부산대학교 도서관

In this paper, a mathematical model is proposed to study the spread of pathogen-induced cholera disease and its control by vaccination. It is assumed in the model that cholera vaccine-induced immunity has a temporary effect and imperfect dose of vaccine does not protect the recipients. From the model, a threshold for the disease dynamics the vaccinated reproduction number RVR0RV<1RV<1RV>1RV>1 is derived, which is compared with the basic reproduction number RVR0RV<1RV<1RV>1RV>1 for without vaccination system. It has been shown that the disease will tend to extinction when RVR0RV<1RV<1RV>1RV>1. The disease-free equilibrium point is asymptotically stable when RVR0RV<1RV<1RV>1RV>1 and unstable when RVR0RV<1RV<1RV>1RV>1. Further, we have also proved that a unique endemic equilibrium point exists when RVR0RV<1RV<1RV>1RV>1. Also used Pontryagin Minimum Principle to find out the optimal rate of vaccination and death rate of pathogen population for the control of cholera disease. Sensitivity analysis of system parameters is performed to show their relative importance to disease transmission and prevalence. Finally, numerical simulations are provided to support the analytical results.