Scholarly Works, Center for the Mathematics of Biosystems

Permanent URI for this collection

https://hdl.handle.net/10919/123757

The Center for the Mathematics of Biosystems was created in 2024 and incorporates the former Interdisciplinary Center for Applied Mathematics (ICAM).

Browse

Now showing 1 - 20 of 20

Mathematical modeling of malaria vaccination with seasonality and immune feedback
Qu, Zhuolin; Patterson, Denis; Zhao, Lihong; Ponce, Joan; Edholm, Christina J.; Prosper-Feldmen, Olivia F.; Childs, Lauren M. (Public Library of Science, 2025-05)
Malaria is one of the deadliest infectious diseases globally, claiming hundreds of thousands of lives each year. The disease presents substantial heterogeneity among the population, with approximately two-thirds of fatalities occurring in children under five years old. Immunity to malaria develops through repeated exposure and plays a crucial role in disease dynamics. Seasonal environmental fluctuations, such as changes in temperature and rainfall, lead to temporal heterogeneity and further complicate transmission dynamics and the utility of intervention strategies. We employ an age-structured partial differential equation model to characterize seasonal malaria transmission and assess vaccination strategies that vary by timing and duration. Our model integrates vector-host epidemiological dynamics across different age groups and nonlinear feedback between transmission and immunity. We calibrate the model to year-round and seasonal malaria settings and conduct extensive sensitivity analyses for both scenarios to systematically assess which assumptions lead to the most uncertainty. We use time-varying sensitivity indices to identify critical disease parameters during low and high transmission seasons. We further investigate the impact of vaccination and its implementation in the seasonal malaria settings. When implementing a three-dose primary vaccination series, seasonally targeted campaigns can prevent significantly more cases per vaccination than constant year-long programs in regions with strong seasonal variation in transmission. In such scenarios, the optimal vaccination interval aligns with the peak in infected mosquito abundance and precedes the peak in malaria transmission. In contrast, seasonal booster programs may provide limited advantages over year-long vaccination. Additionally, while increasing annual vaccination counts can reduce overall disease incidence, it yields marginal improvements in cases prevented per vaccination.
Unveiling an Immunological Mystery: Deciphering the Durability Divide Between Infection and Vaccine-Elicited Antibody Responses
Lewis, George K.; Ciupe, Stanca M.; Sajadi, Mohammad (Bentham Science Publishers, 2025-07-23)
Achieving durable antibody-mediated protection remains critical in vaccine develop-ment, particularly for viral diseases like COVID-19 and HIV. We discuss factors influencing an-tibody durability, highlighting the role of long-lived plasma cells (LLPCs) in the bone marrow, which are essential for sustained antibody production over many years. The frequencies and prop-erties of bone marrow LLPC are critical determinants of the broad spectrum of antibody durability for different vaccines. Vaccines for diseases like measles and mumps elicit long-lasting antibod-ies; those for COVID-19 and HIV do not. High epitope densities in the vaccine are known to favor antibody durability, but we discuss three underappreciated variables that also play a role in long-lived antibody responses. First, in addition to high epitope densities, we discuss the im-portance of CD21 as a critical determinant of antibody durability. CD21 is a B cell antigen recep-tor (BCR) complex component. It significantly affects BCR signaling strength in a way essential for generating LLPC in the bone marrow. Second, all antibody-secreting cells (ASC) are not cre-ated equal. There is a four-log range of antibody secretion rates, and we propose epigenetic im-printing of different rates on ASC, including LLPC, as a factor in antibody durability. Third, antibody durability afforded by bone marrow LLPC is independent of continuous antigenic stim-ulation. By contrast, tissue-resident T-bet+CD21low ASC also persists in secondary lymphoid tissues and continuously produces antibodies depending on persisting antigen and the tissue mi-croenvironment. We discuss these variables in the context of making an HIV vaccine that elicits broadly neutralizing antibodies against HIV that persist at protective levels without continuous vaccination over many years.
