Biomathematics
Department of Mathematics and Statistics
Texas Tech University
No abstract.
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(presentation for SMB 2022) Collective human behavior has a strong impact on global ecosystems, but humans’ overall behavior is driven by individual decision-making. These decisions are often shaped by complex interactions between people with differing ideas. They may also be informed by historical human behaviors and, either directly or indirectly, the current ecosystem-level effects of those behaviors. In order to understand changing impacts on ecosystem, it is necessary to incorporate this potential feedback loop between social decisions and ecosystem outcomes. To demonstrate this, we consider a preliminary problem describing human food choices. We model a toy system in which humans are sustained by an aquatic ecosystem and can allocate harvesting efforts on different species. The choice of an aquatic ecosystem is to facilitate the use of simple, generalizable models in which feeding strengths are constrained by allometric (size-based) relationships. To determine allocation of harvesting efforts, we model harvesting preference as diffusion along a social network. The speed of diffusion is determined by the current abundance of potential food sources. Over discrete intervals, prevailing sentiment on the social network informs harvesting rates; this simulates a delay between growing consensus and behavior change. We demonstrate that, even for this very simple scenario, incorporating feedback between humans and ecosystems allows us to describe a range of ecosystem outcomes. At the end of the presentation, we build towards future work with more complex models informed by social networks from the archaeological past.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
Overweight and obesity have become a global epidemic due to increasing unhealthy eating habits and sedentary lifestyles. Since excess weight gain can be considered a disease transmitted through social influence, understanding its interpersonal dynamics is crucial for effective intervention and prevention programs. This project proposes a compartment model by considering social effects on weight gain. We study the local stability of disease-free equilibrium and derive a closed-form formula for the occurrence of backward bifurcation. Moreover, applying fluctuation lemma to prove the global stability of disease-free equilibrium provides parameter conditions for elimination of the overweight and obesity epidemic. Due to the fact that the overweight and obesity prevalence in the United States appears to be leveled off, we analyze the global stability of the non-trivial equilibrium by a geometric approach to establish a condition for the plateau of the overweight and obesity epidemic. Numerical simulations support the analytical results and show that the proposed model adequately describes complex epidemic patterns of the overweight and obesity epidemic.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
The body's process for modulating its response to an immune insult, such as infection or injury, involves numerous pathways and regulatory feedback mechanisms from not only the immune system, but also the cardiovascular and endocrine systems. Each of these systems has been well-studied individually both from an experimental and modeling perspective, but details surrounding their interactions during an immune event are still not well understood within the scientific community. Here, we construct the first dynamic mathematical model incorporating immune, cardiovascular, and endocrine mechanisms during a 2 ng/kg endotoxin challenge studying responses over multiple 24-hour cycles. Our model outputs time-varying concentrations of essential innate immune system components (monocytes and cytokines), cardiovascular markers (heart rate, blood pressure, resistance), hypothalamic-pituitary-adrenal (HPA) axis hormone concentrations, body temperature, and pain threshold. The model is calibrated to mean experimental data from two endotoxin challenges. Because all three systems include mechanisms on various time scales, we use our model to study the effects of changes in endotoxin administration timing, dosing, and method on the model output and recovery time.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
 | Monday
Oct. 3
4 PM
online
|
| TBA
Mohammadi Ain
Department of Mathematics and Statistics, Texas Tech University
|
Drug resistance is a common phenomenon in the treatment of cancer. As with other cancer therapies, treatment failure due to resistance also occurs for the oncolytic viral therapy (OVT). In this talk, we introduce mathematical models of tumor-virus interaction to investigate OVT resistance. The free oncolytic viruses are modeled explicitly as one compartment and the tumor cells are classified as either susceptible, resistant, or infected. Since there is a time delay from the initial viral infection to the time when infected cells are able to infect other tumor cells, we also consider a model of delay differential equations. It is shown that the OVT fails no matter how large the viral dose is if no treatment upon the resistant tumor cells is applied. When the treatment for resistance is adopted, the delay has no effect on the stability of the OVT escaped equilibrium and the model can have a unique positive equilibrium. A critical delay is derived under which a Hopf bifurcation occurs for the positive equilibrium. The critical delay, however, depends on several model parameters. We conclude that combined therapy is essential for the control of the tumor, and as delay is a characteristic of the virus, the virus should be engineered carefully to avoid tumor oscillations.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
Mathematical models of cell migration in the context of wound healing, embryonic development, and cancer growth have been developed using a wide variety of frameworks, including reaction-diffusion equations, continuum mechanics, and agent-based models. However, studying model uncertainty or model selection in these settings is less common. We develop a method for studying the appropriateness of model equation components that combines approximate Bayesian computation (ABC) and sensitivity analysis (SA). We provide two case studies in cell migration where we apply this method to sparse experimental data sets of retina development in the eye and tumor-immune dynamics in the brain. We identify model components that can be removed via model reduction using ABC+SA and potential cancer treatment pathways.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
