### Abstract

A mathematical model is developed to assess the role of gametocytes (the infectious sexual stage of the malaria parasite) in malaria transmission dynamics in a community. The model is rigorously analysed to gain insights into its dynamical features. It is shown that, in the absence of disease-induced mortality, the model has a globally-asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number (denoted by R_{0}), is less than unity. Further, it has a unique endemic equilibrium if R_{0} > 1. The model is extended to incorporate an imperfect vaccine with some assumed therapeutic characteristics. Theoretical analyses of the model with vaccination show that an imperfect malaria vaccine could have negative or positive impact (in reducing disease burden) depending on whether or not a certain threshold (denoted by ∇) is less than unity. Numerical simulations of the vaccination model show that such an imperfect anti-malaria vaccine (with a modest efficacy and coverage rate) can lead to effective disease control if the reproduction threshold (denoted by R_{vac}) of the disease is reasonably small. On the other hand, the disease cannot be effectively controlled using such a vaccine if R_{vac} is high. Finally, it is shown that the average number of days spent in the class of infectious individuals with higher level of gametocyte is critically important to the malaria burden in the community.

Original language | English (US) |
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Pages (from-to) | 63-93 |

Number of pages | 31 |

Journal | Bulletin of mathematical biology |

Volume | 72 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2010 |

Externally published | Yes |

### Keywords

- Equilibria
- Gametocyte
- Malaria
- Stability
- Vaccine

### ASJC Scopus subject areas

- Neuroscience(all)
- Immunology
- Mathematics(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Environmental Science(all)
- Pharmacology
- Agricultural and Biological Sciences(all)
- Computational Theory and Mathematics

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## Cite this

*Bulletin of mathematical biology*,

*72*(1), 63-93. https://doi.org/10.1007/s11538-009-9437-3