Dynamics of Dengue epidemics using optimal control

TL;DR

This paper applies optimal control theory to model and optimize interventions in Dengue epidemics, demonstrating that computational tools can effectively reduce infection rates and associated costs.

Contribution

It introduces a nonlinear dynamic model for Dengue epidemics incorporating control strategies and compares solution methods using optimal control theory and nonlinear programming.

Findings

Optimal control solutions reduce infection and mosquito populations efficiently.

Discretized nonlinear programming approaches are effective for solving epidemic control problems.

Computational tools enable better epidemic management with lower costs.

Abstract

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.