2014/01/28 by Helena Sofia Rodrigues, Rodrigues, Helena Sofia
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #34H05 #92B05 #92D30 #93C15 #93C95 #COVID-19 epidemiological studies #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC) #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1401.7390
openalex publication_date 2014/01/28 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The relationship between epidemiology, mathematical modeling and\ncomputational tools allows to build and test theories on the development and\nbattling of a disease. This PhD thesis is motivated by the study of\nepidemiological models applied to infectious diseases in an Optimal Control\nperspective, giving particular relevance to Dengue. Dengue is a subtropical and\ntropical disease transmitted by mosquitoes, that affects about 100 million\npeople per year and is considered by the World Health Organization a major\nconcern for public health. The mathematical models developed and tested in this\nwork, are based on ordinary differential equations that describe the dynamics\nunderlying the disease, including the interaction between humans and\nmosquitoes. An analytical study is made related to equilibrium points, their\nstability and basic reproduction number. The spreading of Dengue can be\nattenuated through measures to control the transmission vector, such as the use\nof specific insecticides and educational campaigns. Since the development of a\npotential vaccine has been a recent global bet, models based on the simulation\nof a hypothetical vaccination process in a population are proposed. Based on\nOptimal Control theory, we have analyzed the optimal strategies for using these\ncontrols, and respective impact on the reduction/eradication of the disease\nduring an outbreak in the population, considering a bioeconomic approach. The\nformulated problems are numerically solved using direct and indirect methods.\nThe first discretize the problem turning it into a nonlinear optimization\nproblem. Indirect methods use the Pontryagin Maximum Principle as a necessary\ncondition to find the optimal curve for the respective control. In these two\nstrategies several numerical software packages are used.\n