Abstract
A simple mathematical model for cholera is presented using a system of ordinary differential equations. Comprehensive analysis of the important mathematical features of the model is carried out. The disease-free and endemic equilibria are obtained and their local stability investigated. We use the centre manifold theory to show the stability of the endemic equilibrium and suitable Lyapunov function for its global stability. Qualitative analysis of the model including positivity and boundedness of solutions are also presented. The cholera model is numerically analysed using published data to explore the effects of the recovery rate, rate of exposure to contaminated water and contribution of infected individuals to the population of Vibrio cholerae in the aquatic environment on the cumulative number of cholera infected individuals. The results demonstrate that proper management of the diseases will reduce the burden of cholera in endemic areas.
| Original language | English |
|---|---|
| Pages (from-to) | 253-265 |
| Number of pages | 13 |
| Journal | Differential Equations and Dynamical Systems |
| Volume | 19 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Jul 2011 |
| Externally published | Yes |
Keywords
- Cholera model
- Equilibria
- Reproduction number
- Stability
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
