Abstract
A new two-group deterministic model for Chlamydia trachomatis, which stratifies the entire population based on risk of acquiring or transmitting infection, is designed and analyzed to gain insight into its transmission dynamics. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium (DFE) co-exists with one or more stable endemic equilibria when the associated reproduction number is less than unity. Unlike in some of the earlier modeling studies on Chlamydia transmission dynamics in a population, this study shows that the backward bifurcation phenomenon persists even if individuals who recovered from Chlamydia infection do not get re-infected. However, it is shown that the phenomenon can be removed if all the susceptible individuals are equally likely to acquire infection (i.e., for the case where the susceptible male and female populations are not stratified according to risk of acquiring infection). In such a case, the DFE of the resulting (reduced) model is globally-asymptotically stable when the associated reproduction number is less than unity and no re-infection of recovered individuals occurs. Thus, this study shows that stratifying the two-sex Chlamydia transmission model, presented in [1], according to the risk of acquiring or transmitting infection induces the phenomenon of backward bifurcation regardless of whether or not the re-infection of recovered individuals occurs.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3653-3673 |
| Number of pages | 21 |
| Journal | Applied Mathematical Modelling |
| Volume | 35 |
| Issue number | 8 |
| DOIs | |
| State | Published - Aug 2011 |
| Externally published | Yes |
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Keywords
- Backward bifurcation
- Chlamydia
- Equilibria
- Low- and high-risk groups
- Re-infection
- Stability
ASJC Scopus subject areas
- Applied Mathematics
- Modeling and Simulation
Cite this
Mathematical study of a risk-structured two-group model for Chlamydia transmission dynamics. / Sharomi, O.; Gumel, Abba.
In: Applied Mathematical Modelling, Vol. 35, No. 8, 08.2011, p. 3653-3673.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Mathematical study of a risk-structured two-group model for Chlamydia transmission dynamics
AU - Sharomi, O.
AU - Gumel, Abba
PY - 2011/8
Y1 - 2011/8
N2 - A new two-group deterministic model for Chlamydia trachomatis, which stratifies the entire population based on risk of acquiring or transmitting infection, is designed and analyzed to gain insight into its transmission dynamics. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium (DFE) co-exists with one or more stable endemic equilibria when the associated reproduction number is less than unity. Unlike in some of the earlier modeling studies on Chlamydia transmission dynamics in a population, this study shows that the backward bifurcation phenomenon persists even if individuals who recovered from Chlamydia infection do not get re-infected. However, it is shown that the phenomenon can be removed if all the susceptible individuals are equally likely to acquire infection (i.e., for the case where the susceptible male and female populations are not stratified according to risk of acquiring infection). In such a case, the DFE of the resulting (reduced) model is globally-asymptotically stable when the associated reproduction number is less than unity and no re-infection of recovered individuals occurs. Thus, this study shows that stratifying the two-sex Chlamydia transmission model, presented in [1], according to the risk of acquiring or transmitting infection induces the phenomenon of backward bifurcation regardless of whether or not the re-infection of recovered individuals occurs.
AB - A new two-group deterministic model for Chlamydia trachomatis, which stratifies the entire population based on risk of acquiring or transmitting infection, is designed and analyzed to gain insight into its transmission dynamics. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium (DFE) co-exists with one or more stable endemic equilibria when the associated reproduction number is less than unity. Unlike in some of the earlier modeling studies on Chlamydia transmission dynamics in a population, this study shows that the backward bifurcation phenomenon persists even if individuals who recovered from Chlamydia infection do not get re-infected. However, it is shown that the phenomenon can be removed if all the susceptible individuals are equally likely to acquire infection (i.e., for the case where the susceptible male and female populations are not stratified according to risk of acquiring infection). In such a case, the DFE of the resulting (reduced) model is globally-asymptotically stable when the associated reproduction number is less than unity and no re-infection of recovered individuals occurs. Thus, this study shows that stratifying the two-sex Chlamydia transmission model, presented in [1], according to the risk of acquiring or transmitting infection induces the phenomenon of backward bifurcation regardless of whether or not the re-infection of recovered individuals occurs.
KW - Backward bifurcation
KW - Chlamydia
KW - Equilibria
KW - Low- and high-risk groups
KW - Re-infection
KW - Stability
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U2 - 10.1016/j.apm.2010.12.006
DO - 10.1016/j.apm.2010.12.006
M3 - Article
VL - 35
SP - 3653
EP - 3673
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
SN - 0307-904X
IS - 8
ER -