Bistability between acute and chronic states in a Model of Hepatitis B Virus Dynamics
Afrin, Nazia; Ciupe, Stanca M.; Conway, Jessica M.; Gulbudak, Hayriye (Elsevier, 2025-05-31)
Understanding the mechanisms responsible for different clinical outcomes following hepatitis B infection requires a systems investigation of dynamical interactions between the virus and the immune system. To help elucidate mechanisms of protection and those responsible from transition from acute to chronic disease, we developed a deterministic mathematical model of hepatitis B infection that accounts for cytotoxic immune responses resulting in infected cell death, non-cytotoxic immune responses resulting in infected cell cure and protective immunity from reinfection, and cell proliferation. We analyzed the model and presented outcomes based on three important disease markers: the basic reproduction number R0, the infected cells death rate δ (describing the effect of cytotoxic immune responses), and the liver carrying capacity K (describing the liver susceptibility to infection). Using asymptotic and bifurcation analysis techniques, we determined regions where virus is cleared, virus persists, and where clearance-persistence is determined by the size of viral inoculum. These results can guide the development of personalized intervention.
Post-recovery viral shedding shapes wastewater-based epidemiological inferences
Phan, Tin; Brozak, Samantha; Pell, Bruce; Ciupe, Stanca M.; Ke, Ruian; Ribeiro, Ruy M.; Gitter, Anna; Mena, Kristina D.; Perelson, Alan S.; Kuang, Yang; Wu, Fuqing (Springer Nature, 2025-05-22)
Background: The prolonged viral shedding from the gastrointestinal tract is well documented for numerous pathogens, including SARS-CoV-2. However, the impact of prolonged viral shedding on epidemiological inferences using wastewater data is not yet fully understood. Methods: To gain a better understanding of this phenomenon at the population level, we extended a wastewater-based modeling framework that integrates viral shedding dynamics, viral load data in wastewater, case report data, and an epidemic model. Results: Our results indicate that as an outbreak progresses, the viral load from recovered individuals gradually becomes predominant, surpassing that from the infectious population. This phenomenon leads to a dynamic relationship between model-inferred and reported daily incidence over the course of an outbreak. Sensitivity analyses on the duration and rate of viral shedding for recovered individuals reveal that accounting for this phenomenon can considerably advance prediction of transmission peak timing. Furthermore, extensive viral shedding from the recovered population toward the conclusion of an epidemic wave may overshadow viral signals from newly infected cases carrying emerging variants, which can delay the rapid recognition of emerging variants based on viral load. Conclusions: These findings highlight the necessity of integrating post-recovery viral shedding to enhance the accuracy and utility of wastewater-based epidemiological analysis.
Investigation of a Two-Patch Within-Host Model of Hepatitis B Viral Infection
Castellano, Keoni; Saucedo, Omar; Ciupe, Stanca M. (Springer, 2025-12)
Chronic infection with hepatitis B virus (HBV) can lead to formation of abnormal nodular structures within the liver. To address how changes in liver anatomy affect overall virus-host dynamics, we developed within-host ordinary differential equation models of two-patch hepatitis B infection, one that assumes irreversible and one that assumes reversible movement between nodular structures. We investigated the models analytically and numerically, and determined the contribution of patch susceptibility, immune responses, and virus movement on within-patch and whole-liver virus dynamics. We explored the structural and practical identifiability of the models by implementing a differential algebra approach and the Monte Carlo approach for a specific HBV data set. We determined conditions for viral clearance, viral localization, and systemic viral infection. Our study suggests that cell susceptibility to infection within modular structures, the movement rate between patches, and the immune-mediated infected cell killing have the most influence on HBV dynamics. Our results can help inform intervention strategies.
