Letters in Biomathematics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib <p><strong><em>Letters in Biomathematics</em></strong> is an open-access journal that lies at the interface of mathematics, statistics, biology, ecology, and the life sciences. The journal publishes Research, Education, and Review articles related to biological, ecological and environmental settings in a very broad sense, as well as other related topic fields.</p> Intercollegiate Biomathematics Alliance en-US Letters in Biomathematics 2373-7867 The wisdom of a crowd of near-best fits https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/261 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">Antibiotic-resistant tuberculosis (TB) strains pose a major challenge to TB eradication. Existing US epidemiological models have not fully incorporated the impact of antibiotic-resistance. To develop a more realistic model of US TB dynamics, we formulated a compartmental model integrating single- and multi-drug resistance. We fit twenty-seven parameters to twenty-two years of historical data using a genetic algorithm to minimize a non-differentiable error function. Since counts for several compartments are not available, many parameter combinations achieve very low error. We demonstrate that a crowd of near-best fits can provide compelling new evidence about the ranges of key parameters. While available data is sparse and insufficient to produce point estimates, our crowd of near-best fits computes remarkably consistent predictions about TB prevalence. We believe that our crowd-based approach is applicable to a common problem in mathematical biological research, namely situations where data are sparse and reliable point estimates cannot be directly obtained.</p> Ellie Mainou Gwen Spencer Dylan Shepardson Robert Dorit Copyright (c) 2020 Letters in Biomathematics 2020-03-03 2020-03-03 7 1 15–35 15–35 A Mathematical model of Malaria transmission dynamics with general incidence function and maturation delay in a periodic environment https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/223 <p>In this paper, we investigate a mathematical model of malaria transmission dynamics with maturation delay of a vector population in a periodic environment. The incidence rate between vector and human hosts is modeled by a general nonlinear incidence function which satisfies a set of conditions. Thus, the model is formulated as a system of retarded functional differential equations. Furthermore, through dynamical systems theory, we rigorously analyze the global behavior of the model. Therefore, we prove that the basic reproduction number of the model denoted by <em>R</em><sub>0</sub> is the threshold between the uniform persistence and the extinction of malaria virus transmission. More precisely, we show that if <em>R</em><sub>0</sub> is less than unity, then the disease-free periodic solution is globally asymptotically stable. Otherwise, the system exhibits at least one positive periodic solution if <em>R</em><sub>0</sub> is greater than unity. Finally, we perform some numerical simulations to illustrate our mathematical results and to analyze the impact of the delay on the disease transmission.</p> Bakary Traoré Ousmane Koutou Boureima Sangaré Copyright (c) 2020 Letters in Biomathematics 2020-03-06 2020-03-06 7 1 37–54 37–54 A Near-Optimal Control Method for Stochastic Boolean Networks https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/207 <p class="pagecontents">One of the ultimate goals of computational biology and bioinformatics is to develop control strategies to find efficient medical treatments. One step towards this goal is to develop methods for changing the state condition of a cell into a new desirable state. Using a stochastic modeling framework generalized from Boolean Networks, we propose a computationally efficient method that determines sequential combinations of network perturbations, that induce the transition of a cell towards a new predefined state. The method requires a set of possible control actions as input, every element of this set represents the silencing of a gene or a disruption of the interaction between two molecules. An optimal control policy defined as the best intervention at each state of the system, can be obtained using theory of Markov decision processes. However, these algorithms are computationally prohibitive for models of tens of nodes. The proposed method generates a sequence of actions that approximates the optimal control policy with a computational efficiency that does not depend on the size of the state space of the system. The methods are validated by using published models where control targets have been identified. Our code in C++ is publicly available through GitHub at https://github.com/boaguilar/SDDScontrol.</p> Boris Aguilar Pan Fang Reinhard Laubenbacher David Murrugarra Copyright (c) 2020 Letters in Biomathematics 2020-05-04 2020-05-04 7 1 67–80 67–80 Statistical decomposition of cumulative epidemiological curves into autochthonous and imported cases https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/271 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">As a pathogen spreads throughout a human population network, understanding the time span between the first reported infection case and the establishment of local transmission relies on the ability to decompose infection incidence into local and travel cases, depending on whether the infected individual was exposed to the pathogen in their location of residence or elsewhere. However, most case data reported to public health agencies do not distinguish between local and travel-associated cases, hampering analysis of the critical early stages of the epidemic spread. We introduce an algorithm, based on the shape of the cumulative incidence curve, to estimate the time a pathogen takes to become locally established, based on the pathogen’s transmission and recovery rates and the network connectivity of the human population. This algorithm can predict the onset of an epidemic without considering any future case data, making it useful for tracking epidemics as they occur.