Abstract: As a pandemic of covid-19 spread across the globe, many complex, highly detailed models have been developed to help policy setters make better decisions. A major goal of modeling covid-19 is to advise those in power how to react, and only the simplest models can be explained to those decision-makers.
The data collection has made this epidemic among the best documented. “Best documented” does not mean “thoroughly documented”. We argue that to understand and predict the epidemic, the simplest models are best. Major documented factors are the varying strains of Covid including delta and the various omicron strains. We describe the advantages of simple models for covid-19. We say a model is simple if its only parameter is the average rate of contact between people in the population. This contact rate can vary over time, depending on choices by policy setters. Transient interventions like lockdowns and intermittent mask campaigns can make the epidemic data confusing.
Abstract: The importance of understanding, predicting, and controlling infectious disease has become increasingly evident during the current COVID-19 pandemic. In particular, the pandemic highlighted the need for interpretable, quantitative models that link mechanism with data while accounting for variability. Despite significant effort and advances, infectious disease dynamics remain incompletely understood, in part due to the lack of heterogeneity considered in immunological, ecological, and epidemiological aspects, which produce complicated, non-linear feedbacks. In this talk, we will focus on an age-structured PDE model of malaria, one of the deadliest infectious diseases globally. Our novel model of malaria specifically tracks acquisition and loss of immunity across a population. We study the role of vaccination and immunity feedback on severe disease and malaria incidence through a combination of our analytical calculation of the basic reproduction number (R0) and numerical simulations. Using demographic and immunological data, we parameterize our model to simulate realistic scenarios in Kenya. Our work sheds new light on the role of natural- and vaccine-acquired immunity in malaria dynamics in the presence of demographic effects.
Abstract: Integro-difference equations (IDEs) are of great interest in the studies of invasions of populations with discrete generations and separate growth and dispersal stages. IDEs with a strong Allee effect can generate a variety of spatiotemporal patterns in population growth and spread. In this talk, we will discuss IDEs with a monotone growth function exhibiting a strong Allee effect, and present rigorous results regarding traveling wave solutions and results on minimal patch size for population persistence. We will also talk about IDEs with a growth function having a strong Allee effect and overcompensation, and provide analytical and numerical results on oscillating traveling wave speeds as well as stationary and oscillating non-spreading solutions.
Abstract: Phytoplankton are the base of the marine food web. They are also responsible for much of the oxygen we breathe, and they remove carbon dioxide from the atmosphere. The mechanisms that govern the timing of seasonal phytoplankton blooms is a highly debated topic in oceanography. Here, we present a macroscale plankton ecology model consisting of coupled, nonlinear reaction-diffusion equations with spatially and temporally changing coefficients to offer insight into the causes of phytoplankton blooms. This model simulates biological interactions between nutrients, phytoplankton and zooplankton. It also incorporates seasonally varying solar radiation, diffusion and depth of the ocean’s upper mixed layer because of their impact on phytoplankton growth. The model’s predictions are dependent on the dynamical behavior of the model. The model is analyzed using seasonal oceanic data with the goals of understanding the model’s dependence on its parameters and of understanding seasonal changes in plankton biomass. A study of varying parameter values and the resulting effects on the solutions, the stability of the steady-states, and the timing of phytoplankton blooms is carried out. The model’s simulated blooms result from a temporary attraction to one of the model’s steady-states. An ongoing undergraduate research project seeks to improve the timing of the model’s blooms by considering some zooplankton to be mixotrophic.
Abstract: The study of animal movement has exploded with the development of GPS and lithium-ion battery technologies, and the Movebank data repository alone records millions of new animal locations per day. In general, data obtained by tracking animals are irregularly sampled time-series, subject to temporal autocorrelation, measurement error, and various seasonal and non-stationary behaviors. Therefore, the natural mathematical framework for these data are continuous-time stochastic process models. Here, I discuss a number of stochastic process movement models that are both biologically useful and mathematically interesting.
Abstract: Public policy and academic debates regarding pandemic control strategies note disease economy trade-offs, often prioritizing one outcome over the other. Using a calibrated, coupled epi-economic model of individual behavior embedded within the broader economy during a novel epidemic, we show that targeted isolation strategies can avert up to 91% of economic losses relative to voluntary isolation strategies. Unlike widely used blanket lockdowns, economic savings of targeted isolation do not impose additional disease burdens, avoiding disease-economy trade-offs. Targeted isolation achieves this by addressing the fundamental coordination failure between infectious and susceptible individuals that drives the recession. Importantly, we show testing and compliance frictions can erode some of the gains from targeted isolation but improving test quality unlocks the majority of the benefits of targeted isolation.
Abstract: It is easy to lose confidence in the capacity for human social and political systems to respond effectively to the challenges from rising average global temperature and associated climate change. A working group of diverse researchers with backgrounds in mathematical modeling, climate science, psychology, sociology, economics, geography and ecology has addressed the question as to whether there is any rational basis to expect that human behavioral changes can sufficiently impact climate to significantly reduce future mean global temperatures. Climate models can readily make assumptions about reductions in future greenhouse gas emissions and project the implications, but they do this with no rational basis for human responses. We have developed models to build such a rational basis to link social system and human behavior with climate. This includes a model from the theory of planned behavior in social psychology, linked to extreme events obtained from a climate model, and feedback to global emissions. Results from these efforts is that there is indeed some rational basis for hope, with social, political and technical feedback processes driving future climate policies and emissions. Under some circumstances these lead to a meaningful reduction of projected future average temperature. =====================================================================
Louis J. Gross is a Chancellor's Professor Emeritus and Emeritus Distinguished Professor of Ecology and Evolutionary Biology and Mathematics and Director of The Institute for Environmental Modeling at The University of Tennessee, Knoxville. He was the founding Director of the National Institute for Mathematical and Biological Synthesis, a National Science Foundation-funded center to foster research and education at the interface between math and biology. He completed a B.S. degree in mathematics at Drexel University and a Ph.D. in applied mathematics at Cornell University, and has been a faculty member at UTK since 1979. His research emphasizes applications of mathematics and computational methods in many areas of ecology, including disease ecology, landscape ecology, spatial control for natural resource management, photosynthetic dynamics, and the development of quantitative curricula for life science undergraduates. He has served as Program Chair of the Ecological Society of America, President of the Society for Mathematical Biology, Treasurer for the American Institute of Biological Sciences and twice as President of the UTK Faculty Senate. He is the 2006 Distinguished Scientist awardee of the American Institute of Biological Sciences and is a Fellow of the American Association for the Advancement of Science and of the Society for Mathematical Biology. As the volunteer sound engineer for over thirty years at the Laurel Theater, he has engineered and recorded more than a thousand performances of traditional music. His live recordings have been included on over a dozen albums, and his free annual workshops have trained several hundred individuals in the basics of live sound engineering.
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