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 Fostering Research https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/521 <p>With the release of the ninth volume, we are proud of the place that Letters in Biomathematics has reached in research and education of the mathematical biology world.</p> Letters in Biomathematics Copyright (c) 2022 Letters in Biomathematics 2022-02-15 2022-02-15 9 1 1 1 Mathematical Analysis of an Epidemic Model for COVID-19 https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/503 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">We construct an SIR-type model for COVID-19, incorporating as a parameter the susceptible individuals' cautiousness level. We determine the model's basic reproduction number, study the stability of the equilibria analytically, and perform a sensitivity analysis to confirm the significance of the cautiousness level. Fixing specific values for all other parameters, we study numerically the model's dynamics as the cautiousness level varies, revealing backward transcritical, Hopf, and saddle-node bifurcations of equilibria, as well as homoclinic and fold bifurcations of limit cycles with the aid of AUTO. Considering some key events affecting the pandemic in Indonesia, we design a scenario in which the cautiousness level varies over time, and show that the model exhibits a hysteresis, whereby, a slight cautiousness decrease could bring a disease-free state to endemic, and this is reversible only by a drastic cautiousness increase, thereby mathematically justifying the importance of a high cautiousness level for resolving the pandemic.</p> Benny Yong Livia Owen Jonathan Hoseana Copyright (c) 2022 Letters in Biomathematics 2022-04-04 2022-04-04 9 1 3–22 3–22 Effects of Contact Tracing and Self-Reporting in a Network Disease Model https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/491 <p>Contact tracing can be an effective measure to control emerging infectious diseases, but the efficacy of contact tracing measures can depend upon the willingness of individuals to get be tested even when they are symptomatic. In this paper, we examine the effects of symptomatic individuals getting tested and the use of contact tracing in a network model of disease transmission. We utilize a network model to resolve the influence of contact patterns between individuals as apposed to assuming mass action where all individuals are connected to each other.&nbsp; We find that the effects of self-reporting and contact tracing vary depending on the structure of the network. We also compare the results from the network model with an analogous ODE model that assumes mass action and demonstrate how the results can be dramatically different.</p> Punit Gandhi Michael A. Robert John Palacios David Chan Copyright (c) 2022 Letters in Biomathematics 2022-05-10 2022-05-10 9 1 23–39 23–39 Mathematical Modeling and Dynamics of SARS-CoV-2 in Colombia https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/297 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">As COVID-19 continues to spread around the globe, it is critical to understand the true burden of a future outbreak in developing countries like Colombia where data may be limited. Here, we estimated the rate of the initial exponential growth of cases and the basic reproductive rate for the disease. We use models with different modeling assumptions to study the differences between five major Colombian cities and between selected Latin American countries. Using an ensemble modeling technique, we estimated that the reproduction number in Colombia varied from 1.10 in Cartagena to 1.75 in Medellin with Cali being 1.47. In Latin America, Ecuador has highest initial epidemic growth rate and Panama the lowest with Colombia in middle of the list. The choice of appropriate model and parameter estimates for a location provided different scenarios in outbreaks. This analysis provides a framework for the decision makers to be better prepared for an outbreak.</p> Jorge Humberto Rojas Marlio Paredes Malay Banerjee Olcay Akman Anuj Mubayi Copyright (c) 2022 Letters in Biomathematics 2022-06-09 2022-06-09 9 1 41–56 41–56 The Influence of Quarantine Before Obtaining a Partially Effective Preventive Measure https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/493 <p>We study an epidemic model for a generic infectious disease with an ongoing spread in a closed community. The disease is assumed to not cause additional mortality and without providing immunity. We also assume the availability of a preventive measure that is both scarce and only partially effective in reducing the infection risk. We analyze the model focusing on the effect of a class of susceptibles that chooses to quarantine itself from the epidemic while waiting for the preventive measure to be available. Of particular interest is the case when the model exhibits bi-stability between the disease-free equilibrium and an endemic state which indicates that the disease may persist even if the epidemic reproductive number is less than one. We investigate the conditions whereby increasing the quarantine rate eliminates the bi-stability scenario thereby improving the predictive value of the model when assessing whether the disease evolves toward an endemic state or not.