Mathematical and Computational Methods in Biology

Duan Chen:
Fast randomized kernel matrix compression algorithms and applications in  biological data.

Our recent work is motivated by two types of biological problems. One is inferring 3D structures of chromatins based on chromosome conformation capture (3C), such as Hi-C, which is a high-throughput sequencing technique that produces millions of contact data between genomic loci pairs. The other problem is computational deconvolution of gene expression data from heterogeneous brain samples, for extracting cell type-specific information for patients with Alzheimer's Disease (AD).  Both problems involve large volumes of data, thus fast algorithms are indispensable in either direct optimization or machine learning methods. A central approach is the low-rank approximation of matrices. Conventional matrix decomposition methods such as SVD, QR, etc, are expensive, so not suitable for repeated implementation in these biological problems. Instead, we develop fast stochastic matrix compressions based on randomized numerical linear algebra (RNLA) theories. In this talk, we will emphasize on a recently developed stochastic kernel matrix compression algorithm. In this algorithm, samples are taken at no (or low) cost and the original kernel matrix is reconstructed efficiently with desired accuracy. Storage and compressing processes are only at O(N) or O(NlogN) complexity. These stochastic matrix compressing can be used to the above-mentioned biological problems to greatly improve algorithm efficiency, they can also be applied to other kernel based machine learning algorithms for scientific computing problems with non-local interactions (such as fractional differential equations), since no analytic formulation of the kernel function is required in our algorithms.

Casey Diekman:
Data Assimilation Methods for Conductance-Based Neuronal Modeling

German Enciso:
Absolute concentration robustness controllers for stochastic chemical reaction network systems

In this work, we provide a systematic control of a given biochemical reaction network through a control module reacting with the existing network system. This control module is designed to confer so-called absolute concentration robustness (ACR) to a target species in the controlled network system. We show that when the deterministic network system is controlled with the ACR controller, the concentration of a species of interest has a steady state at the desired value for any initial amounts, and it converges to the value under some mild conditions. For the stochastic counterparts of reaction network systems, we further show that when the abundance of the control species is high enough, the ACR controller can be utilized to make a target species approximately follow a Poisson distribution centered at the desired value. For this framework, we use the deficiency zero theorem (Anderson et al, 2010) in chemical reaction network theory and multiscaling model reduction methods. This control module also brings robust perfect adaptation, which is a highly desirable goal of the control theory, to the target species against transient perturbations and uncertainties in the model parameters.

Daniel Forger:
The mathematics of the wearable revolution

Jeffrey Gaither
SNPDogg: Feature-importances  in the identification of harmful missense SNPs

Recent years have seen an explosion in the use of machine-learning algorithms to classify  human mutations. There are now at least 30 scores designed to identify mutations likely to be deleterious to humans, but almost all are "black boxes" that provide no explanation of how they arrived at their predictions. In this talk I'll introduce a new mutational pathogenicity score, SNPDogg, that is transparent, insofar as every prediction can be decomposed as a sum of contributions from the model's features. SNPDogg's feature-importance ​values are computed via a game-theoretic approach implemented in the "shap" python package.

Juan B. Gutierrez:
Investigating the Impact of Asymptomatic Carriers on COVID-19 Transmission

Authors:
Jacob B Aguilar, PhD, Saint Leo University.
Jeremy Samuel Faust, MD, Brigham and Women's Hospital
Lauren M. Westafer, MD, University of Massachusetts, Medical School-Baystate
Juan B. Gutierrez, PhD, University of Texas at San Antonio

It is during critical times when mathematics can shine and provide an unexpected answer. Coronavirus disease 2019 (COVID-19) is a novel human respiratory disease caused by the SARS-CoV-2 virus. Asymptomatic carriers of the virus display no clinical symptoms but are known to be contagious. Recent evidence reveals that this sub-population, as well as persons with mild, represent a major contributor in the propagation of COVID-19. The asymptomatic sub-population frequently escapes detection by public health surveillance systems. Because of this, the currently accepted estimates of the basic reproduction number (Ro) of the virus are too low. In this talk, we present a traditional compartmentalized mathematical model taking into account asymptomatic carriers, and compute Ro exactly.  Our results indicate that an initial value of the effective reproduction number could range from 5.5 to 25.4, with a point estimate of 15.4, assuming mean parameters. It is unlikely that a pathogen can blanket the planet in three months with an Ro in the vicinity of 3, as reported in the literature; in fact, no other plausible explanation has been offered for the rapid profession of this disease. This model was used to estimate the number of cases in every county in the USA.

