Purpose The COVID-19 pandemic has spread widely through the world. Most countries impose severe intervention measures to contain the spread of the virus, and this worldwide scenario has motivated the development of researches in all areas of knowledge. In this context, this paper presents a study about how intervention measures such as lockdown, partial lockdown, and no-lockdown help to impede the extent of the severe outbreak of COVID-19. Methods Since mathematical models are used to describe population dynamics and the behavior of epidemics, this paper presents a fuzzy approach to describe the behavior of new daily cases of COVID-19 in Brazil based on the p-fuzzy dynamic systems, considering as input variables, the infected population and the environment action. The evaluated output variable is the level of infestation. Results The results of a fuzzy model showed that intervention measures play a crucial role in determining the success of COVID-19 eradication programs, while there is no vaccine available for all the population. The proposed fuzzy model was developed by posing intervention measures and the results showed that to consider partial-lockdown helped to slow down the transmission rates of COVID-19 in the population, however the total lockdown is more effective, while the vaccine is not available. Conclusion Therefore, mathematical models consist of an effective tool to investigate the situation with intervention strategies and estimate the potential benefits and costs of different strategies. The fuzzy model proposed assists government decision-making in order to minimize the economic impacts caused by the pandemic.

A dynamic optimization model for weed infestation control using selective herbicide application in a corn crop system is presented. The seed bank density of the weed population and frequency of dominant or recessive alleles are taken as state variables of the growing cycle. The control variable is taken as the dose-response function. The goal is to reduce herbicide usage, maximize profit in a pre-determined period of time and minimize the environmental impacts caused by excessive use of herbicides. The dynamic optimization model takes into account the decreased herbicide efficacy over time due to weed resistance evolution caused by selective pressure. The dynamic optimization problem involves discrete variables modeled as a nonlinear programming (NLP) problem which was solved by an active set algorithm (ASA) for box-constrained optimization. Numerical simulations for a case study illustrate the management of the Bidens subalternans in a corn crop by selecting a sequence of only one type of herbicide. The results on optimal control discussed here will Communicated by Natasa Krejic.

Agradecimentos Primeiramente a Deus, por estar presente em todos os momentos da minha vida, por guiar os meus caminhos e me conceder sabedoria e saúde. A minha família, em especial a minha mãe Neiva Weber, pelo amor, carinho e apoio incondicional. Ao meu avô (in memoriam), Eugem Albino Weber, que tanto fez por mim. A Profa. Dra. Vilma Alves de Oliveira, ao Prof. Dr. Geraldo Nunes Silva e ao Dr. Décio Karam, pela atenção, compreensão e ensinamentos. Ao meu namorado, Renan Corrêa, que sempre esteve ao meu lado, me apoiando em todos os momentos. A todos os meus amigos e colegas do LAC, pela companhia e amizade ao longo destes anos. Ao Marcos Furlan e ao Pedro Munari, pela atenção e ajuda na realização deste trabalho.

This paper investigates how optimal controle can support weed management by looking specifically at an optimal control problem with an interval-valued objective function based on dynamic optimization. The dynamic optimization problem involves continuous variables modeled as an interval-valued nonlinear programming (INLP) problem. In this study, we converted the INLP problem into into a multi-objective problem using the concept of order relation and solver the multi-objetive problem using the weight method. We solved the resultant NLP problem with an active-set algorithm (ASA) for box-constrained optimization. Finally, we carried out an application in a weed management problem.

Modelagem matemática de problemas agrícolas utilizando programação linearMathematical modeling of agricultural problems using linear programming Resumo Os setores agroindustriais têm buscado o aprimoramento e o conhecimento tecnológico de suasáreas de atuação, devidoà acirrada concorrência no mercado. Esse fato motiva o desenvolvimento de ações que busquem otimizar os processos, tais como produzir alimentos evitando-se desperdício de matéria prima e insumos, ou preservar o meio ambiente, aumentando aárea plantada. A produção agrícola, por sua vez, tem adaptado antigas práticasàs mais atuais tecnologias de produção com o objetivo de aumentar a produtividade, cultivando produtos mais saudáveis e reduzindo impactos ambientais. Assim, o objetivo deste trabalhó e a formulação matemática de problemas utilizando programação linear em problemas agrícolas. Os estudos de caso apresentados envolvem a maximização de lucros de uma produção agrícola e de uma propriedade de reflorestamento. Os problemas foram resolvidos com apoio computacional para obtenção das soluções através do método SIMPLEX, buscando a eficiência no planejamento da rotação de culturas em propriedades agrícolas. Palavras-chave:Programação Linear; Método Simplex; Produção Agrícola; Problema de Reflorestamento. AbstractThe agroindustrial sectors have been seeking the improvement and the technological knowledge of their expertise areas, due to the strong competition in the market. This fact motivates the development of actions that optimize processes, such as to produce food avoiding waste of raw materials and inputs, or preserve the environment, by increasing the planted area. Agricultural production, in its turn, has adapted old practices to more current production technologies with the goal of increasing productivity, cultivating healthier products and reducing environmental impacts. Thus, the goal of this work is to formulate problems using linear programming in agricultural problems. The presented case studies involve the maximization of profits of an agricultural production and of a reforestation property. The problems were solved with computational support in order to obtain the solutions by running the SIMPLEX method, providing efficiency in the planning of cultures rotation in agricultural properties.