Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 251-287 |
| Number of pages | 37 |
| Journal | Differential Equations and Dynamical Systems |
| Volume | 16 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jul 2008 |
| Externally published | Yes |
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Keywords
- Backward bifurcation
- Endemic equilibrium
- Global asymptotic stability
- Malaria transmission dynamics
- Repeated exposure
- Simulations
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Mathematical analysis of the role of repeated exposure on malaria transmission dynamics. / Niger, Ashrafi M.; Gumel, Abba.
In: Differential Equations and Dynamical Systems, Vol. 16, No. 3, 07.2008, p. 251-287.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Mathematical analysis of the role of repeated exposure on malaria transmission dynamics
AU - Niger, Ashrafi M.
AU - Gumel, Abba
PY - 2008/7
Y1 - 2008/7
N2 - 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.
AB - 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.
KW - Backward bifurcation
KW - Endemic equilibrium
KW - Global asymptotic stability
KW - Malaria transmission dynamics
KW - Repeated exposure
KW - Simulations
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UR - http://www.scopus.com/inward/citedby.url?scp=80054854637&partnerID=8YFLogxK
U2 - 10.1007/s12591-008-0015-1
DO - 10.1007/s12591-008-0015-1
M3 - Article
AN - SCOPUS:80054854637
VL - 16
SP - 251
EP - 287
JO - Differential Equations and Dynamical Systems
JF - Differential Equations and Dynamical Systems
SN - 0971-3514
IS - 3
ER -