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Letters in Biomathematics
Scopus
ISSN 2373-7867 · Intercollegiate Biomathematics Alliance · 77 articles in the index
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Journal Article
Model justification and stratification for confounding of Chlamydia trachomatis disease
This study involves statistical analysis of reported cases of sexually transmitted diseases (STDs) of Chlamydia infection in the United States. The data are collected from 2007 to 2016. The research studies incidence of sexually transmitted diseases and survival among different age groups and…
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Journal Article
Quantitative modelling biology undergraduate assessment
The Quantitative Modelling Biology Undergraduate Assessment (QM BUGS Version II) assesses undergraduate biology students’ quantitative modelling abilities and confidence. The assessment is intended to be given in undergraduate biology courses where instructors are engaging students in quantitative…
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Journal Article
A short note on analysis and application of a stochastic open-ended logistic growth model
A minimal stochastic generalization of a deterministic open-ended logistic growth model is proposed for efficiently describing the biological growth of individual organisms under natural environment. The model is a system of stochastic differential equations. Its unique solvability in a strong…
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Journal Article
Mathematical modelling, analysis and simulation of the spread of gangs in interacting youth and adult populations
Youth that live in public housing communities with high social and financial needs are at risk of getting involved in illegal drug trafficking gangs that are controlled by adults. This social disease spreads like an epidemic in these densely populated sectors and metropolitan area. In this work, a…
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Journal Article
Modeling the average population of La Crosse vectors in Knox County, Tennessee
La Crosse Virus (LACV) is an arbovirus found in Eastern Appalachia and can cause pediatric encephalitis in prepubescent children. To assess the risk and transmission of this disease, it is particularly important to understand the average population of Aedes mosquitoes, which are the vectors of this…
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Journal Article
Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations
In this paper, the static and dynamic behaviour of a fractional-order predator–prey model are studied, where the nonlinear interactions between the two species lead to multiple stable states. As has been found in many previous systems, the stability of such states can be dependent on the fractional…
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Journal Article
Stability preserving non-standard finite difference schemes for diabetes with tuberculosis infectious model
In this article, we study the non-standard finite difference (NSFD) schemes for the diabetes mellitus with tuberculosis infection. We have classified diabetes mellitus into two categories such as diabetes without complications and with complications and studied diabetes with tuberculosis infection…
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Journal Article
A household model of German cockroach infestations and their effects on symptoms of atopic asthma
Asthma is a chronic respiratory condition which affects 25 million people in the United States. Improper extermination of cockroaches and their associated allergens significantly increases the occurrence of atopic asthma, a type of asthma stemming from exposure to allergens. To date, dynamical…
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Journal Article
Using mathematical modelling to investigate the effect of the sexual behaviour of asymptomatic individuals and vector control measures on Zika
Zika is a vector borne disease for which the latest world wide outbreak inspired a renewed interest in epidemiological modelling of vector borne diseases. However, due to the possibility of sexual transmission and the high proportion of asymptomatic individuals, models for similar diseases, such as…
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Journal Article
Cross-diffusion induced Turing and non-Turing patterns in Rosenzweig–MacArthur model
Pattern formation is widely studied in spatio-temporal prey– predator models with only self-diffusion terms. Models with cross-diffusion, besides self-diffusion, take care of the situation in which presence, absence, abundance or scarcity of one species affect the movement of a population of…
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Journal Article
On parameter estimation approaches for predicting disease transmission through optimization, deep learning and statistical inference methods
In this paper, we consider compartmental disease transmission models and discuss the importance of determining model parameters that provide an insight into disease transmission and prevalence. After a brief review and comparison of the performance of some heuristic approaches, the paper introduces…
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Journal Article
Dynamics of two pathogens in a single tick population
A mathematical model for a two-pathogen, one-tick, one-host system is presented and explored. The goal of this model is to determine how long an invading pathogen persists within a tick population in which a resident pathogen is already established. The numerical simulations of the model…
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Journal Article
Stochastic models of influenza outbreaks on a college campus
Disease outbreaks on residential college campuses provide an ideal opportunity for mathematical modelling. Unfortunately, publicly available data are rare and many of these outbreaks are relatively small, confounding traditional data-fitting techniques such as least-squares. Using data from three…
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Journal Article
The concentration of digoxin after intravenous and oral administration studied by a two-compartment model
The present paper is designed to compare the distribution of digoxin administered through an Intravenous (i.v.) and Oral (p.o.) in central and peripheral compartments. The model under consideration is denoted by a system of three non-linear ordinary differential equations. The Eigenvalue and the…
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Journal Article
Synthetic drugs transmission: stability analysis and optimal control
The synthetic drugs that are becoming increasingly popular in drug-markets are some of the most destructive drugs which have made headlines causing serious social and health care issues in the past few years. In this work, a synthetic drug transmission model with general contact rate and Holling…
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Journal Article
Treating cancerous cells with viruses: insights from a minimal model for oncolytic virotherapy
In recent years, interest in the capability of virus particles as a treatment for cancer has increased. In this work, we present a mathematical model embodying the interaction between tumour cells and virus particles engineered to infect and destroy cancerous tissue. To quantify the effectiveness…
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Journal Article
A model for cross-institutional collaboration: how the intercollegiate biomathematics alliance is pioneering a new paradigm in response to diminishing resources in academia
We present an emerging model of shared academic, intellectual and infrastructure resources that addresses the need for institutions to sustain their educational and scholarship missions under ever-declining funding. The (IBA) was created in 2014 by Illinois State University for this purpose…
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Journal Article
Activation of the immune response by cytokines and its effect on tumour cells: a mathematical model
In this paper, we present a mathematical model at the cellular level of the tumour–immune competition mediated by the cytokines. The model consists of a system of nonlinear differential equations describing the intracellular interactions between the tumour and the immune cells in the presence of…
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Journal Article
A mathematical model of cytotoxic and helper T cell interactions in a tumour microenvironment
We develop a mathematical model to examine the role of helper and cytotoxic T cells in an anti-tumour immune response. The model comprises three ordinary differential equations describing the dynamics of the tumour cells, the helper and the cytotoxic T cells, and implicitly accounts for…