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 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 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