Wenrui Hao:
Homotopy methods for solving nonlinear systems arising from biology

Many nonlinear systems are arising from biology such as the pattern formation of nonlinear differential equations and data-driven modeling by using neural networks. In this talk, I will present a systematic homotopy method to solve these nonlinear systems in biology. In specific, I will introduce the homotopy continuation technique to compute the multiple steady states of nonlinear differential equations and also to explore the relationship between the number of steady states and parameters. Two benchmark problems will be used to illustrate the idea, the first is the Schnakenberg model which has been used to describe biological pattern formation due to diffusion-driven instability. The second is the Gray-Scott model which was proposed in the 1980s to describe autocatalytic glycolysis reactions.  Then I will also introduce a homotopy training algorithm to solve the nonlinear optimization problem of biological data-driven modeling via building the neural network adaptively. Examples of assessing cardiovascular risk by pulse wave data will be used to demonstrate the efficiency of the homotopy training algorithm.

Hye Won Kang:
A stochastic model for enzyme clustering in glucose metabolism

A sequence of metabolic enzymes tightly regulates glycolysis and gluconeogenesis. It has been hypothesized that these enzymes form multienzyme complexes and regulate glucose flux. In the previous work, it was identified that several rate-limiting enzymes form multienzyme complexes and control the direction of glucose flux between energy metabolism and building block biosynthesis. A recent study introduced a mathematical model to support this finding, in which the association of the rate-limiting enzymes into multienzyme complexes in included. However, this model did not fully account for dynamic and random movement of the enzyme clusters, as observed in the experiment.

In this talk, I will introduce a stochastic model for enzyme clustering in glucose metabolism. The model will describe both the enzyme kinetics and the spatial organization of metabolic enzyme complexes. Then, I will discuss underlying model assumptions and approximation methods.

Jae Kyoung Kim:
Analysis of dynamic data: from molecule to behavior

The circadian (~24h) clock is a self-sustained oscillator, which times diverse behavioral, physiological, and developmental process including our sleep cycle. The key oscillatory mechanism of the clock is a transcriptional-translational negative feedback loop. The suppression of the feedback loop occurs at the same time every day to maintain circadian period although it involves daily nuclear entry of thousands of clock molecules after diffusion through a crowded cytoplasm. Furthermore, the circadian period is robust to environmental temperature change affecting reaction rates, which has been a mystery for last 60 years. In this talk, I will describe how we identified underlying molecular mechanisms for such robust rhythms by analyzing the spatio-temporal dynamic data of clock molecules via mathematical modeling. Furthermore, I will also describe how we used a mathematical model to analyze the irregular sleep patterns of shift-workers obtained with a wearable device to identify sleep patterns improving their sleep quality. This opens the chance for the development of an app providing personalized optimal sleep schedule.

Sean Lawley:
Extreme First Passage Times of Diffusion

Why do 300 million sperm cells search for the oocyte in human fertilization when only a single sperm cell is necessary? Why do 1000 calcium ions enter a dendritic spine when only two ions are necessary to activate the relevant Ryanodine receptors? The seeming redundancy in these and many other biological systems can be understood in terms of extreme first passage time (FPT) theory.

While FPT theory is often used to estimate timescales in biology, the overwhelming majority of studies focus on the time it takes a given single searcher to find a target. However, in many scenarios the more relevant timescale is the FPT of the first searcher to find a target from a large group of searchers. This so-called extreme FPT depends on rare events and is often orders of magnitude faster than the FPT of a given single searcher. In this talk, we will explain recent results in extreme FPT theory and show how they modify traditional notions of diffusion timescales.

King-Yeung Lam:
PDEs in Evolution of Dispersal

Beginning with the work of Alan Hastings in 1983, PDE models have played a major role in the mathematical study of evolution of dispersal. In this talk, I will discuss two classes of PDE models that comes from evolution of dispersal. In the first part, I will discuss existence/non-existence of evolutionarily stable strategies (ESS) in two-species competition models, which is motivated by the adaptive dynamics approach. In the second part, I will introduce a new class of models that describes a population structured by a quantitative trait, which describes the competition of an infinite number of species in a certain sense. We show the convergence to ESS in these models of a quantitative trait, and explain how that is connected to the aforementioned adaptive dynamics framework. This talk contains projects in collaboration with R.S. Cantrell, C. Cosner, M. Golubitsky, W. Hao, B. Perthame, Y. Lou, and F. Lutscher.

