Mathematical Model for the Transmission Dynamics of Typhoid Fever Infection with Treatment

In this paper, we develop a mathematical model for the transmission dynamics of typhoid fever infection and applied optimal control strategy for controlling the spread of the disease. We considered two control strategies such as sanitation and treatment of the infected individuals in order to minimize the transmission of the disease so as to maximize the number of susceptible and recovered individuals. We found the necessary conditions for the optimal solution for controlling the spread of the infection using Pontryagin’s Maximum Principle (PMP). Runge-Kutta of order four was used for the numerical simulation to demonstrate the achievability of the control strategies in curtailing the transmission dynamics of the disease