Analysis of the effect of a medical treatment in a SIC model

In this work, we consider an epidemic model with indirect transmission of the disease. We apply a medical treatment as a control strategy when the disease is not eradicated. The effect of this treatment is to reduce the amount of bacteria in the environment. We analyze two assumptions and compare their effect on the evolution of the model behavior: a medical treatment on a constant percentage of the infected population applied either at all times or periodically. Finally, an optimal control strategy is analyzed to minimize the cost of the control application. We use a numerical simulation to clarify and discuss the goodness of the obtained results.