Bo Li:
Spatiotemporal Dynamics of Bacterial Colony Growth with Cell-Cell Mechanical Interactions

The growth of bacterial colony exhibits striking complex patterns and robust scaling laws. Understanding the principles that underlie such growth has far-reaching consequences in biological and health sciences. In this work, we develop a mechanical theory of cell-cell and cell-environmental interactions and construct a hybrid three-dimensional computational model for the growth of E. coli colony on a hard agar surface. Our model consists of microscopic descriptions of the growth, division, and movement of individual cells, and macroscopic diffusion equations for the nutrients. The cell movement is driven by the cellular mechanical interactions. Our large-scale simulations and analysis predict the linear growth of the colony in both the radial and vertical directions in a good agreement with the experimental observations. We find that the mechanical buckling and nutrient penetration are the key factors in determining the underlying growth scalings. This work is the first step toward detailed computational modeling of bacterial growth with mechanical and biochemical interactions. This is joint work with Mya Warren, Hui Sun, Yue Yan, Jonas Cremer, and Terence Hwa.

Tiejun Li:
Some Recent Results on scRNA-seq Data Analysis

scRNA-seq data analysis is one of the most exciting topics in computational biology and it is currently in the fast developing stage. In this talk I will introduce the main issues in this area and some recent methods developed by our group. The covered topics include the stemness identification, lineage inference, cell clustering  and batch removal.

Sookkyung Lim:
How do bacteria swim? Modeling, Simulations & Analysis

Swimming bacteria with helical flagella are self-propelled micro-swimmers in nature, and the swimming strategies of such bacteria vary depending on the number of flagella and where the flagella are positioned on the cell body. In this talk, I will introduce two microorganisms, multi-flagellated E. coli and single-flagellated Vibrio A. We describe a rod-shaped cell body as a rigid body that can translate and rotate, and each helical flagellum as an elastic rod using the Kirchhoff rod theory. The hydrodynamic interaction of the bacterium is described by the regularized Stokeslet formulation. In this talk, I will focus on how bacteria can swim and reorient their swimming course for survival and how Mathematics can help to understand the swimming mechanism of such bacteria.

Yoichiro Mori:
Planar front Instabilities of the Bidomain Allen-Cahn Equation

The bidomain model is the standard model describing electrical activity of the heart. We discuss the stability of planar front solutions of the bidomain equation with a bistable nonlinearity (the bidomain Allen‐Cahn equation) in two spatial dimensions. In the bidomain Allen‐Cahn equation a Fourier multiplier operator whose symbol is a positive homogeneous rational function of degree two (the bidomain operator) takes the place of the Laplacian in the classical Allen‐Cahn equation. Stability of the planar front may depend on the direction of propagation given the anisotropic nature of the bidomain operator. We establish various criteria for stability and instability of the planar front in each direction of propagation. Our analysis reveals that planar fronts can be unstable in the bidomain Allen‐Cahn equation in striking contrast to the classical or anisotropic Allen‐Cahn equations. We identify two types of instabilities, one with respect to long‐wavelength perturbations, the other with respect to medium‐wavelength perturbations. Interestingly, whether the front is stable or unstable under long‐wavelength perturbations does not depend on the bistable nonlinearity and is fully determined by the convexity properties of a suitably defined Frank diagram. On the other hand, stability under intermediate‐wavelength perturbations does depend on the choice of bistable nonlinearity. Intermediate‐wavelength instabilities can occur even when the Frank diagram is convex, so long as the bidomain operator does not reduce to the Laplacian. We shall also give a remarkable example in which the planar front is unstable in all directions. Time permitting, I will also discuss properties of the bidomain FitzHugh Nagumo equations. This is joint work with Hiroshi Matano, Mitsunori Nara and Koya Sakakibara.

Qing Nie:
Multiscale inference and modeling of cell fate via single-cell data

Cells make fate decisions in response to dynamic environmental and pathological stimuli as well as cell-to-cell communications.  Recent technological breakthroughs have enabled to gather data in previously unthinkable quantities at single cell level, starting to suggest that cell fate decision is much more complex, dynamic, and stochastic than previously recognized. Multiscale interactions, sometimes through cell-cell communications, play a critical role in cell decision-making. Dissecting cellular dynamics emerging from molecular and genomic scale in single-cell demands novel computational tools and multiscale models. In this talk, through multiple biological examples we will present our recent effort in the center to use single-cell RNA-seq data and spatial imaging data to uncover new insights in development, regeneration, and cancers. We will also present several new computational tools and mathematical modeling methods that are required to study the complex and dynamic cell fate process through the lens of single cells.

