An optimal control problem for carrier dependent diseases.

In developing countries, several diseases spread in human population due to the abundance of houseflies (a kind of carrier). The main reason behind the spread of these diseases is the lack of awareness among peoples regarding the sanitation practices and economic constraints. To understand the dynamics of the spread and control of these diseases, in this paper, we propose a mathematical model by considering logistic growth of houseflies. In the model formulation, it is assumed that houseflies transport the bacteria responsible for the disease transmission from the environment to the edibles of human population. To reduce the density of houseflies and number of infected individuals, an optimization problem is also formulated and analyzed. Numerical simulations are performed to support analytically obtained results.