University of South Florida
College of Arts and Sciences
Speaker: Natalia Hritonenko, Prarie View A&M University, Texas
We live, produce, consume, and pollute. Industrial production supports our wellbeing. On the other side, it badly contaminates the environment. Environment adaptation and pollution mitigation as two main strategies for the environmental protection will be discussed. A brief overview of quantitative and qualitative modelling approaches to solve related contemporary issues will be presented. The presented deterministic ODE model that depicts complex connections among production, pollution, and the environmental protection is a result of intensive collaborative efforts of mathematicians, economists, and environmentalists. Its different extensions and modifications as well as developed methods of their investigation and applied interpretation of obtained results will be discussed.
Carbon sequestration in forestry is one of important mitigation techniques. The second part of a talk will be devoted to a PDE model and related optimal control problem that led to recommendations for sustainable forest management under different climate scenarios.
Brief overview of other on-going research directions and future goal will conclude the presentation.
Title: Network structure and mathematical modeling of Binocular Rivalry
Speaker: Yunjiao Wang, Texas Southern University, Houston, TX
Binocular rivalry is a phenomenon that occurs when two dissimilar images are presented to different eyes simultaneously: instead of seeing one coherent image, one experiences percept alternating between different images. In this talk, I will discuss network structures that may account for various existing experimental results and a mathematical model that captures generalized Levelt’s Propositions.
Title: Rate-induced tipping in non-autonomous systems
Speaker: Peter Ashwin, Exeter University, UK
Modelling of non-autonomous dynamical systems subject to arbitrary inputs is probably a hopelessly difficult task to say anything particular useful beyond generic results that have limited application. For non-autonomous systems where the inputs vary smoothly and limit to constant as time becomes infinite (parameter shift systems) it is possible to say a lot more. In particular, novel instabilities such as “rate-induced tipping” can appear where the system and input timescales become comparable and the adiabatic (quasistatic) approximation breaks down. In this lecture I present some theory and simple examples that illustrate this effect.
Title: COVID-19: Modeling the impact of human behavior and perception of risks on disease transmission
Speaker: Folashade Agusto, Ecology and Evolutionary Biology, University of Kansas
COVID-19 is caused by the novel coronavirus, SARS-COV2 has led to over 614 million cases, with close to 7 million deaths worldwide. The current social and political climate affects people's perception of the risks of the infection. Studies have shown that human behavior drives disease burden, and several factors drive these behaviors namely peoples' perception of disease risk which include peoples’ beliefs, previous knowledge about a disease, and information from traditional and social media. In this seminar, I will present two models for COVID-19, one is driven by peoples' behavior and their perception of the risks of the disease. The second model uses Twitter tweets to account for peoples' sentiments about the disease. The model also considers negative sentiments driven by misinformation. Results from these models show the possibility of multiple waves of the pandemic due to the behavior of infected individuals. Another result shows the importance of incentivizing altruistic behavior by infected individuals to voluntarily self-isolate. Therefore, to reduce the burden of diseases in the community, it is necessary to ensure both positive behavior and sentiments, especially in this current social and political climate.
Title: The Spatio-Temporal Dynamics of Synthetic Microbial Consortia
Speaker: Kresimir Josic, University of Houston
Modeling is essential in the design of genetic circuits with desired properties. I will review several examples where mathematical models have been central to the development and understanding of the dynamic of synthetic organisms. I will start with a discussion of synthetic bacterial consortia that exhibit emergent oscillatory behavior — when co-cultured, the interaction between two bacterial strains results in population-level transcriptional oscillations. The spatio-temporal dynamics of such consortia, including synchrony between distant parts of the population, depend sensitively on the architecture of the underlying genetic circuits. I will then describe how oscillations, and other spatiotemporal patterns can arise in consortia of cells that individually exhibit bistable dynamics. I will show how simplified mathematical models can help us understand how order emerges in these system, how robust oscillations and other patterns can arise, and how they are maintained.