Letters in Biomathematics

Welcome to Volume 10

Editorial Board — Tue, 10 Jan 2023 08:23:07 -0800

The editorial board is pleased to introduce the tenth volume of Letters in Biomathematics.

Modeling Seasonal Malaria Transmission

Tue, 24 Jan 2023 07:03:37 -0800

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.

Mathematical Analysis and Parameter Estimation of a Two-Patch Zika Model

Kifah Al-Maqrashi, Fatma Al-Musalhi, Ibrahim Elmojtaba, Nasser Al-Salti — Mon, 30 Jan 2023 12:04:24 -0800

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 R₀ and sensitivity analysis. Our results show that R₀ 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.

Unidirectional Migration of Populations with Allee Effect

Gergely Röst, AmirHosein Sadeghimanesh — Wed, 08 Feb 2023 06:50:05 -0800

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 steady states or 9, 7, 9, 3 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 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.

Modeling the Spread of Curly Top Disease in Tomatoes

Rachel Frantz, Claudia Nischwitz, Tyson Compton, Luis Gordillo — Mon, 06 Mar 2023 09:23:33 -0800

Curly Top disease (CT), caused by a family of curtoviruses, 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.

Substrate Transport in Cylindrical Multi-Capillary Beds with Axial Diffusion

Liang Sun, Eric Choi — Wed, 26 Apr 2023 09:10:29 -0700

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. 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 supply in multicapillary beds near the arterial ends, in the central regions, and near the venous ends in capillaries is introduced in the remainder of the article. Our prime model builds on known solutions involving circular regions by adding a $Z$-axis and by accounting for circular cylindrical tissue around multiple capillaries. To account for relatively small longitudinal diffusivities, we use perturbation methods to solve the associated governing equations.

Epidemiology, Game Theory, and Evolutionary Rescue

Wed, 10 May 2023 08:48:32 -0700

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.

GillesPy2

Fri, 26 May 2023 08:45:59 -0700

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 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.

Quantum Mechanics for Population Dynamics

Olcay Akman, Leon Arriola, Ryan Schroeder, Aditi Ghosh — Tue, 01 Aug 2023 12:35:18 -0700

A standard single species immigration, emigration and fission ordinary differential equation (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) standard macroscopic ODE models can be derived from first principles of quantum mechanics instead of making macroscopic heuristic assumptions and (ii) high impact events with low probability of occurrence can be explicitly calculated.