Session abstracts

Session S15 - Mathematics of Planet Earth



Wednesday, July 14, 16:00 ~ 16:25 UTC-3

Mathematical control models for the COVID-19 epidemic

Justina Gianatti

CIFASIS - CONICET - Universidad Nacional de Rosario, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this work we study control models for the COVID-19 epidemic. We start by analyzing a model that takes into account the infection age of the population. We introduced a confinement variable as control and by applying optimal control techniques we are able to evaluate some of the best confinement policies for this initial model. Afterwards,  we introduce a different compartmental model, which also includes undetected cases, and based on the data available so far, we calibrate the parameters involved. We end up adding a vaccination policy as a control variable to our model and show some numerical results referring to the evolution of the epidemic in Argentina.

Joint work with J. Frédéric Bonnans (INRIA-Saclay and CMAP, Ecole Polytechnique), Pablo A. Lotito (PLADEMA-UNCPBA-CONICET) and Lisando A. Parente (CIFASIS-CONICET-UNR).

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Wednesday, July 14, 16:30 ~ 16:55 UTC-3

On mobility trends analysis of COVID–19 dissemination in Mexico City

Jhoana P. Romero-Leiton

Centro de estudios interdisciplinarios básicos y aplicados CEIBA/Universidad Cesmag, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

This work presents a forecast of the spread of the new coronavirus in Mexico City based on a metapopulation structure mathematical model using Bayesian Statistics inspired in a data-driven approach. The mobility of humans on a daily basis in Mexico City is mathematically represented by a matrix origin-destination using the open mobility data from Google and a Transportation Mexican Survey. This matrix origin-destination was incorporated in a compartmental model. We calibrate the model against borough-level incidence data collected between February 27, 2020 and October 27, 2020 using Bayesian inference to estimate critical epidemiological characteristics associated with the coronavirus dispersion. Since working with metapopulation models lead to rather high computational time consume, we did a clustering analysis based on mobility trends in order to work on these clusters of borough separately instead of taken all the boroughs together at once. This clustering analysis could be implemented in smaller or lager scale in different part of the world. In addition, this clustering analysis is divided in the phases that the government of Mexico City has set up to restrict the individuals movement in the city. Also, the reproductive number in Mexico City is calculated using the next generation operator method and the inferred model parameters. The analysis of mobility trends can be helpful for public health officials for the evaluations of interventions of the largest city of Mexico.

Joint work with Kernel Prieto (Universidad Autónoma de México, México) and and M. Victoria Chávez–Hernández (Universidad Autónoma de Nuevo León, México).

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Wednesday, July 14, 17:00 ~ 17:25 UTC-3

Assessment of event-triggered policies of nonpharmaceutical interventions based on epidemiological indicators

Héctor Ramírez

Universidad de Chile, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Nonpharmaceutical interventions (NPI) such as banning public events or instituting lockdowns have been widely applied around the world to control the current COVID-19 pandemic. Typically, this type of intervention is imposed when an epidemiological indicator in a given population exceeds a certain threshold. Then, the nonpharmaceutical intervention is lifted when the levels of the indicator used have decreased sufficiently. What is the best indicator to use? In this paper, we propose a mathematical framework to try to answer this question. More specifically, the proposed framework permits to assess and compare different event-triggered controls based on epidemiological indicators. Our methodology consists of considering some outcomes that are consequences of the nonpharmaceutical interventions that a decision maker aims to make as low as possible. The peak demand for intensive care units (ICU) and the total number of days in lockdown are examples of such outcomes. If an epidemiological indicator is used to trigger the interventions, there is naturally a trade-off between the outcomes that can be seen as a curve parameterized by the trigger threshold to be used. The computation of these curves for a group of indicators then allows the selection of the best indicator the curve of which dominates the curves of the other indicators. This methodology is illustrated using indicators in the context of COVID-19 using deterministic compartmental models in discrete-time, although the framework can be adapted for a larger class of models.