Chromosomal inversions and their impact on insect evolution
Sharakhov, Igor V.; Sharakhova, Maria V. (Elsevier, 2024-12)
Insects can adapt quickly and effectively to rapid environmental change and maintain long-term adaptations, but the genetic mechanisms underlying this response are not fully understood. In this review, we summarize studies on the potential impact of chromosomal inversion polymorphisms on insect evolution at different spatial and temporal scales, ranging from long-term evolutionary stability to rapid emergence in response to emerging biotic and abiotic factors. The study of inversions has recently been advanced by comparative, population, and 3D genomics methods. The impact of inversions on insect genome evolution can be profound, including increased gene order rearrangements on sex chromosomes, accumulation of transposable elements, and facilitation of genome divergence. Understanding these processes provides critical insights into the evolutionary mechanisms shaping insect diversity.
Mechanistic modeling of mitosis: Insights from three collaborative case studies
Chen, Jing; Cimini, Daniela (Elsevier, 2025-11-01)
Mechanistic mathematical modeling has become an essential tool in modern biological research due to its powerful ability to integrate diverse data, generate hypotheses, and guide experimental design. It is particularly valuable for studying complex cellular mechanisms involving numerous interacting components. While the full dynamics of such systems usually elude direct experimental observation, modeling provides a means to integrate fragmented data with reasonable and/or informed assumptions into coherent mechanistic frameworks, simulate system behavior, and identify promising directions for further experimentation. When closely integrated with experiments, modeling can greatly accelerate progress in cell biology. However, the value of modeling is not automatic—it must be earned through careful model construction, critical interpretation of results, and thoughtful design of follow-up experiments. To demystify this process, we review three of our collaborative projects in mitosis, drawing on our experiences as a modeler and an experimentalist. We describe how the projects were initiated, why specific modeling approaches were chosen, how models were developed and refined, how model predictions guided new experiments, and how integrated modeling and experimentation led to deeper mechanistic insights. Finally, we emphasize that at the heart of every successful collaboration lies human connection. Productive cross-disciplinary communication is fundamental to bridging experimental and modeling perspectives and fully realizing the potential of integrative approaches in modern cell biology.
Computing Functional Gains for Designing More Energy-Efficient Buildings Using a Model Reduction Framework
Akhtar, Imran; Borggaard, Jeffrey T.; Burns, John A. (MDPI, 2018-11-23)
We discuss developing efficient reduced-order models (ROM) for designing energy-efficient buildings using computational fluid dynamics (CFD) simulations. This is often the first step in the reduce-then-control technique employed for flow control in various industrial and engineering problems. This approach computes the proper orthogonal decomposition (POD) eigenfunctions from high-fidelity simulations data and then forms a ROM by projecting the Navier-Stokes equations onto these basic functions. In this study, we develop a linear quadratic regulator (LQR) control based on the ROM of flow in a room. We demonstrate these approaches on a one-room model, serving as a basic unit in a building. Furthermore, the ROM is used to compute feedback functional gains. These gains are in fact the spatial representation of the feedback control. Insight of these functional gains can be used for effective placement of sensors in the room. This research can further lead to developing mathematical tools for efficient design, optimization, and control in building management systems.
Model Reduction for DAEs with an Application to Flow Control
Borggaard, Jeffrey T.; Gugercin, Serkan (Springer-Verlag Berlin, 2015-01-01)
Learning-based Robust Stabilization for Reduced-Order Models of 2D and 3D Boussinesq Equations
Benosman, Mouhacine; Borggaard, Jeffrey T.; San, Omer; Kramer, Boris (2017-09)
We present some results on the stabilization of reduced-order models (ROMs) for thermal fluids. The stabilization is achieved using robust Lyapunov control theory to design a new closure model that is robust to parametric uncertainties. Furthermore, the free parameters in the proposed ROM stabilization method are optimized using a data-driven multiparametric extremum seeking (MES) algorithm. The 2D and 3D Boussinesq equations provide challenging numerical test cases that are used to demonstrate the advantages of the proposed method.
