Mathematical Modelling of Infectious Diseases

In this book, I have presented a mathematical epidemiology model of cholera using differential equations. I have formulated the optimal control problem with four time-dependent control functions namely vaccination, personal hygiene, treatment, and sanitation.I have also applied forward-backward sweep method and fourth order Runge-Kutta method to solve the initial boundary problem. My numerical simulations suggest that the mathematical model with controls shows a decrease in the amount of environmental vibrios in both high and low concentration as compared to the model without opcontrols. A similar observation was made in model that has controls where there was a significant decrease in the number of infected individuals which affected both the susceptible and recovery population. All numerical simulations in this book were performed using the MATLAB software.