Joint work with Carla Castillo-Laborde (Universidad del Desarrollo, Santiago, Chile), Taco de Wolff (Centro de Modelamiento Matemático (CNRS UMI 2807), Universidad de Chile), Pedro Gajardo (Universidad Técnica Federico Santa María, Valparaíso, Chile), Rodrigo Lecaros (Universidad Técnica Federico Santa María, Valparaíso, Chile) and Gerard Olivar (Universidad de Aysén, Coyhaique, Chile).

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Wednesday, July 14, 17:30 ~ 17:55 UTC-3

Optimizing COVID-19 second-dose vaccine delays saves ICU admissions

Claudia Sagastizábal

Unicamp, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The current production level of coronavirus vaccines is setting the rhythm for the deployment of vaccination campaigns. As most vaccines require two doses, delivery delays reduce the initial impact on transmission and increase the risk of the emergence and spread of new SARS-CoV-2 strains. Governments consider delaying the second-dose to increase the number of first-dose vaccinated individuals. Such a delicate decision depends on the first-dose efficacy and the time window of the second-dose. To assess the desirability of stretching doses, we propose an optimization model based on an extended SEIR dynamics that find the best gap between doses. Robot Dance is a mathematical optimization platform developed for intervention against Covid-19 in a complex network. In the considered instance, the model infers the lightest social distancing profile required from the society while deploying vaccines. Such optimal strategy is chosen among multiple scenarios of postponement of the second-dose, keeping the intensive care unit (ICU) use below maximum capacity by means of a probabilistic constraint. Our results show that the decision depends strongly on whether the vaccine blocks infection or alleviates symptoms. With a vaccine-like AZD1222 with two-dose efficacy of 82.4%, assuming the first-dose efficacy is 55-65% or more and the vaccine blocks infections, the algorithm recommends delaying the second-dose as much as possible. By contrast, if the vaccine only alleviates symptoms, stretching the gap between doses to its maximum time is the best strategy only after the first-dose efficacy is at least 70-75%. Our results show that, when the vaccine blocks infection and the efficacy of the first dose is about 70%, delaying the second-dose saves 400 ICU admissions per million people in 200 days thus leading to a sharp contribution in saved lives.

Joint work with Paulo J. S. Silva (Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, São Paulo, Brazil), Claudia Sagastizábal (Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, São Paulo, Brazil), Luis Gustavo Nonato (Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, São Paulo, Brazil), Claudio Struchiner (Fundação Getúlio Vargas, Rio de Janeiro, Brazil) and Tiago Pereira (Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, São Paulo, Brazil).

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Wednesday, July 14, 18:00 ~ 18:25 UTC-3

Optimal observation placement in variational data assimilation models

Juan Carlos De los Reyes

MODEMAT, Escuela Politécnica Nacional, Ecuador   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Variational data assimilation problems have been widely studied in numerical weather prediction as a technique for reconstruction of the atmosphere initial condition. Taking this problem as motivation, our goal consists in finding the solution to an optimal placement problem on a parabolic equation, such that the initial condition will be optimally reconstructed. Within the framework of supervised learning methods, we consider a bilevel optimization problem where the lower level task is the reconstruction of the initial condition of the system’s state, and the upper level solves the optimal placement. The training set is constituted by simulations of the initial condition and the state of the system. To solve the data assimilation problem we use the variational approach (4D−VAR). Existence and uniqueness of solutions to the data assimilation problem are proven using the direct method of the calculus of variations, whereas to derive the optimality system we used the Lagrangian approach. Due to the objective functional structure, an adjoint system with Borel measures on the right-hand side is obtained for the lower level problem. To show existence of a very weak solution we used the transposition method and extra regularity results for parabolic systems. To derive the optimality system for the upper-level problem, we again use the Lagrangian approach. The constraint in this case is given by the optimality system of the lower level problem, which contains regular Borel measures on the right hand side. Existence of Lagrange multipliers is justified.

Joint work with Paula Castro (MODEMAT, Escuela Politécnica Nacional, Ecuador).