A new wavelet family based on second-order LTI-systems
Abuhamdia, Tariq; Taheri, Saied; Burns, John A. (SAGE, 2016)
In this paper, a new family of wavelets derived from the underdamped response of second-order Linear-Time-Invariant (LTI) systems is introduced. The most important criteria for a function or signal to be a wavelet is the ability to recover the original signal back from its continuous wavelet transform. We show that it is possible to recover back the original signal once the Second-Order Underdamped LTI (SOULTI) wavelet is applied to decompose the signal. It is found that the SOULTI wavelet transform of a signal satisfies a linear differential equation called the reconstructing differential equation, which is closely related to the differential equation that produces the wavelet. Moreover, a time-frequency resolution is defined based on two different approaches. The new transform has useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying harmonic signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The results obtained are presented with analytical and numerical examples. Signals with constant harmonics and signals with time-varying frequencies are analyzed, and their evolutionary spectrum is obtained. Contour mapping of the transform in the time-scale and the time-frequency domains clearly detects the change of the frequency content of the analyzed signals with respect to time. The results are compared with other wavelets results and with the short-time fourier analysis spectrograms. At the end, we propose the method of reverse wavelet transform to mitigate the edge effect.
Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition
Hay, Alexander; Borggaard, Jeffrey T.; Pelletier, Dominique (Cambridge University Press, 2009-06)
The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis accurately represents the flow data used to generate it, but may not be accurate when applied 'off-design'. Thus, the reduced-order model may lose accuracy for flow parameters (e.g. Reynolds number, initial or boundary conditions and forcing parameters) different from those used to generate the POD basis and generally does. This paper investigates the use of sensitivity analysis in the basis selection step to partially address this limitation. We examine two strategies that use the sensitivity of the POD modes with respect to the problem parameters. Numerical experiments performed on the flow past a square cylinder over a range of Reynolds numbers demonstrate the effectiveness of these strategies. The newly derived bases allow for a more accurate representation of the flows when exploring the parameter space. Expanding the POD basis built at one state with its sensitivity leads to low-dimensional dynamical systems having attractors that approximate fairly well the attractor of the full-order Navier-Stokes equations for large parameter changes.
Shape Sensitivity Analysis in Flow Models Using a Finite-Difference Approach
Akhtar, Imran; Borggaard, Jeffrey T.; Hay, Alexander (Hindawi Publishing Corporation, 2010)
Reduced-order models have a number of practical engineering applications for unsteady flows that require either low-dimensional approximations for analysis and control or repeated simulation over a range of parameter values. The standard method for building reduced-order models uses the proper orthogonal decomposition (POD) and Galerkin projection. However, this standard method may be inaccurate when used "off-design" (at parameter values not used to generate the POD). This phenomena is exaggerated when parameter values describe the shape of the flow domain since slight changes in shape can have a significant influence on the flow field. In this paper, we investigate the use of POD sensitivity vectors to improve the accuracy and dynamical system properties of the reduced-order models to problems with shape parameters. To carry out this study, we consider flows past an elliptic cylinder with varying thickness ratios. Shape sensitivities (derivatives of flow variables with respect to thickness ratio) computed by finite difference approximations are used to compute the POD sensitivity vectors. Numerical studies test the accuracy of the new bases to represent flow solutions over a range of parameter values.
Issues related to least-squares finite element methods for the stokes equations
Deang, Jennifer M.; Gunzburger, Max D. (Siam Publications, 1998-10)
Least-squares finite element methods have become increasingly popular for the approximate solution of first-order systems of partial differential equations. Here, after a brief review of some existing theories, a number of issues connected with the use of such methods for the velocity-vorticity-pressure formulation of the Stokes equations in two dimensions in realistic settings are studied through a series of computational experiments. Finite element spaces that are not covered by existing theories are considered; included in these are piecewise linear approximations for the velocity. Mixed boundary conditions, which are also not covered by existing theories, are also considered, as is enhancing mass conservation. Next, problems in nonconvex polygonal regions and the resulting nonsmooth solutions are considered with a view toward seeing how accuracy can be improved. A conclusion that can be drawn from this series of computational experiments is that the use of appropriate mesh-dependent weights in the least-squares functional almost always improves the accuracy of the approximations. Concluding remarks concerning three-dimensional problems, the nonlinear Navier-Stokes equations, and the conditioning of the discrete systems are provided.