David Rand:
TimeTeller: a New Tool for Precision Circadian Medicine and Cancer Prognosis

Recent research has shown that the circadian clock has a much more profound effect on human health than previously thought. I will present a machine-learning approach to measuring circadian clock functionality from the expression levels of key genes in a single tissue sample and then apply this to study survival in a breast cancer clinical trail.

A principal aim of circadian medicine is to develop techniques and methods to integrate the relevance of biological time into clinical practice. However, it is difficult to monitor the functional state of the circadian clock and its downstream targets in humans. Consequently, there is a critical need for tools to do this that are practical in a clinical context and our approach tackles this. We apply our algorithm to breast cancer and show that in a large cohort of patients with non-metastatic breast cancer the resulting dysfunction metric is a prognostic factor for survival providing evidence that it is independent of other known factors. While previous work in this area is focused on individual genes, our approach directly assesses the systemic functionality of a key regulatory system, the circadian clock, from one sample.

Alexandria Volkening:
Modeling and analysis of agent-based dynamics

Agent-based dynamics appear across the natural and social world; applications include swarming and flocking, pedestrian crowd movement, traffic flow, and the self-organization of cells during early development of organisms. Though disparate in application, many of these emergent patterns and collective dynamics share similar features (e.g. long-range communication, noise, fluctuations in population size, and multiple types of agents) and face some of the same modeling and analysis challenges. In this talk, I will use the concrete example of pigment-cell interactions during zebrafish-pattern formation to illustrate various ways of modeling agent behavior, including cellular automaton, agent-based, and continuum (PDE) models. We will discuss how these different approaches are related and highlight new ways of analyzing agent-based models and data using topological techniques.

Martin Wechselberger:
Geometric singular perturbation theory beyond the standard form

In this talk I will review geometric singular perturbation theory, but with a twist— I focus on a coordinate-independent setup of the theory. The need for such a theory beyond the standard form is motivated by looking at biochemical reaction, electronic and mechanical oscillator models that show relaxation-type behaviour. While the corresponding models incorporate slow and fast processes leading to multiple time-scale dynamics, not all of these models take globally the form of a standard slow–fast system. Thus from an application point of view, it is desirable to provide tools to analyse singularly perturbed systems in a coordinate-independent manner.

Padi Fuster Aguilera:
A PDE model for chemotaxis with logarithmic sensitivity and logistic growth

We study a particular model derived from a chemotaxis model with logarithmic sensitivity and logistic growth. We obtain existence and uniqueness of solutions as well as results for the limit diffusion of the solutions with Neumann boundary conditions.

Yonatan Ashenafi
Statistical Mobility Properties of Choanoflagellate Colonies

We study the stochastic hydrodynamics of aggregate random walkers (ARWs) typified by organisms called Choanoflagellates. The objective is to link cell-scale dynamics to colony-scale dynamics for Choanoflagellate rosettes and chains. We use a synthesis of linear autoregressive stochastic processes to explain the effective statistical dynamics of the Choanoflagellate colonies in terms of colony parameters. We model and characterize the non-linear chemotactic reaction of the aggregates to a local chemical gradient in terms of colony parameters.

Zviiteyi Chazuka
A mathematical model for in host dynamics of an immune evading virus

High risk human papillomaviruses (HPV) 16, 18, 31, 45 are one of the major causative agents of cervical cancer in women globally and it is estimated that about 80% of women are infected by HPV mainly due to sexual activities within their life time [2]. Out of these infections and re-infections some develop into persistent infections that lead to cancer lesions while some can be cleared provided they are detected by the immune system. Immune response within the body plays a pivotal role in clearing most infections that constantly affect us. Interestingly viruses such as HPV are seemingly very “clever” in concealing their presence within cells as they devise many ways of avoiding detection by the immune system and therefore manage to create an anti-inflammatory micro environment[1, 3]. This leads us to interesting mathematical modeling research of a little ’‘clever immune evading virus”. We create a mathematical model for the dynamics of HPV in the presence of immune response and rigorous mathematical calculation show that there exist three equilibrium points whose stability both local and global is shown. An investigation into the probable possibility of a bifurcation is done using the center manifold theory. Results show that a forward bifurcation exists and hence the endemic equilibrium is locally asymptotically stable provided that R0 > 1 and unstable otherwise. Numerical simulations prove and support the theoretical work presented. Numerical simulations establish that HPV can be eliminated from the body when R0 < 1 and persistence occurs either when there is immune response evasion R0 > 1, RCT L < 1 or when there is immune response R0 > 1, RCT L > 1. It is envisaged that the results of the study will be used further on to analyse the epidemiological link within the complex dynamics of HIV/HPV in the presence of stochastic perturbations, which is the core of the PhD work.