</p> Daniel Maxin Laurentiu Sega Copyright (c) 2022 Letters in Biomathematics 2022-08-19 2022-08-19 9 1 57–69 57–69 Data-Driven Approaches for Predicting Spread of Infectious Diseases Through DINNs: Disease Informed Neural Networks https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/513 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">In this work, we present an approach called Disease Informed Neural Networks (DINNs) that can be employed to effectively predict the spread of infectious diseases. We build on the application of physics informed neural network (PINNs) to SIR compartmental models and expand it to a scaffolded family of mathematical models describing various infectious diseases. We show how the neural networks are capable of learning how diseases spread, forecasting their progression, and finding their unique parameters (e.g., death rate). To demonstrate the robustness and efficacy of DINNs, we apply the approach to eleven highly infectious diseases that have been modeled in increasing levels of complexity. Our computational experiments suggest that DINNs is a reliable candidate to effectively learn the dynamics of their spread and forecast their progression into the future from available real-world data. Code and data can be found here: <a href="https://github.com/Shaier/DINN">https://github.com/Shaier/DINN</a></p> Sagi Shaier Maziar Raissi Padmanabhan Seshaiyer Copyright (c) 2022 Letters in Biomathematics 2022-08-22 2022-08-22 9 1 71–105 71–105 Building Model Prototypes from Time-Course Data https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/535 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">A primary challenge in building predictive models from temporal data is selecting the appropriate model topology and the regulatory functions that describe the data. In this paper we introduce a method for building model prototypes. The method takes as input a collection of time course data. After network inference, we use our toolbox to simulate the model as a stochastic Boolean model. Our method provides a model that can qualitatively reproduce the patterns of the original data and can further be used for model analysis, making predictions, and designing interventions. We applied our method to a time-course, gene-expression data that were collected during salamander tail regeneration under control and intervention conditions. The inferred model captures important regulations that were previously validated in the research literature and gives novel interactions for future testing. The toolbox for inference and simulations is freely available at <a href="https://github.com/alanavc/prototype-model">github.com/alanavc/prototype-model</a>.</p> Alan Veliz-Cuba Stephen Randal Voss David Murrugarra Copyright (c) 2022 Letters in Biomathematics 2022-08-27 2022-08-27 9 1 107–120 107–120 Saving the Devils Is in the Details https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/555 <p>Tasmanian Devils facial tumor disease (DFTD) is severely impacting the population of this wild animal. We developed a computational model of the population of Tasmanian Devils, and the change induced by DFTD. We use this model to test possible intervention strategies Tasmanian conservationists could do. We investigate bait drop vaccination programs, diseased animal removals programs, and evolution of natural immunity. We conclude that a combination of intervention strategies gives the most favorable outcome. An additional goal of this paper is reproducibility of our results. Our StochSS software platform features the ability to share and reproduce the computational notebooks that created all of the results in the paper. We endeavor that all readers should be able to reproduce our results with minimum effort.</p> Brian Drawert Andrew Flies Sean Matthew Megan Powell Bryan Rumsey Copyright (c) 2022 Letters in Biomathematics 2022-09-01 2022-09-01 9 1 121–140 121–140 A Hybrid Differential Equations Model for the Dynamics of Single and Double Strand Breaks of Cancer Cells Treated by Radiotherapy https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/487 <p>According to the Target Theory, the tumor population is divided into multiple different subpopulations, called targets, based on the diverse effects of ionizing radiation on human cells. Radiation particles can cause single or double-strand break(s). As such, cells are divided into three subpopulations, namely cells with no DNA fragmentation, cells with DNA single-strand breaks, and cells with DNA double-strand breaks. This work introduces a hybrid differential equation model, with coefficients described by random variables representing transition rates between targets. The model is utilized to simulate the dynamics of targets and describes the cell damage heterogeneity and the repair mechanism between two consecutive dose fractions. Therefore, a new definition of tumor lifespan based on population size is achieved. Stability and bifurcation analysis are performed. Finally, the probability of target inactivity after radiation and the probability of target re-activation following the repair mechanism are evaluated with respect to the tumor lifespan.</p> Shantia Yarahmadian Amin Oroji Anna Katherine Williams Copyright (c) 2022 Letters in Biomathematics 2022-09-08 2022-09-08 9 1 141–158 141–158