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> en-US biomath@ilstu.edu (Olcay Akman) rcbunge@ilstu.edu (Ryan Bunge) Tue, 10 Jan 2023 00:00:00 -0800 OJS http://blogs.law.harvard.edu/tech/rss 60 Welcome to Volume 10 https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/609 <p>The editorial board is pleased to introduce the tenth volume of <em>Letters in Biomathematics</em>.</p> Editorial Board Copyright (c) 2023 Letters in Biomathematics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/609 Tue, 10 Jan 2023 08:23:07 -0800 Modeling Seasonal Malaria Transmission https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/561 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">Increasing temperatures have raised concerns over the potential effect on disease spread. Temperature is a well known factor affecting mosquito population dynamics and the development rate of the malaria parasite within the mosquito, and consequently, malaria transmission. A sinusoidal wave is commonly used to incorporate temperature effects in malaria models, however, we introduce a seasonal malaria framework that links data on temperature-dependent mosquito and parasite demographic traits to average monthly regional temperature data, without forcing a sinusoidal fit to the data. We introduce a spline methodology that maps temperature-dependent mosquito traits to time-varying model parameters. The resulting non-autonomous system of differential equations is used to study the impact of seasonality on malaria transmission dynamics and burden in a high and low malaria transmission region in Malawi. We present numerical simulations illustrating how temperature shifts alter the entomological inoculation rate and the number of malaria infections in these regions.</p> Olivia Prosper, Katharine Gurski, Miranda Teboh-Ewungkem, Angela Peace, Zhilan Feng, Margaret Reynolds, Carrie Manore Copyright (c) 2023 Letters in Biomathematics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/561 Tue, 24 Jan 2023 07:03:37 -0800 Mathematical Analysis and Parameter Estimation of a Two-Patch Zika Model https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/529 <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">In this paper, we developed a multi-patch model for the spread of Zika virus infection taking, into account direct and indirect transmissions along with vertical transmission. The model was analyzed to gain insights into the disease's spread. The model was fitted to a data set collected from two neighboring countries, Brazil and Colombia, to estimate some of its parameters and use it for calculating <em>R</em><sub>0</sub> and sensitivity analysis. Our results show that <em>R</em><sub>0</sub> is less than one in both countries, which indicates that the disease will die out. Also, our results show that direct transmission is the most important route for spreading the disease; hence, it has to gain more focus in any controlling strategy.</p> Kifah Al-Maqrashi, Fatma Al-Musalhi, Ibrahim Elmojtaba, Nasser Al-Salti Copyright (c) 2023 Letters in Biomathematics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/529 Mon, 30 Jan 2023 12:04:24 -0800 Unidirectional Migration of Populations with Allee Effect https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/553 <p>In this note we consider two populations living on identical patches, connected by unidirectional migration, and subject to strong Allee effect. We show that by increasing the migration rate, there are more bifurcation sequences than previous works showed. In particular, the number of steady states can change from 9 (small migration) to 3 (large migration) at a single bifurcation point, or via a sequence of bifurcations with the system having 9, 7, 5, 3&nbsp;steady states or 9, 7, 9, 3&nbsp;steady states, depending on the Allee threshold. This is in contrast with the case of bidirectional migration, where the number of steady states always goes through the same bifurcation sequence of 9, 5, 3&nbsp;steady states as we increase the migration rate, regardless of the value of the Allee threshold. These results have practical implications as well in spatial ecology.</p> Gergely Röst, AmirHosein Sadeghimanesh Copyright (c) 2023 Letters in Biomathematics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/553 Wed, 08 Feb 2023 06:50:05 -0800 Modeling the Spread of Curly Top Disease in Tomatoes https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/557 <p>Curly Top disease (CT), caused by a family of <em>curtoviruses</em>, infects a wide variety of agricultural crops. Historically, CT has caused extensive damage in tomato crops resulting in substantial economic loss for the tomato industry. Control methods for CT are scarce, and methods for predicting and assessing the scope of CT outbreaks are limited. In this paper, we formulate a stochastic model for the spread of CT in a heterogeneous environment, which consists of beet plants, the preferred hosts, and tomato plants. The model is composed of two susceptible classes and two infected classes, where the beet plants are the primary reservoir of the pathogen. We parameterize the model using data from a field experiment and assess the variability of CT incidence in tomato plants at any point in time through extensive simulations.