Veronica Ciocanel:
Topological data analysis for biological ring channels

Contractile rings are cellular structures made of actin filaments that are important in development, wound healing, and cell division. In the reproductive system of the roundworm C. elegans, ring channels allow nutrient exchange between developing egg cells and the worm and are regulated by forces exerted by myosin motor proteins.

In this work, we use and agent-based modeling and data analysis framework for the interactions between actin filaments and myosin motor proteins inside cells. This approach may provide key insights for the mechanistic differences between two motors that are believed to maintain the rings at a constant diameter. In particular, we propose tools from topological data analysis to understand time-series data of filamentous network interactions. Our proposed methods clearly reveal the impact of certain parameters on significant topological circle formation, thus giving insight into ring channel formation and maintenance.

Judy Day:
Modeling inhalation anthrax infection: a research journey

From work initiated at the Mathematical Biosciences Institute, a mathematical model was published in 2011 that investigated the immune response to inhalation anthrax infection. That publication led to a collaboration with the U.S. Environmental Protection Agency which blossomed into a Investigative Working Group effort supported by the National Institute for Mathematical and Biological Synthesis. This group included experts from both the anthrax research community as well as mathematical modelers. Over a period of several years, members of this group explored the utility of mathematical modeling in understanding risk in low dose inhalation anthrax infection. This poster describes the journey of the research that was inspired by these events and discusses the results and relationships it generated.

Dan Dougherty:
Techniques for Driving Progress in Industrial Biotechnology

Amyris (NASDAQ: AMRS) is a science and technology leader in the research, development and production of pure, sustainable ingredients for the Health & Wellness, Clean Beauty and Flavors & Fragrances markets. Amyris applies its exclusive, advanced technology, including state-of-the-art machine learning, robotics and artificial intelligence to engineer yeast, that when combined with sugarcane syrup through fermentation, is converted to highly pure molecules for specialty ingredients. Amyris manufactures sustainably-sourced ingredients at industrial scale for B2B partners and further distribution to over 3,000 of the world's top brands, reaching more than 200 million consumers. Amyris stands by its No Compromise® promise that everything it makes is better for people and the planet. In this presentation, we provide examples of computational techniques used throughout the design, build, test, and learn phases of research and development. We’ll highlight prominent aspects of the natural biology of yeast and how they inform the computational approaches used. Measures of statistical and computational efficiency will be provided and we’ll conclude with some recommendations for future developments.

Daniel J. Glazar:
Tumor volume dynamics as an early biomarker for patient-specific evolution of resistance and progression in recurrent high-grade glioma

Recurrent high-grade glioma (HGG) remains incurable with inevitable evolution of resistance and high inter-patient heterogeneity in time to progression (TTP). A predictive model is needed to predict patient-specific resistance evolution and develop opportunities for treatment adaptation for patients with high risk of imminent progression. Here we evaluate if early tumor volume response dynamics can calibrate a mechanistic mathematical model to predict patient-specific resistance and progression. In a phase I clinical trial, Response Assessment in Neuro-Oncology (RANO) criteria were used to assess response to hypofractionated stereotactic radiation (HFSRT; 6 Gy x 5) plus Pembrolizumab (100 mg or 200 mg, every 3 weeks) and Bevacizumab (10 mg/kg, every 2 weeks) in HGG patients (NCT02313272). A total of 95 T1post MRIs from 14 patients were delineated to derive longitudinal tumor volumes. We develop, calibrate, and validate a mathematical model that simulates and forecasts tumor volume dynamics with rate of resistance evolution as the single patient-specific parameter. Model prediction performance is evaluated based on how early progression is predicted and the number of false negatives. In a leave-one-out study, the model was able to predict progression in 9 patients a median of 9.7 (range: 3–39.3) weeks early (median progression-free survival was 27.4 weeks). Our results demonstrate that early tumor volume dynamics measured on T1post imaging have the potential to predict progression following the protocol therapy in select patients with recurrent HGG. Future work will include testing on an independent patient dataset and evaluation of the developed framework on T2/FLAIR-derived data.

