Abstract: • I consider myself a moderately well informed amateur in artificial intelligence. I started giving talks on artificial intelligence in UMD in 2017.
• I believe one can better understand how people think by discussing how AIs think. Such understanding might benefit our students. We can’t discuss questions about whether AI programs can think or have General Intelligence without understanding what these terms mean for people, without figuring out what we mean when we say people think. Do people hallucinate as often as LLMs (large language model AIs)?
• I will propose a mini model for testing how people or more specifically mathematicians/scientists think, and I will describe how AIs process ideas.
I will refer to a paper with B. Hasselblatt entitled Finding Tactics in Proofs- to appear in JJIAM: https://www.dropbox.com/scl/fi/mvjezmhinpgt9vvyj9cwu/FINDING-TACTICS-IN-PROOFS-B- HASSELBLATT-AND-JY-JJIAM-AUG-2025.pdf?rlkey=7o6hae0w9isgssuyqm8d1l0d6&dl=0
Abstract: Lyme disease, transmitted by ticks, is endemic in several regions of the United States (including the Northeast), and the lifecycle of ticks is significantly affected by changes in local climatic variables. In this study, we modeled the dynamics of Lyme disease across the U.S. state of Maryland. We used a mechanistic model, calibrated using case and temperature data, to assess the impact of temperature fluctuations on the geospatial distribution and burden of Lyme disease across Maryland. Our results demonstrate that tick activity and Lyme disease intensity peak when temperature reaches $17.0^{\circ}$C---$20.5^{\circ}$C. We estimate that moderate projected global warming will cause a range expansion of Lyme disease, increasing burden in Central Maryland and extending risk into Western counties, while reducing the
disease burden in Southern and most Eastern counties. High projected warming will cause a westward shift, with new Lyme disease hotspots emerging in Western counties, and reduction of burden in Central, Southern and Eastern regions. Maryland will experience reductions in overall Lyme disease burden under both projected global warming scenarios (with more reductions under the high warming scenario). Disease elimination is feasible using a hybrid strategy, which combines rodents baiting, habitat clearance, and personal protection against tick bites, with moderate coverages.
Abstract: The risk and intensity of mosquito-borne disease outbreaks are tightly linked to the frequency at which mosquitoes feed on blood, also known as the biting rate. Standard mosquito-borne disease transmission models assume that mosquitoes bite only once per reproductive cycle – an assumption commonly violated in nature. For example, host defensive behaviors or climate factors can increase the occurrence of multiple biting while simultaneously impacting the mosquito gonotrophic cycle duration (GCD), the quantity customarily used to determine biting rates.
We present a framework for incorporating complex mosquito biting behaviors into transmission models, to account for the heterogeneity in and linkages between the biting rate and the multiple biting number. We derive general formulas for the basic offspring number, N0, and basic reproduction number, R0, and introduce specific models arising from empirical, phenomenological, and mechanistic perspectives. Using the gonotrophic cycle duration as a standard quantity to compare these models, we show how assumptions about the biting process strongly affect the relationship between the GCD and R0. This work highlights the importance of behavioral dynamics on mosquito-borne disease transmission while providing a tool for evaluating how individual-level interventions against biting scale up to affect population-level disease risk.
Abstract: Evolutionary dynamics shape social and biological systems across scales, from the evolution of multicellularity to the emergence of underground fungal symbioses to the formation and maintenance of animal groups and human societies. In these complex adaptive systems, small-scale interactions and associations can lead to emergent, large-scale phenomena. These interactions are often greatly influenced by various forms of heterogeneity, such as personality differences in human populations and variation in altruistic tendencies in animals. In this talk, I will present several models of complex social and biological systems, motivated by real-world phenomena and observations. These models are driven by evolutionary game theory, opinion dynamics frameworks, and agent-based modeling, and employ tools from stochastic processes, differential equations, and dynamical network analysis. I will discuss applications such as the evolution of cooperation, social group formation, the effects of environmental shocks on political opinions and activism, and altruistic tensions in social insect populations.
Abstract: Social dynamics are an integral part of the spread of disease affecting contact rates and the adoption of pharmaceutical and non-pharmaceutical interventions. This talk will present behavioural-epidemiological models that feature tipping-point dynamics in which behaviour can undergo rapid changes. Health, economic costs, and social payoffs are all unified into payoff functions that determine changes in behaviour, potentially creating collective action problems. Key findings include: nonlinear responses to key epidemiological parameters, increased public awareness can undermine disease control, and behavioural synchronization. A discussion of optimal public policies in light of these findings will also be discussed.
