### Abstract

In this paper, we propose and analyse a mathematical model that describes the dynamics of Cholera. The main aim of this model is to investigate the role of houseflies in the transmission of Cholera. Our analysis showed that the disease free equilibrium is globally asymptotically stable whenever the basic reproduction number is less than unity; and unstable otherwise; and our model posses only one endemic equilibrium which is locally asymptotically stable whenever basic reproduction number is greater than unity. Our sensitivity analysis showed that the basic reproduction number is very sensitive to ingesting vibrios rate from aquatic environment by vectors, the rate of contribution to V. cholera in the aquatic environment and the death rate of vector and death rate of vibrios in aquatic environment which indicates that the vector (i.e. the houseflies) play a very important role in the transmission procedure.Numerically, we shown that the rate of water contamination by infectious people shedding V. cholera into the environment has no impact in the infection because it depends on both bacteria shedding of the infected individuals and the level of sanitation in the environment and since the environment is safe, then it is obviously has no effects. In addition, if the contact rate of vectors with contaminated water is high in the presence of increased contribution of each infected vector to the aquatic environment then cholera will persist in the population. Therefore, to obtain a significant and effective control, the contribution of each infected vector to the aquatic environment and the rate of exposure to contaminated water must be reduced.

Original language | English |
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Article number | 31 |

Journal | Communications in Mathematical Biology and Neuroscience |

Volume | 2019 |

DOIs | |

Publication status | Published - Jan 1 2019 |

Externally published | Yes |

### Keywords

- Basic reproduction number
- Bifurcation analysis
- Cholera model
- Sensitivity analysis

### ASJC Scopus subject areas

- Neuroscience(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Applied Mathematics

## Cite this

*Communications in Mathematical Biology and Neuroscience*,

*2019*, [31]. https://doi.org/10.28919/cmbn/4281