Agricultural pests can be controlled in part by using pesticides, but natural populations of generalist predators also play a significant role. Pest control in agricultural fields depends on the potential interaction of species in the natural predator community. Predation by natural communities of beetles and spiders is influenced by intraguild interactions, species traits, and environmental factors. Temperature plays a crucial role in this context because changes in species traits occur in accordance with temperature fluctuations. Due to global warming, it’s more important than ever to understand how predator-prey interactions change with temperature. In our model, we have incorporated the effect of temperature on the foraging activity of predators. Using simulations, we show how temperature-dependent behaviors may alter the expected efficacy of the generalist predators seen in agricultural fields. To find the most effective combination of predator communities for pest management, we then use an optimization technique. Finally, we investigate how the most effective predator compositions might change with increasing average daily temperature and temperature variability under climate change. This study emphasizes the significance of understanding how climate change influences natural predator communities and how to create pest management strategies that are appropriate for future biological control under various climate scenarios.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
Plasmodium falciparum is the most virulent malaria species that affects humans. During its lifecycle, the parasite exists in two forms, asexual and sexual. Within the human host, the asexual parasites primarily replicate in the bloodstream. During the replication cycle, some asexual parasites commit to produce sexual parasites, which cannot reproduce in the human host. The sexual parasites are necessary continue the malaria life-cycle through the mosquito host. The proportion of asexual parasites committed to forming sexual parasites in a given replication cycle is known as the “conversion rate.” The determination of the conversion rate is paramount to the understanding of the transmission and therefore control of Plasmodium falciparum. In 2000, Diebner et al. created a collection of deterministic models for the sexual parasite levels determined by conversion rate, asexual parasite levels, and sexual parasite mortality. Continuing this work in 2001, Eichner et al. determined a range of conversion rates through fitting their chosen best model from Diebner et al. to over 100 individual patient infections. The range of conversion rates generated from this work is used in some modelling studies. Here, we evaluate the practical identifiability of parameters for the chosen best model and simplifications of this model. Focusing on a small collection of well-documented patients, we fit all parameters of the model, including the conversion rates, and obtain predicted sexual parasite levels. Using these predicted trajectories as a baseline truth, we simulate a collection of sexual parasite trajectories with varying levels of noise. We fit all parameters for each simulated data set in the collection and then evaluate the measure of accuracy to our original parameters to determine if we have practical identifiability. We find that we do not have practical identifiability of parameters, except for one patient with the simplest model assumptions. Without parameter identifiability, the reported conversion rates may need to be reconsidered.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
Extracellular matrix (ECM) is a key part of the cellular microenvironment and critical in multiple disease and developmental processes. Representing ECM and cell-ECM interactions is a challenging multi-scale problem that acts across both the tissue and individual cell levels. While several computational frameworks exist for ECM modeling, they often focus on either very detailed modeling of individual ECM fibers or only a single aspect of the ECM and in both cases are often computationally unscalable. In this presentation, using the PhysiCell agent-based modeling platform, we combine aspects of previous modeling efforts and develop a framework of intermediate detail that addresses direct cell-ECM interactions. We accomplish this using a three-variable representation of ECM — anisotropy, density, and orientation — and place these elements of ECM throughout space. Cells alter their motility in response to the local ECM variables and remodel ECM based on their velocity. With stepwise introduction of the framework features, we show a wide range of cell actions and ECM patterns that can be created. We then demonstrate this framework with a model of cancer cell invasion where the cell’s motile phenotype is driven by the ECM microstructure that is patterned by prior cell motility. When paired with the ECM, the cell invasion model captures a diverse range of tissue-level behaviors — from recapitulating a homeostatic tissue, to indirect communication of paths (stigmergy), to collective migration. This result suggests that cell-cell communication mitigated via the ECM enables and constitutes an important mechanism for pattern formation in dynamic cellular patterning. Finally, we talk generally about the tissue microenvironment, cell-cell interactions, and the use of agent-based models to explore and hypothesize explanations of those dynamics.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
The tumor suppressor p53 oscillates in response to DNA double-strand breaks, a behavior that has been suggested to be essential to its anti-cancer function. Nearly all human cancers have genetic alterations in the p53 pathway; a number of these alterations have been shown to be oncogenic by experiment. These alterations include somatic mutations and copy number variations as well as germline polymorphisms. Intriguingly, they exhibit a mixed pattern of interactions in tumors, such as co-occurrence, mutual exclusivity, and paradoxically, mutual antagonism. Using a differential equation model of p53-Mdm2 dynamics, I employ Hopf bifurcation analysis to show that these alterations have a common mode of action, to abolish the oscillatory competence of p53, thereby impairing its tumor suppressive function. In this analysis, diverse genetic alterations, widely associated with human cancers clinically, have a unified mechanistic explanation of their role in oncogenesis. In this talk, I will also discuss the role of physiological oscillations in health and disease broadly.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09