Abstract: Inflation is a method to select a model from within a large hierarchy of models with the goal of finding the simplest model that economically simulates a small set of objective functions with near optimal fidelity. It begins with an extremely large model, the parameters of which each have an associated intrinsic uncertainty. A hierarchy of smaller models is constructed from a family of reductions of this large model. Starting from a small model in the hierarchy, adjoint sensitivity analysis is used to select a slightly larger model from within the hierarchy that improves the fidelity of a small set of objective functions. This process is repeated until the improved fidelity of these functions becomes comparable to their intrinsic fidelity. This model inflation method will be illustrated on a family of quadratic population models.
Abstract:Â In this talk I will discuss different mathematical and computational methods to study diseases in cellular level (cancer) and population level. In the first part, I aim to talk about stochastic and deterministic models to investigate the impact of cellular heterogeneity and micro environmental fluctuations on the efficiency of radiotherapy in cancer treatment. For this purpose, a modified Gillespie algorithm for discontinuous time changing rates is applied to explore the impact of plasticity, as well as random demographic factors on tumor control probability. The results show that the random modification of tumor microenvironment influences the efficiency of radiotherapy, leading to an initial increase in tumor control probability, which thereafter drops over time if a tumor is not eradicated entirely.
In the second part of this seminar, I will talk about system level policy models that I developed to support decision making process for Hepatitis B and C care. I will talk about a new back-calculation modeling approach base on Bayesian Markov Chain Monte Carlo (MCMC) algorithm informed by provincial population-level health administrative data to estimate the prevalence and undiagnosed proportion of chronic Hepatitis C infection in Canada. The results can provide evidence to guide decision making about HCV strategies and help meeting WHO elimination target by 2030.
Abstract: The use of pre-exposure prophylaxis (PrEP), where approved antivirals are administered to uninfected high-risk individuals, is universally regarded as a promising strategy to prevent susceptible high-risk individuals from acquiring HIV infection from their infected partners. A number of antiviral drugs (and their combinations) have been developed and are being used as prophylaxis against the HIV epidemic here in the U.S. and globally. We will first present a risk-structured mathematical model for assessing the population-level impact of PrEP in an MSM (men who have sex with men) population. An extended model, which considers several high-risk populations, will also be presented and used to assess the potential spillover effect, where the administration of PrEP to individuals in one risk group induces a reduction of disease burden in other risk group(s). The central aim is to determine whether the use of the aforementioned strategies can aid the End the HIV Epidemic initiative, aimed at eliminating the disease in the U.S. by 2030.
Abstract: Using a reaction-diffusion model with free boundaries in one space dimension for a single population species with density $u(t,x)$ and population range $[g(t), h(t)]$, we demonstrate that the Allee effects can be eliminated if the species maintains its population density at a suitable level at the range boundary by advancing or retreating the fronts. It is proved that with such a strategy at the range edge the species can invade the environment successfully with all admissible initial populations, exhibiting the dynamics of super invaders. Numerical simulations are used to help understand what happens if the population density level at the range boundary is maintained at other levels. If the invading cane toads in Australia used this strategy at the range boundary to become a super invader, then our results may explain why toads near the invading front evolve to have longer legs and run faster.
Abstract: Emerging infectious diseases can drive severe host population declines, yet recovery outcomes vary widely across species and communities. To examine the roles of host defense strategies in shaping these dynamics, we developed a mechanistic eco-evolutionary epidemic model that explicitly incorporates an environmental pathogen reservoir and considered heritable variation of disease tolerance in host. In this single-species system, without costs of tolerance, the coexistence of multiple defense classes is possible only when the pathogen ultimately goes extinct, whereas persistent infection selects for maximal tolerance. Introducing a reproductive cost removes such disease-free coexistence and allows for endemic equilibria with multiple strategies. Motivated by discrepancies between these analytical predictions and real-world observations, we extend the model to multi-species communities with habitat overlap and overlap-dependent competition. This reveals that resistant hosts suffer larger population declines and slower recovery under greater overlap, although communities dominated by resistant species rebound faster and more evenly because tolerant hosts promote pathogen persistence. Competition linked to habitat overlap reduces species-level declines, but increases unevenness in community recovery. Our results, supported by classical reproduction number analyses yet driven by transient dynamics, demonstrate how host defense strategies, habitat structure, and inter-specific interactions jointly determine post-outbreak resilience across biological scales.
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