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Wednesday, July 14, 18:30 ~ 18:55 UTC-3

Dealing with uncertainties in weather and climate prediction: role of multiscaling through nonlinear resonance

Pedro Silva Dias

University of São Paulo, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Prediction of the climate system depends on an initial value problem based on a complex fluid mechanical system, involving interactions between several components (atmosphere, ocean, biosphere, criosphere) through conservation laws. Each component of the climate system is nonlinear and the interaction among components frequently involves highly nonlinear processes. In addition, the models are imperfect in view of the incomplete knowledge of the physical processes or the fact that processes of smaller resolution than the resolved scales are not always properly formulated. Each component of the climate system has characteristic spatial and temporal time scales. A simplified model based on the interaction of the atmosphere and ocean will be reviewed and explored from the point of view of phase space associated to the normal modes of each simplified model components (ocean and atmosphere). Basically, the original set of nonlinear partial differential equations of the simplified model in physical space will be solved in the phase space. Nonlinear resonance involving the interaction of ocean and atmospheric modes help understanding the dynamics of slow climatic variability in several relevant timescales. Relevant results come out of the analysis of the interacting resonating triads under the periodic or quasi-periodic solar forcing. This is particularly important topic to explore issues related to the attribution of causes to the observed climate change under the influence of global warming.

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Wednesday, July 14, 19:00 ~ 19:25 UTC-3

Dynamical systems analysis of the Maasch–Saltzman model for glacial cycles

Hans Kaper

Georgetown University, Washington, DC, and Mathematics and Climate Research Network (MCRN), USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The geological record shows great variability of Earth’s climate.  During the Pleistocene Epoch (from approximately 2.6 Myr before present (BP) until approximately 11.7 Kyr BP), continental ice sheets expanded and contracted over significant areas, especially in the Northern Hemisphere. This happened in a more or less cyclical fashion, with periods of approximately 40 Kyr during the early Pleistocene and approximately 100 Kyr during the late Pleistocene.  In this talk I will discuss a conceptual model first presented by Maasch and Saltzman (1990) to explain this persistence of glacial cycles as the result of the interaction of atmospheric carbon dioxide and the strength of the North Atlantic overturning circulation. The model consists of a system of three ordinary differential equations with a rich bifurcation structure.

Joint work with H. Engler (Georgetown University), T.J. Kaper (Boston University) and T. Vo (Boston University, currently at Monash University, Clayton, Victoria, Australia).

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Thursday, July 15, 16:00 ~ 16:25 UTC-3

Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area

Marianne AKIAN

Inria and CMAP, Ecole polytechnique, France   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

I will present a work done during the Covid-19 epidemic crisis of March–April 2020. We portray the evolution of the epidemic in the Paris area, by analyzing the medical emergency calls received by the EMS of the four central departments of this area (Centre 15 of SAMU 75, 92, 93 and 94). Our study reveals strong dissimilarities between these departments. We show that the logarithm of each epidemic observable can be approximated by a piecewise linear function of time. Such an approximation allows us to distinguish the different phases of the epidemic, and to identify the delay between sanitary measures and their influence on the load of EMS. This also leads to an algorithm, allowing one to detect epidemic resurgences, by identifying nondifferentiability points.

Piecewise linearity is established from a transport PDE epidemiological model, using methods from Perron–Frobenius theory and tropical geometry. In order to compute a piecewise linear approximation, we minimize the $\ell^1$ norm of the error. This is done using a dynamic programming approach. We provide metric estimates showing that this method is robust with respect to perturbations of epidemic observables.

The main part of this work was done jointly by the following team of physicians of the SAMU of AP-HP and applied mathematicians from INRIA and École polytechnique: Stéphane Gaubert, Marianne Akian, Xavier Allamigeon, Marin Boyet, Baptiste Colin, Théotime Grohens, Laurent Massoulié, David P. Parsons, Frédéric Adnete, Érick Chanzy, Laurent Goix, Frédéric Lapostolle, Éric Lecarpentier, Christophe Leroy, Thomas Loeb, Jean-Sébastien Marx, Caroline Télion, Laurent Tréluyer, and Pierre Carli. It has been published in Comptes Rendus Mathématique, vol. 358, n7, p. 843-875, 2020.