Wasiur KhudaBukhsh:
Survival Dynamical Systems: individual-level survival analysis from population-level epidemic models 

Ruby Kim:
A mathematical model of circadian rhythms and dopamine

The superchiasmatic nucleus (SCN) serves as the primary circadian (24hr) clock in mammals, and is known to control important physiological functions such as the sleep-wake cycle, hormonal rhythms, and neurotransmitter regulation. Experimental results suggest that some of these functions reciprocally influence circadian rhythms, creating a complex and highly homeostatic network. Among the clock's downstream products, orphan nuclear receptors REV-ERB and ROR are particularly interesting because they coordinately modulate the core clock circuitry. Recent experimental evidence shows that REV-ERB and ROR are not only crucial for lipid metabolism, but are also involved in dopamine (DA) synthesis and degradation, which could have meaningful clinical implications for conditions such as Parkinson's disease and mood disorders.

We create a mathematical model that includes the circadian clock, REV-ERB and ROR and their feedback to the clock, and the influences of REV-ERB, ROR, and BMAL1-CLOCK on the dopaminergic system. We compare our model predictions to experimental data on clock components in different light-dark conditions and in the presence of genetic perturbations. Our model results are consistent with experimental results on REV-ERB and ROR and allow us to predict circadian oscillations in extracellular dopamine and homovanillic acid that correspond well with observations.

The predictions of the mathematical model are consistent with a wide variety of experimental observations. Our calculations show that the mechanisms proposed by experimentalists by which REV-ERB, ROR, and BMAL1-CLOCK influence the DA system are sufficient to explain the circadian oscillations observed in dopaminergic variables. Our mathematical model can be used for further investigations of the effects of the mammalian circadian clock on the dopaminergic system. \RR{The model can be used to predict how perturbations in the circadian clock disrupt the dopamine system and could potentially be used to find drug targets that ameliorate these disruptions.

Fahad Mostafa
Better model selection for optimal prediction of breast cancer using machine learning with multivariate statistical analysis

Breast cancer is a chronic disease and costly diagnosis. According to U.S. breast cancer statistics, almost 276,480 new cases of invasive breast cancer are expected in 2020. The primary aim of this study is to illustrate the use of many statistical techniques to analyze multivariate data arising from a breast cancer study. To do this we start with an exploratory study to develop and assess a predictive model, which can potentially be used as a bio-marker of breast cancer, based on anthropometric data that were gathered in routine blood analysis of 116 women. A main aim of this research is to reduce dimensionality of the data using an eigen-decomposition of the data matrix. To perform it, we use the common principal component analysis (PCA) method. Then we test hypotheses based on the exploratory analysis for checking distributional assumptions and evaluating claims about the mean vector and covariance matrix for the breast cancer data. We also find simultaneous confidence intervals for our data to illustrate differences between patients with and without breast cancer.  Based on these results, we then use advance statistical models as well as machine learning techniques to find predictors for the presence of breast cancer in patients. Finally, we use Fisher’s Discriminant Analysis to classify within- and between-groups for magnetic resonance (MR) and computed tomography (CT) imaging data. To validate our model, we use k-fold cross validation. Between several technique we found NBC and SVM are better performer and only BMI, Glucose and Resistin are competent out of nine different predictors.

Bismark Oduro:
Initial aggressive treatment strategies for controlling vector-borne disease like Chagas

Chagas disease is a major health problem in rural South and Central America where an estimated 8 to 11 million people are infected. It is a vector-borne disease caused by the parasite Trypanosoma cruzi, which is transmitted to humans mainly through the bite of insect vectors from several species of so-called kissing bugs. One of the control measures to reduce the spread of the disease is insecticide spraying of housing units to prevent infestation by the vectors. However, re-infestation of units by vectors has been shown to occur as early as four to six months after insecticide-based control interventions. I will present ordinary differential

equation models of type SIRS that shed light on long-term cost effectiveness of certain strategies for controlling re-infestation by vectors. The results show that an initially very high spraying rate may push the system into a region of the state space with low endemic levels of infestation that can be maintained in the long run at relatively moderate cost.

Marissa Renardy
Temporal and spatial analyses of TB granulomas to predict long-term outcomes