An epidemiological model for direct and indirect transmission of typhoid fever

The modified SIS epidemiological model considers the usual direct transmission (short cycle) and indirect transmission (long cycle) of typhoid fever. Thresholds are determined, and the equilibrium points are shown to be globally stable. Local stability of the equilibrium points is shown in the corresponding model with vaccines. After estimating parameters using current statistical data for typhoid fever in Chile, computer simulations are used to obtain the numerical behavior of this disease and to estimate the effect of several control policies.