Mathematical analysis of the role of repeated exposure on malaria transmission dynamics

被引：64

作者：

Niger A.M. ^{[1
]}

Gumel A.B. ^{[1
]}

机构：

[1] Department of Mathematics, University of Manitoba, Winnipeg

来源：

Differential Equations and Dynamical Systems | 2008年 / 16卷 / 3期

关键词：

Backward bifurcation; Endemic equilibrium; Global asymptotic stability; Malaria transmission dynamics; Repeated exposure; Simulations;

D O I：

10.1007/s12591-008-0015-1

中图分类号：

学科分类号：

摘要：

This paper presents a deterministic model for assessing the role of repeated exposure on the transmission dynamics of malaria in a human population. Rigorous qualitative analysis of the model, which incorporates three immunity stages, reveals the presence of the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction threshold is less than unity. This phenomenon persists regardless of whether the standard or mass action incidence is used to model the transmission dynamics. It is further shown that the region for backward bifurcation increases with decreasing average life span of mosquitoes. Numerical simulations suggest that this region increases with increasing rate of re-infection of first-time infected individuals. In the absence of repeated exposure (re-infection) and loss of infection-acquired immunity, it is shown, using a non-linear Lyapunov function, that the resulting model with mass action incidence has a globally-asymptotically stable endemic equilibrium when the reproduction threshold exceeds unity. © 2008 Foundation for Scientific Research and Technological Innovation.

引用

页码：251 / 287

页数：36

共 40 条

[1]

Aneke S.J., Mathematical modelling of drug resistant malaria parasites and vector population, Mathematical Methods in the Applied Sciences, 90, pp. 385-396, (2002)

[2]

Aron J.L., Acquired immunity dependent upon exposure in an SIRS epidemic model, Math. Biosci., 88, pp. 37-47, (1988)

[3]

Aron J.L., Mathematical modelling of immunity to malaria, Math. Biosci., 90, pp. 385-396, (1988)

[4]

Baird J., Resurgent malaria at the millennium: control strategies in crisis, Drugs, 59, (2000)

[5]

Bowman C., Gumel A.B., van den Driessche P., Wu J., Zhu H., A mathematical model for assessing control strategies against West Nile virus, Bull. Of Math. Bio., 67, pp. 1107-1133, (2005)

[6]

Carr J., Applications Centre Manifold Theory, (1981)

[7]

Castillo-Chavez C., Song B., Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 2, pp. 361-404, (2004)

[8]

Castillo-Chavez C., Cooke K., Huang W., Levin S.A., Results on the dynamics for models for the sexual transmission of the human immunodeficiency virus, Appl. Math. Letters, 2, pp. 327-331, (1989)

[9]

Castillo-Chavez C., Cooke K., Huang W., Levin S.A., The role of long incubation periods in the dynamics of HIV/AIDS, Multiple group models, In Carlos Castillo-Chavez, ed, 83, pp. 200-217, (1989)

[10]

Chitnis N., Cushing J.M., Hyman J.M., Bifurcation analysis of a mathematical model for malaria transmission, SIAM J. Of Appl. Math., 67, pp. 24-45, (2006)

← 1 2 3 4 →