The part on $\ell^1$ norm optimization is a joint work with Ayoub Foussoul, Jérôme Bolte, Stéphane Gaubert, and Laurent Massoulié.

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Thursday, July 15, 16:30 ~ 16:55 UTC-3

Optimal fishery management of the Black Sea anchovy with a food chain model

Suzanne Lenhart

University of Tennessee, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We present a model to represent a food chain on the Turkish coast of the Black Sea. Using data from the anchovy landings in Turkey, optimal control of the harvesting rate of the anchovy population in a system of three ordinary differential equations (anchovy, jellyfish and zooplankton) will give management strategies. We also discuss the benefits of using food chain models rather than using single species models.

Joint work with Mahir Demir (Michigan State University, USA).

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Thursday, July 15, 17:00 ~ 17:25 UTC-3

Decision Making: Combining Dynamical Systems with Participatory Modelling

Gerard Olivar-Tost

Universidad de Aysén, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Participatory modelling is very well-known in social sciences. We use the integration of participatory modeling and system dynamics as a novel methodology for decision making. In our talk we include the consolidation of social dynamic models for the subsequent evaluation and prioritization of green projects in Colombian post-conflict communities.

Through participatory work carried out along with the Tame community, it was possible to identify, evaluate and systematize citizen factors in relation to the problems and needs of the region. As a second step, based on the results obtained, we calibrated a simulation model based on system dynamics that facilitates decision making with regards to the evaluation of green projects.

The proposed methodology allowed us to conclude that, with the participation of the community and with a model based on the dynamics of variables such as supply and demand for natural resources of water, and land use, it is possible to warn decision makers.

We identified the variables that can lead to the maximization of investments and thus prioritize and select the most appropriate environmental, social or economic initiatives, that certainly meet the needs or expectations of the involved community. In the future, the model could be used to facilitate the management, administration and control of water and land resources by creating alerts called reserve margins.

Joint work with Johnny Valencia-Calvo (Universidad de Aysén, Chile) and Julián Castrillón-Gómez (Universidad Nacional de Colombia, Colombia).

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Thursday, July 15, 18:00 ~ 18:25 UTC-3

Causality and extreme event attribution. Or, did climate change flood my house?

Michael Wehner

Lawrence Berkeley National Laboratory, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Extreme event attribution is an exercise in causal inference. Rather than some deep philosophical statement, an attribution statement is a probabilistic one. However, it is also a conditional statement and is incomplete if the conditions and uncertainties are not clearly specified. We will review a hierarchy of extreme attribution statements types and their uncertainties ranging from those with very few conditions to those that are highly constrained. Real world examples will include interpretations of recent attributions statements about Hurricanes Harvey, Florence, Maria and Irma. In particular, we will explore the confidence in the human induced portion of the Harvey’s record rainfall in the greater Houston area as well as the associated flood and cost of this disastrous event.

Joint work with Mark Risser, Lawrence Berkeley National Laboratory, USA.

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Thursday, July 15, 18:30 ~ 18:55 UTC-3

Sterile Insect Technique (SIT) for vector and pest control: the partial sterile case and nonlinear control strategies for release

Maria Soledad Aronna

Escola de Matemática Aplicada (FGV EMAp), Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The Sterile Insect Technique (SIT) is a biological control method that consists of releasing males that have been sterilized using ionizing radiation; these males will mate with wild females that will not produce viable offsprings.

In this talk we present a minimalist model for SIT, assuming that residual fertility can occur in the sterile male population after radiation. Taking into account that we are able to get regular measurements from the biological system along the control duration, such as the size of the wild insect population, we study different control strategies that involve either continuous or periodic impulsive releases. We show that a combination of open-loop control with constant large releases and closed-loop nonlinear control leads to the best strategy in terms of both number of releases and total quantity of sterile males to be released.

