Boston
12. J.E. Marsden, and M.F. McCracken The Hopf Bifurcation and its Applications 1976 Springer New York
13. J. Maynard-Smith, and M. Slatkin The stability of predator-prey systems Ecology 54 1973 384 391
14. P.J. McCall, and W.K. David Learning and memory in disease vectors. Research Update Trends Parasitol 18 2002 429 433
15. G.A. Ngwa On the population dynamics of the malaria vector Bull. Math. Biol. 68 2005 2161 2189
16. T. Porphyre, D.J. Bicout, and P. Sabatier Modelling the abundance of mosquito vectors versus flooding dynamics Ecol. Model 183 2005 173 181
17. S. Ruan, J. Wei, On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion, IMA, J. Math. Appl. Med. Biol., 2001.
18. H.R. Thieme Persistence under relaxed point dissipativity with application to an epidemic model SIAM J. Math. Anal. 24 1993 407 435
19. Y. Song, M. Han, and J. Wei Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays Physica D 200 2005 185 204
20. C. Sun, Y. Lin, and M. Han Stability and Hopf bifurcation for an epidemic disease model with delay Chaos. Soliton. Fract. 30 2006 204 216