Asian Journal of Pure and Applied Mathematics

Cholera is a disease caused by a bacteria called Vibrio cholera. Cholera is common in rural areas, where there is poor personal hygiene, poor environmental sanitation, insufficient health facilities, and inadequate access to clean water and safe food. Cholera remains a global health challenge with its frequent outbreaks. This study aims at modifying a mathematical model to understand the progression dynamics of the disease and intervention strategies. The study tends to determine the effectiveness of awareness campaigns and compliance to (personal hygiene, environmental sanitation, access to clean water and food, alongside regular medical check-up), vaccination, treatment, or direct observed therapy shortcuts (DOTS) as preventive measures against cholera progression in the population. The analysis of this model reveals that there exists a region where the model is mathematically and epidemiologically well posed because its solutions were positive and bounded. The next-generation matrix approach was used to investigate the effective reproduction number R_e . Stability analysis of the cholera model shows that the disease-free equilibrium is both locally and globally asymptotically stable when R_e < 1 . This means that when R_e is less than 1 R_e < 1 the disease continues to die out due to time. The endemic equilibrium shows that the disease exists in the population when R_{e > 1}. In an attempt to examine the effect of some parameters of the dynamics of the disease, sensitivity analysis is employed. Finally, numerical simulations are also performed to verify the analytic results. The simulation study revealed that the increase in awareness campaigns and compliance to (personal hygiene, environmental sanitation, access to clean water and food, alongside regular medical check-up), vaccination, and timely treatment such as direct observed therapy short-cut (DOTS) is necessary to achieve a significant and effective control of cholera in the environment.