Additionally, we show that SIT fails if the residual fertility is greater than a threshold value that depends on the wild population biological parameters. Moreover, even for small values, the residual fertility induces the use of such large releases, that SIT alone is not always reasonable from a practical point of view. We provide applications against a mosquito species, Aedes albopictus, and a fruit fly, Bactrocera dorsalis.

Joint work with Yves Dumont (CIRAD, Reunion Island, France; and AMAP, University of Montpellier, CIRAD, France; and Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa).

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Thursday, July 15, 19:00 ~ 19:25 UTC-3

On the Lorenz '96 model and some generalization

Hans Engler

Georgetown University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In 1996, the meteorologist and mathematician Edward Lorenz introduced a system of ordinary differential equations that describes a scalar quantity evolving on a circular array of sites, undergoing forcing, dissipation, and rotation invariant advection. Essentially, this is simplified weather on a one-dimensional planet. Lorenz constructed the system as a test problem for numerical weather prediction. Since then, the system has also found use as a test case in data assimilation. Mathematically, this is a dynamical system with a sparse quadratic nonlinear term that preserves energy, and it shares these properties with several other truncated models in geophysics and fluid dynamics. The system has a single bifurcation parameter (rescaled forcing), leading to multiple bifurcations, and it exhibits chaotic behavior for large forcing.

In this talk, after introducing the model and some of its properties and phenomena, the main characteristics of the advection term in the model will be identified and used to describe and classify possible generalizations of the system. A graphical method to study the bifurcation behavior of constant solutions for the general class of models will be introduced, and it will be shown how to compute normal forms of all these systems analytically. Problems with site-dependent forcing, dissipation, or advection will also be considered.

Joint work with John Kerin, Georgetown University.

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Tuesday, July 20, 16:00 ~ 16:25 UTC-3

Control strategies for a population dynamics model of Aedes aegypti with seasonal variability and their effects on dengue incidence and some ideas on estimating regional carrying capacity from the study of mathematical models that allow quantifying the productivity of mosquito breeding sites.

Andres Fraguela Collar

Benemerita Universidad Autonoma de Puebla, México   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Aedes aegypti female mosquitoes are the principal transmitters of dengue and other vector borne infections. This species is closely associated with human habitation, due to its blood-feeding habits and the presence of breeding sites widely available around house holds. We introduce a mathematical model for the life cycle of Aedes aegypti mosquitoes comprising two stages, aerial and aquatic, that reflects seasonal changes in the mosquito abundance. This model is further amended by three season-dependent control actions. Two coercive actions are introduced during the hot seasons characterized by higher abundance and enhanced growth rates of mosquitoes. They consist in the application of two chemical substances, insecticide and larvicide, acting upon the aerial and aquatic mosquito stages, respectively. During the cool seasons, characterized by the slower growth rates of mosquitoes and abundance of quiescent unhatched eggs, we introduce a preventive vector control measure consisting in mechanical elimination of mosquito breed ing sites. Using the framework of optimal control in combination with the cost-benefit ap proach and epidemiological assessment, we identify the most efficient strategy capable of essentially reducing the population of adult and immature mosquitoes during both seasons and provide a sketch for its modus operandi. For the study of the control problem it is very important to be able to obtain reliable estimates of the regional carrying capacity. For this reason, we will end by announcing some ideas on how we are studying this problem by introducing models of the evolution of the mosquito in the aquatic state that allow us to reasonably quantify the productivity of the hatcheries.

Joint work with Emilene Pliego Pliego (Benemerita Universidad Autonoma de Puebla, Mexico),, Tishbe Pilar Herrera Ramírez (Benemerita Universidad Autonoma de Puebla, Mexico),, Jorge Velázquez Castro (Benemerita Universidad Autonoma de Puebla, Mexico),, Olga Vasilieva (Universidad del Valle, Colombia) and Antonio Abella Medrano (Universidad Nacional Autónoma de México).

