### AIMS Mathematics

2018, Issue 4: 448-463. doi: 10.3934/Math.2018.4.448
Research article Topical Sections

# A cholera mathematical model with vaccination and the biggest outbreak of world’s history

• Received: 07 July 2018 Accepted: 11 October 2018 Published: 19 October 2018
• We propose and analyse a mathematical model for cholera considering vaccination. We show that the model is epidemiologically and mathematically well posed and prove the existence and uniqueness of disease-free and endemic equilibrium points. The basic reproduction number is determined and the local asymptotic stability of equilibria is studied. The biggest cholera outbreak of world's history began on 27th April 2017, in Yemen. Between 27th April 2017 and 15th April 2018 there were 2 275 deaths due to this epidemic. A vaccination campaign began on 6th May 2018 and ended on 15th May 2018. We show that our model is able to describe well this outbreak. Moreover, we prove that the number of infected individuals would have been much lower provided the vaccination campaign had begun earlier.

Citation: Ana P. Lemos-Paião, Cristiana J. Silva, Delfim F. M. Torres. A cholera mathematical model with vaccination and the biggest outbreak of world’s history[J]. AIMS Mathematics, 2018, 3(4): 448-463. doi: 10.3934/Math.2018.4.448

### Related Papers:

• We propose and analyse a mathematical model for cholera considering vaccination. We show that the model is epidemiologically and mathematically well posed and prove the existence and uniqueness of disease-free and endemic equilibrium points. The basic reproduction number is determined and the local asymptotic stability of equilibria is studied. The biggest cholera outbreak of world's history began on 27th April 2017, in Yemen. Between 27th April 2017 and 15th April 2018 there were 2 275 deaths due to this epidemic. A vaccination campaign began on 6th May 2018 and ended on 15th May 2018. We show that our model is able to describe well this outbreak. Moreover, we prove that the number of infected individuals would have been much lower provided the vaccination campaign had begun earlier.
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