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

TL;DR

This paper develops and analyzes a mathematical model for cholera that incorporates vaccination, demonstrating its ability to describe the largest outbreak in history and highlighting the importance of early vaccination.

Contribution

The paper introduces a new cholera model with vaccination, proves its mathematical properties, and applies it to the 2017-2018 Yemen outbreak to assess vaccination timing effects.

Findings

Model accurately describes the Yemen cholera outbreak.

Early vaccination could have significantly reduced infections.

The model's stability analysis supports its epidemiological relevance.

Abstract

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 2275 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.