Mathematical modelling of the transmission dynamics of cholera

Abstract

In the present research, analysis of a mathematical model of cholera which includes vaccinated individuals was performed. It is proved that if control reproduction number RC < 1, a suitable Lyapunov function is used to establish the global stability of the disease free equilibrium, which means that the disease will die out over time. Global stability analysis shows that when RC < 1, there exists at least one endemic equilibrium. If RC > 1, there exists a unique endemic equilibrium which is globally asymptotically stable. Sensitivity analysis of parameters indicates that the ingestion rate of Vibrio cholerae by humans due to contact with contaminated sources greatly influences RC followed by rate of natural loss of Vibrio cholerae, B. An extension of the model to include possible optimal control strategies targeting to reduce such as hygiene and improved sanitation are considered. Numerical simulations indicate that the number of infected individuals reduces when controls are in place to reduce ingestion of cholera pathogens, which shows that control measures are effective.