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Tuesday, July 20, 16:30 ~ 16:55 UTC-3

To Adapt or Mitigate Global Climate Change: Modelling approach

Natali Hritonenko

Prairie View A&M University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Pollution mitigation and environmental adaptation are two long term policies to combat environmental damages. Both of them play a vital role in protection of our surrounding but are very expensive to implement. Mitigation and adaptation are thoroughly considered while designing long-term policies and regulations on both international and national levels. A suggested economic-environmental model analyzes a rational investment to environmental mitigation and adaptation. Both cooperative and non-cooperative strategies are discussed. The non-cooperative strategy is a dynamic game in which each country makes its own environmental decision following the open-loop Nash equilibrium. The cooperative social planner assumes an international environmental agreement in force. Non-cooperative and cooperative solutions are compared in the symmetric case of two countries and extended to several identical countries. The modelling approach to the asymmetric case is also discussed. New integral model that fits realistic infectivity distribution of COVID-19 and describes different government preventive measures is presented. Its simulation matches real data on US in 2020-2021.

Joint work with Yuri Yatsenko (Dunham College of Business, Houston Baptist University) and Victoria Hritonenko (University of California Extension, Berkeley).

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Tuesday, July 20, 17:00 ~ 17:25 UTC-3

Modeling pheromone control and trapping of the Asian citrus psyllid, Diaphorina citri


Universidad del Valle, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Diaphorina citri or Asian citrus psyllids (ACP) are small insects that live on citrus trees and feed on young stems, sprouts, and leaves during all stages of development. This insect is also the major vector of the most serious citrus plant disease known as Huanglongbing (HLB or Citrus Greening) that affects citrus production in various parts of the world [1]. At the moment, there is no cure for this infectious plant disease, and the major control efforts are centered on controlling the local ACP populations.

In this presentation, we propose a sex-structured mathematical model that encompasses only the adult population of D. citri, even though the ACP life cycle also includes the immature phase (consisting of eggs and five nymphal instars). Following [2], the model is based on the behavioral and biological features of this particular insect species, and special attention is paid to the ACP mating behavior.

When seeking to mate, the female psyllids emit sex pheromones that attract the male insects. Pheromone traps are considered as an eco-friendly component of integrated pest control, and our model readily accommodates this type of external intervention. Sticky pheromone traps are usually set up for pursuing two simultaneous goals of pest control: (1) mating disruption leading to the offspring reduction, and (2) mass trapping of male insects followed by their direct removal.

We also outline the theoretical analysis of the model and revise several scenarios that accentuate its practical value for controlling the ACP adult population by pheromone traps.


[1] J.V. da Graça, L. Korsten, Citrus Huanglongbing: Review, Present Status and Future Strategies. In: Naqvi S.A.M.H. (Eds.) Diseases of Fruits and Vegetables Volume I. Springer, Dordrecht, 2004.

[2] R. Anguelov, C. Dufourd, Y. Dumont, Mathematical model for pest–insect control using mating disruption and trapping, Appl. Math. Model. 52 (2017) 437–457.

Joint work with Daiver Cardona-Salgado (Universidad Autonoma de Occidente, Cali, Colombia) and Yves Dumont (CIRAD, UMR AMAP, St Pierre, Réunion Island; AMAP, Univ. Montpellier, CIRAD, CNRS, INRAE, IRD, Montpellier, France; University of Pretoria, South Africa).

