Uma metodologia multiobjetivo para o controle de epidemias através de vacinação impulsiva via algoritmo genético com operador de busca local baseado em aproximação quadrática convexa e validação estocástica

Abstract

Epidemiology is a science that studies the patterns of health and disease and its associated factors in a population. It is based on public health research to identify risks for disease and determining optimal treatment approaches in clinical and preventive medicine. Epidemiology Mathematical models the dynamics of the spread of diseases and allows the quantitative study provide tools to determine effective interventions to control. Mathematical modeling contributes to the design and analysis of epidemiological studies, suggests what are the crucial data to be collected, identifies trends, generates predictions, helps to analyze a possible pre-intervention and determines uncertainties. This dissertation presents a multiobjective methodology to optimize and validate a set of nondominated solutions containing control policies that minimizes the infected population and the cost with the implementation of vaccination campaigns in a finite time horizon. The epidemiological model that governs the system during the optimization is the Susceptible-Infected-Recovered (SIR). The solutions have a number of campaigns, the necessary amount of vaccine in each campaign and the time intervals between each campaign. The optimization engine is the NSGA-II, embedded with a local search to accelerate convergence and improve the quality of solutions, based on the optimization of weighted sums of convex quadratic approximations of the objective functions on a neighborhood of points. The approximation of the Pareto set is validated in an Individual Based Model (IBM) through a Monte Carlo procedure. Information about probability of eradication and confidence intervals are extracted.