We present an application of optimal control theory to Dengue epidemics. This
epidemiologic disease is an important theme in tropical countries due to the
growing number of infected individuals. The dynamic model is described by a set
of nonlinear ordinary differential equations, that depend on the dynamic of the
Dengue mosquito, the number of infected individuals, and the people's
motivation to combat the mosquito. The cost functional depends not only on the
costs of medical treatment of the infected people but also on the costs related
to educational and sanitary campaigns. Two approaches to solve the problem are
considered: one using optimal control theory, another one by discretizing first
the problem and then solving it with nonlinear programming. The results
obtained with OC-ODE and IPOPT solvers are given and discussed. We observe that
with current computational tools it is easy to obtain, in an efficient way,
better solutions to Dengue problems, leading to a decrease of infected
mosquitoes and individuals in less time and with lower costs.Comment: Submitted to Mathematical and Computer Modelling 25/Oct/2009;
accepted for publication, after revision, 22/June/201