On efficient solutions to the continuous sensitivity equation using automatic differentiation
Borggaard, Jeffrey T.; Verma, Arun (Siam Publications, 2000-06)
Shape sensitivity analysis is a tool that provides quantitative information about the influence of shape parameter changes on the solution of a partial differential equation (PDE). These shape sensitivities are described by a continuous sensitivity equation (CSE). Automatic differentiation (AD) can be used to perform this sensitivity analysis without writing any additional code to solve the sensitivity equation. The approximate solution of the PDE uses a spatial discretization (mesh) that often depends on the shape parameters. Therefore, the straightforward application of AD introduces derivatives of the mesh. There are two drawbacks to this approach. First, extra computational effort (especially memory) is used in these calculations due to mesh sensitivities. Second, this mesh sensitivity information needs to be computed in order to obtain accurate results. In this work, we provide a methodology that avoids mesh sensitivities (and their drawbacks) by defining a modified PDE on a fixed domain (i.e., independent of the shape parameter) such that AD provides the desired approximation of the CSE. Using two examples, we demonstrate significant improvement in the computational effort, both in terms of floating point operations and memory requirements. We explain how these code modifications can be applied to a wide variety of practical problems with minimal changes to the original code. These changes are negligible when compared to the complexity of writing a separate solver for the sensitivity equation.
Inexact Kleinman-Newton method for Riccati equations
Feitzinger, Franziska; Hylla, Timo; Sachs, Ekkehard W. (Siam Publications, 2009-03)
In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results illustrate the efficiency of this method.
Mesh independence of Kleinman-Newton iterations for Riccati equations in Hilbert space
Burns, John A.; Sachs, Ekkehard W.; Zietsman, Lizette (Siam Publications, 2008)
In this paper we consider the convergence of the infinite dimensional version of the Kleinman-Newton algorithm for solving the algebraic Riccati operator equation associated with the linear quadratic regulator problem in a Hilbert space. We establish mesh independence for this algorithm and apply the result to systems governed by delay equations. Numerical examples are presented to illustrate the results.
On the Lawrence-Doniach and Anisotropic Ginzburg-Landau models for layered superconductors
Chapman, S. Jonathan; Du, Qiang; Gunzburger, Max D. (Siam Publications, 1995-02)
The authors consider two models, the Lawrence-Doniach and the anisotropic Ginzburg-Landau models for layered superconductors such as the recently discovered high-temperature superconductors. A mathematical description of both models is given and existence results for their solution are derived. The authors then relate the two models in the sense that they show that as the layer spacing tends to zero, the Lawrence-Doniach model reduces to the anisotropic Ginzburg-Landau model. Finally, simplified versions of the models are derived that can be used to accurately simulate high-temperature superconductors.
Comment on "A numerical study of periodic disturbances on two-layer Couette flow" [Phys. Fluids 10, 3056 (1998)]
Renardy, Yuriko Y.; Li, Jie (AIP Publishing, 1999-10)
The flow of fluids with different viscosities, subjected to an interfacial perturbation, can lead to fingering and migration...
A numerical study of periodic disturbances on two-layer Couette flaw
Li, Jie; Renardy, Yuriko Y.; Renardy, Michael J. (AIP Publishing, 1998-12)
The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds numbers, and a second-order velocity interpolation. The code is validated against linear theory for the stability of two-layer Couette flow, and weakly nonlinear theory for a Hopf bifurcation. Examples of long-time wave saturation are shown. The formation of fingers for relatively small initial amplitudes as well as larger amplitudes are presented in two and three dimensions as initial-value problems. Fluids of different viscosity and density are considered, with an emphasis on the effect of the viscosity difference. Results at low Reynolds numbers show elongated fingers in two dimensions that break in three dimensions to form drops, while different topological changes take place at higher Reynolds numbers. (C) 1998 American Institute of Physics. [S1070-6631(98)00612-6].

Browse

Recent Submissions