</p> Brandon Lieberthal Aiman Soliman Allison Gardner Copyright (c) 2020 Letters in Biomathematics 2020-09-17 2020-09-17 7 1 111–125 111–125 A Discrete Age Structured Model of Hantavirus in a Rodent Reservoir in Paraguay https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/333 <p>Many rodent-borne hantaviruses are zoonotic pathogens that can cause disease in humans through inhalation of aerosolized rodent excreta. To evaluate the prevalence of Jaborá virus (JABV) over time within its rodent reservoir, <em>Akodon montensis</em>, we formulated a mathematical model with multiple rodent age classes and unique infection class progression features. We then parameterized the model with data collected from a survey of JABV harbored by <em>Akodon montensis</em> in the Mbaracayú Reserve in Paraguay. Our model incorporates three types of infection over the lifetime of the rodent as well as a recovered class. A new feature of the model allows transition from the latent to the persistently-infected class. With a more complete age and infection structure, we are better able to identify the driving forces of epidemiology of hantaviruses in rodent populations.</p> Morganne Igoe E. Joe Moran Theresa Sheets Jeff DeSalu Colleen B. Jonsson Suzanne Lenhart Robert D. Owen Megan A. Rúa Copyright (c) 2020 Letters in Biomathematics 2020-09-17 2020-09-17 7 1 127–142 127–142 Numerical Approaches to Division and Label Structured Population Models https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/395 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">Division and label structured population models (DLSPMs) are a class of partial differential equations (PDEs) that have been used to study intracellular dynamics in dividing cells. DLSPMs have improved the understanding of cell proliferation assays involving measurements such as fluorescent label decay, protein production, and prion aggregate amplification. One limitation in using DLSPMs is the significant computational time required for numerical approximations, especially for models with complex biologically relevant dynamics. Here we develop a novel numerical and theoretical framework involving a recursive formulation for a class of DLSPMs. We develop this framework for a population of dividing cells with an arbitrary functional form describing the intracellular dynamics. We found that, compared to previous methods, our framework is faster and more accurate. We illustrate our approach on three common models for intracellular dynamics and discuss the potential impact of our findings in the context of data-driven methods for parameter estimation.</p> Suzanne Sindi Fabian Santiago Kevin Flores Copyright (c) 2020 Letters in Biomathematics 2020-11-02 2020-11-02 7 1 153–170 153–170 A Mathematical Model to Study the Fundamental Functions of Phagocytes and Inflammatory Cytokines During the Bone Fracture Healing Process https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/349 <p>A mathematical model is presented to study the effects of phagocytes and inflammatory cytokines on bone fracture healing during the early stages of the process. The model incorporates the interactions among macrophages, mesenchymal stem cells, osteoblasts, inflammatory cytokines, and the cartilage and bone extracellular matrices. The resulting system of nonlinear ordinary differential equations is studied analytically and numerically. The stability analysis revealed that the excessive accumulation of phagocytes and inflammatory cytokines at the injury site can lead to unsuccessful fracture healing, while the numerical simulations showed that optimal healing depends on the abilities of phagocytes to efficiently engulf debris.&nbsp; A variety of numerical simulations are also presented to monitor the healing of a broken bone under different biological conditions, suggesting multiple possible ways to guide clinical experiments and factors that can be manipulated to achieve optimal outcomes.</p> Imelda Trejo Hristo Kojouharov Copyright (c) 2020 Letters in Biomathematics 2020-11-03 2020-11-03 7 1 171–189 171–189 Modeling and analysis of the firefly luciferase reaction and the G-protein coupled receptor signaling pathway with ordinary differential equations increases self confidence in mathematical cell biology for novice graduate students https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/205 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">The push for mathematics and computation in biology is greater than ever before. However, perceptions among biology students on the difficulty of mathematics and programming are a barrier to their implementation. A teaching module introducing quantitative skills to biology students is needed. We implemented modeling of firefly luciferase and G-protein coupled receptor signaling with ordinary differential equations in a course for novice graduate students. We assessed whether the course helped the students increase self confidence in application of mathematics in biology. Two concept inventories tracked learning gains in both general and cell biology knowledge. Pre- and post-semester surveys quantified changes in student confidence and their opinions of the usefulness of these techniques in cell biology. We found that the modeling and analysis activities appeared to improve self confidence in and appreciation of quantitative mathematical biology techniques. We describe our assessment methods to determine the suitability of our module.