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Tuesday, July 20, 17:30 ~ 17:55 UTC-3

The dynamics of predatory mite and the pest leafhopper with stage structure in a tea plantation

Huaiping Zhu

York University, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The tea green leafhopper \textit{Empoasca onukii} Matsuda (Hemiptera: Cicadellidae) is one of the most predominant insect pest threatening the tea production. Based on our earlier studies of the surveillance data, I will present pest control models in tea plantations where a generalist predator mite (Anystis baccarum) serves as a natural enemy to control green leafhopper Empoasca (E. onukii). These models contain life cycle of the pest leafhopper \textit{E. onukii} in three stages, including egg, nymph and adults. In this talk, I will presented bifurcations including saddle-node bifurcation of codimension 1 and 2, Hopf bifurcation, Bogdanov-Takens bifurcation, in particular, I will focus on the nilpotent singularities and their bifurcations. The existence of two or three limit cycles suggest that the tri-stability is possible. This study will help to develop the plausible control mechanism of \textit{E. onukii} by stages.

Joint work with Pei Yuan (York University) and Lilin Chen (Fujian Agriculture and Forestry University).

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Tuesday, July 20, 18:00 ~ 18:25 UTC-3

Modeling Agricultural Decision Making: Physical and Social Approaches

Lea Jenkins

Clemson University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

According to facts reported on the UN Water website, billions of people experience water scarcity every year. Over 1/3 of the world's groundwater systems are currently in distress, and hundreds of millions of people worldwide will be displaced due to water shortages in the coming decades.

In regions where agricultural water use is high, these effects can be more pronounced. In California, for instance, the effects of a several-year, severe drought are exacerbated by the heavy agriculture production throughout the state. Thus, water management decisions, and limited availability of water, have a drastic effect on the livelihood of local residents as well as the U.S. as a whole.

Our multidisciplinary research team has worked to develop a software environment for simulating the decision processes conducted by farmers in managing their water usage and associated crop portfolios. Previous simulation efforts have modeled farmers as a consortium, each planting from the same portfolio and each with the same objectives tied to profit and water usage. More recently, we have begun to use agent-based modeling to increase the fidelity in our models and allow distinct farmers to make decisions based on personal preferences. This talk will include information on the effects of this modeling environment on the overall decision-making process, especially in comparison with our earlier efforts to guide decision makers in agricultural regions.

Joint work with Kathleen Fowler (Clarkson University) and Kristen Goebel (Clarkson University).

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Tuesday, July 20, 18:30 ~ 18:55 UTC-3

Optimal control techniques applied to the final open pit problem in mining.

Emilio Molina

Universidad de Chile and Sorbonne Université, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In mine planning, the Final Open Pit problem consists in finding an optimal design for an open pit mine. It has been studied mostly as a binary optimization problem until a continuous model was introduced in 2011 by Alvarez et al as an alternative to the binary one. In this talk we will show an optimal control version for this problem and taking advantage of this framework, we will present optimality conditions and numerical experiments using the Bocop solver, an open source toolbox for optimal control problems developed by Inria, which uses direct and global methods.

Joint work with Pierre Martinon (Inria, Francia) and Héctor Ramírez (Universidad de Chile, Chile).

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Tuesday, July 20, 19:00 ~ 19:25 UTC-3

On the set of robust sustainable thresholds

Pedro Gajardo

Universidad Técnica Federico Santa María, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In natural resource management, or more generally in the study of sustainability issues, the objective often consists of maintaining the state of a given system within a desirable configuration, typically established in terms of standards or thresholds. For instance, in fisheries management, the procedure for designing policies may include maintaining the spawning stock biomass over a precautionary threshold and ensuring minimal catches. With the evolution of some natural resources, under the action of controls and uncertainties, being represented by a dynamical system in discrete time, the aim of our work was to characterize the set of robust sustainable thresholds. That is, the thresholds for which there exists a trajectory satisfying, for all possible uncertainty scenarios, prescribed constraints parametrized by such thresholds. This set provides useful information to users and decision-makers, illustrating the tradeoffs between constraints. Using optimal control, maximin and level-set approaches, we characterize the weak Pareto front of the set of robust sustainable thresholds and derive a numerical method for computing the entire set.

Joint work with Cristopher Hermosilla (Universidad Técnica Federico Santa María, Chile) and Athena Picarelli (Università di Verona, Italy).

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