</p> Rachel Frantz, Claudia Nischwitz, Tyson Compton, Luis Gordillo Copyright (c) 2023 Letters in Biomathematics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/557 Mon, 06 Mar 2023 09:23:33 -0800 Substrate Transport in Cylindrical Multi-Capillary Beds with Axial Diffusion https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/613 <p>It is known that in oxygen concentration profiles for capillary beds of skeletal muscles, radial diffusion most likely has considerably more effect on oxygen transport in long and parallel capillary beds than axial diffusion. However, axial diffusion may still play a significant role in oxygen transport in tissue, especially in relatively short pathways.&nbsp;Our model adds to known solutions the component of axial diffusion to multi-capillary beds inside a tissue cylinder, where arbitrary characteristics include random locations and uneven oxygen strengths. Discussion of the solutions for oxygen&nbsp;supply in multicapillary beds near the arterial ends, in the central&nbsp;regions, and near the venous ends in capillaries is introduced in&nbsp;the remainder of the article. Our prime model builds on&nbsp;known solutions involving circular regions by adding a&nbsp;$Z$-axis and by accounting for circular cylindrical tissue around multiple&nbsp;capillaries. To account for relatively small&nbsp;longitudinal diffusivities, we use perturbation methods to solve&nbsp;the associated governing equations.</p> Liang Sun, Eric Choi Copyright (c) 2023 Letters in Biomathematics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/613 Wed, 26 Apr 2023 09:10:29 -0700 Epidemiology, Game Theory, and Evolutionary Rescue https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/485 <p>Evolutionary game theory (EGT) analyzes the stability of competing strategies for withstanding selective pressures within a population over generations. Under rapid shifts in selective pressures (e.g., introduction of a novel pathogen), evolutionary rescue may preserve a population, but how it may re-stabilize over generations is also critical for estimations of population persistence. Here, we present a simple model that couples EGT with epidemiology to investigate evolutionary rescue under a novel and epidemiologically-driven dynamic selective pressure from an infectious outbreak. We consider a hypothetical population where payoffs from competing wild-type and mutant strategies reflect immune-reproductive trade-offs. Our study shows evolutionary rescue occurs under higher wild-type fecundity and a lower-bounded boost in mutant immunity prolongs the timescale of evolutionary rescue. Higher disease-induced mortality in the wild-type and a larger mutant immunity significantly reinforce the pattern. This model reveals transient synergies between epidemiological and evolutionary dynamics during evolutionary rescue during novel infectious outbreaks.</p> Brandon Grandison, Hannah Yin, Ana Kilgore, Matthew Young, Jing Jiao, Nina Fefferman Copyright (c) 2023 Letters in Biomathematics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/485 Wed, 10 May 2023 08:48:32 -0700 GillesPy2 https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/591 <p>Stochastic modeling has become an essential tool for studying biochemical reaction networks. There is a growing need for user-friendly and feature-complete software for model design and simulation. To address this need, we present GillesPy2, an open-source framework for building and simulating mathematical and biochemical models. GillesPy2, a major upgrade from the original GillesPy package, is now a stand-alone Python&nbsp;3 package. GillesPy2 offers an intuitive interface for robust and reproducible model creation, facilitating rapid and iterative development. In addition to expediting the model creation process, GillesPy2 offers efficient algorithms to simulate stochastic, deterministic, and hybrid stochastic-deterministic models.</p> Sean Matthew, Fin Carter, Joshua Cooper, Matthew Dippel, Ethan Green, Samuel Hodges, Mason Kidwell, Dalton Nickerson, Bryan Rumsey, Jesse Reeve, Linda Petzold, Kevin Sanft, Brian Drawert Copyright (c) 2023 Letters in Biomathematics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/591 Fri, 26 May 2023 08:45:59 -0700 Quantum Mechanics for Population Dynamics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/599 <p>A standard single species immigration, emigration and fission ordinary differential equation&nbsp;(ODE) model is derived from a quantum mechanics approach. The stochasticity introduced via quantum mechanics is very different than that of the standard approaches such as demographic stochasticity in the state variables or environmental stochasticity as in uncertainty quantification. This approach yields a standard ODE and predicts the effects of quantum tunneling of probabilities. This approach is explained in such a way that epidemiologists, mathematicians, mathematical biologists, etc who are not familiar with quantum mechanics can understand the methods described here and apply them to more sophisticated situations. The two main results of this approach are (i)&nbsp;standard macroscopic ODE models can be derived from first principles of quantum mechanics instead of making macroscopic heuristic assumptions and (ii)&nbsp;high impact events with low probability of occurrence can be explicitly calculated.</p> Olcay Akman, Leon Arriola, Ryan Schroeder, Aditi Ghosh Copyright (c) 2023 Letters in Biomathematics https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/599 Tue, 01 Aug 2023 12:35:18 -0700