</p> Renee Dale Naohiro Kato Bill Wischusen Copyright (c) 2020 Letters in Biomathematics 2020-02-28 2020-02-28 7 1 3–13 3–13 21st Century Reform Efforts in Undergraduate Quantitative Biology Education https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/215 <p>In the United States, there are multiple reports from both mathematics and biology communities that address the quantitative preparation of undergraduate life science students. Many of them make broad recommendations for the revision of life science curriculum to incorporate more quantitative techniques. Here, we review initiatives and progress in the United States on the state of quantitative biology education in the context of the mathematics education, biology research frontiers, and the funding system and other sources of support for systemic change to meet new demands.</p> Carrie Diaz Eaton M. Drew LaMar Maeve McCarthy Copyright (c) 2020 Letters in Biomathematics 2020-05-04 2020-05-04 7 1 55–66 55–66 Algebraic models, inverse problems, and pseudomonomials from biology https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/291 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">In contrast to the extensive use of linear algebra in biology, problems involving nonlinear polynomials—the field of <em>algebraic biology</em>—are more conspicuous. In this article, we highlight two biological problems where similar algebraic structures arise in very different contexts. Specifically, we will look at algebraic models of molecular networks, and combinatorial codes of place fields in neuroscience. Both of these topics involve inverse problems where the data is encoded with <em>pseudomonomials</em>, simple algebraic objects that do not seem to have been studied much on their own, but have gained considerable attention lately from their visibility in mathematical biology. Though this article is algebraic in nature, it is written for the general mathematician with a minimal algebra background assumed. It provides two distinctive features that have not yet appeared in the literature: (i)&nbsp;a survey of Boolean and logical modeling from a computational algebra perspective, and (ii)&nbsp;a unification of this topic with algebraic neuroscience by highlighting the role of pseudomonomials in both fields.</p> Matthew Macauley Raina Robeva Copyright (c) 2020 Letters in Biomathematics 2020-07-12 2020-07-12 7 1 81–104 81–104 An Important Milestone Reached https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/251 Olcay Akman Copyright (c) 2020 Letters in Biomathematics 2020-01-15 2020-01-15 7 1 1 1 Battling Epidemics & Disparity with Modeling https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/393 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">Policymakers are under intense pressure to respond effectively to the ongoing COVID-19 situation. Epidemiological models, which have been helpful in many previous infectious diseases’ epidemics, have been inconsistent and often incorrect in predicting burden of COVID-19 outbreak. Modelers are struggling to identify and capture appropriate drivers of the current outbreak giving conflicting conclusions. COVID-19 is not only exerting unprecedented social pressure on the vulnerable population but also its patterns are getting impacted by existing and aggravating social problems. The present article stresses the role of this dual nature of the impact of COVID-19 and suggests modelers to incorporate challenges at the interface of COVID-19 preparedness and social epidemics such as homelessness and opioid use. There is an urgent need to encourage social distancing policies to protect people and prevent the spread of the virus, while ensuring that other social crises and vulnerable populations are not ignored.</p> Anuj Mubayi Jeff Sullivan Jason Shafrin Oliver Diaz Aditi Ghosh Anamika Mubayi Olcay Akman Phani Veeranki Copyright (c) 2020 Letters in Biomathematics 2020-08-28 2020-08-28 7 1 105–110 105–110 Should N95 Respirators be Recommended for the General Public https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/415 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">Public health advisories recommend against the use of the N95 respirator by the general public in the current COVID-19 pandemic. These advisories are primarily motivated by the collective goal of reducing the reproduction number to below one. However, cultural factors may dissuade the public from adopting recommendations from models optimized for the collective good. This article presents a discussion of mathematical issues that ought to guide an advisory from an individualistic perspective. In particular, we argue that the public health advisory does not appear justified if one considers non-linearity in the dose-response relationship and heterogeneity in infection load in the context of the COVID-19 pandemic. The N95 respirator promises far greater effectiveness than homemade or surgical masks. However, due to a considerable variation in masks' brands and efficiencies, the public should look into the specific details of each available mask option.</p> Ashok Srinivasan Anuj Mubayi Olcay Akman Copyright (c) 2020 Letters in Biomathematics 2020-10-08 2020-10-08 7 1 143–152 143–152