### Abstract

A new deterministic model for assessing the role of age-structure on the transmission dynamics of malaria in a community is designed. Rigorous qualitative analysis of the model reveals that it undergoes the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model co-exists with a stable endemic equilibrium when the associated reproduction number (denoted by R0) is less than unity. It is shown that the backward bifurcation phenomenon is caused by the malaria-induced mortality in humans. A special case of the model is shown to have a unique endemic equilibrium whenever the associated reproduction threshold exceeds unity. Further analyses reveal that adding age-structure to a basic model for malaria transmission in a community does not alter the qualitative dynamics of the basic model, with respect to the existence and asymptotic stability of the associated equilibria and the backward bifurcation property of the model. Numerical simulations of the model show that the cumulative number of new cases of infection and malaria-induced mortality increase with increasing average lifespan and birth rate of mosquitoes.

Original language | English (US) |
---|---|

Pages (from-to) | 80-94 |

Number of pages | 15 |

Journal | Mathematical Biosciences |

Volume | 247 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2014 |

Externally published | Yes |

### Fingerprint

### Keywords

- Age-structure
- Equilibria
- Malaria
- Reproduction number
- Stability

### ASJC Scopus subject areas

- Medicine(all)
- Immunology and Microbiology(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)
- Modeling and Simulation
- Statistics and Probability
- Applied Mathematics

### Cite this

*Mathematical Biosciences*,

*247*(1), 80-94. https://doi.org/10.1016/j.mbs.2013.10.011

**Mathematical analysis of an age-structured model for malaria transmission dynamics.** / Forouzannia, Farinaz; Gumel, Abba.

Research output: Contribution to journal › Article

*Mathematical Biosciences*, vol. 247, no. 1, pp. 80-94. https://doi.org/10.1016/j.mbs.2013.10.011

}

TY - JOUR

T1 - Mathematical analysis of an age-structured model for malaria transmission dynamics

AU - Forouzannia, Farinaz

AU - Gumel, Abba

PY - 2014/1

Y1 - 2014/1

N2 - A new deterministic model for assessing the role of age-structure on the transmission dynamics of malaria in a community is designed. Rigorous qualitative analysis of the model reveals that it undergoes the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model co-exists with a stable endemic equilibrium when the associated reproduction number (denoted by R0) is less than unity. It is shown that the backward bifurcation phenomenon is caused by the malaria-induced mortality in humans. A special case of the model is shown to have a unique endemic equilibrium whenever the associated reproduction threshold exceeds unity. Further analyses reveal that adding age-structure to a basic model for malaria transmission in a community does not alter the qualitative dynamics of the basic model, with respect to the existence and asymptotic stability of the associated equilibria and the backward bifurcation property of the model. Numerical simulations of the model show that the cumulative number of new cases of infection and malaria-induced mortality increase with increasing average lifespan and birth rate of mosquitoes.

AB - A new deterministic model for assessing the role of age-structure on the transmission dynamics of malaria in a community is designed. Rigorous qualitative analysis of the model reveals that it undergoes the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model co-exists with a stable endemic equilibrium when the associated reproduction number (denoted by R0) is less than unity. It is shown that the backward bifurcation phenomenon is caused by the malaria-induced mortality in humans. A special case of the model is shown to have a unique endemic equilibrium whenever the associated reproduction threshold exceeds unity. Further analyses reveal that adding age-structure to a basic model for malaria transmission in a community does not alter the qualitative dynamics of the basic model, with respect to the existence and asymptotic stability of the associated equilibria and the backward bifurcation property of the model. Numerical simulations of the model show that the cumulative number of new cases of infection and malaria-induced mortality increase with increasing average lifespan and birth rate of mosquitoes.

KW - Age-structure

KW - Equilibria

KW - Malaria

KW - Reproduction number

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=84892428604&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892428604&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2013.10.011

DO - 10.1016/j.mbs.2013.10.011

M3 - Article

VL - 247

SP - 80

EP - 94

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 1

ER -