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Mathematical Biosciences

Subhas Khajanchi, Sandip Banerjee
We present a mathematical model which describes the growth of malignant gliomas in presence of immune responses by considering the role of immunotherapeutic agent T11 target structure (T11TS). The model consider five populations, namely, glioma cells, macrophages, cytotoxic T-lymphocytes, TGF - β and IFN - γ. The model system has highly nonlinear terms with four discrete time lags, but remains tractable. The goal of this work is to better understand the effect of multiple delays on the interaction between gliomas and immune components in conjunction with an administration of T11 target structure...
June 13, 2018: Mathematical Biosciences
Xiaoli Wang, Guohong Zhang, Ju Lai
In this paper, an intraguild predation model with an adaptive IGpredator is studied. IGpredator is assumed to adopt adaptive predation strategy to gain more fitness and the adaptive strength is variable. The existence and stability of the boundary equilibria and interior equilibrium are analyzed and it is found that the adaptive strength of IGpredator does not affect the stability of the boundary equilibria while it may change the stability of the interior equilibrium. Then we investigate numerically the effects of adaptive intraguild predation on the community structure along a gradient in environment productivity and find that it is possible for the appearance of the paradox of enrichment for intermediate speed of adaptivity...
June 2, 2018: Mathematical Biosciences
K Renee Fister, Maeve L McCarthy, Seth F Oppenheimer
This paper develops an optimal control framework to investigate the introduction of sterile type mosquitoes to reduce the overal moquito population. As is well known, mosquitoes are vectors of disease. For instance the WHO lists, among other diseases, Malaria, Dengue Fever, Rift Valley Fever, Yellow Fever, Chikungunya Fever and Zika. [ ] The goal is to establish the existence of a solution given an optimal sterilization protocol as well as to develop the corresponding optimal control representation to minimize the infiltrating mosquito population while minimizing fecundity and the number of sterile type mosquitoes introduced into the environment per unit time...
May 30, 2018: Mathematical Biosciences
Mohamed Dellal, Mustapha Lakrib, Tewfik Sari
Understanding and exploiting the inhibition phenomenon, which promotes the stable coexistence of species, is a major challenge in the mathematical theory of the chemostat. Here, we study a model of two microbial species in a chemostat competing for a single resource in the presence of an external inhibitor. The model is a four-dimensional system of ordinary differential equations. Using general monotonic growth rate functions of the species and absorption rate of the inhibitor, we give a complete analysis for the existence and local stability of all steady states...
May 24, 2018: Mathematical Biosciences
Edwin Barrios, Pedro Gajardo, Olga Vasilieva
In this paper, we introduce a method for computing sustainable thresholds for controlled cooperative models described by a system of ordinary differential equations, a property shared by a wide class of compartmental models in epidemiology. The set of sustainable thresholds refers to constraints (e.g., maximal "allowable" number of human infections; maximal "affordable" budget for disease prevention, diagnosis and treatments; etc.), parameterized by thresholds, that can be sustained by applying an admissible control strategy starting at the given initial state and lasting the whole period of the control intervention...
May 22, 2018: Mathematical Biosciences
Hasifa Nampala, Livingstone S Luboobi, Joseph Y T Mugisha, Celestino Obua, Matylda Jablonska-Sabuka
Enzyme alanine aminotransferase (ALT) elevation which reflects hepatocellular injury is a current challenge in people infected with human immunodeficiency virus (HIV) on antiretroviral therapy (ART). One of the factors that enhance the risk of hepatotoxicity is underlying diseases such as hepatitis caused by hepatitis B virus (HBV). HIV/HBV coinfected patients stand a greater risk of hepatotoxicity because all ART are toxic and liver cells (hepatocytes) that are responsible for metabolising the toxic ART, support all stages of HIV and HBV viral production...
May 22, 2018: Mathematical Biosciences
Rigobert C Ngeleja, Livingstone S Luboobi, Yaw Nkansah-Gyekye
The plague disease model that include the effect of seasonal weather variation in its transmission is investigated in this paper. The disease is caused by an extremely virulent bacteria Yersinia pestis named after a French bacteriologist Alexandre Yersin. The analysis shows that, when the periodic reproduction number (RT ) is greater than one there exist a globally asymptotically stable disease free equilibrium solution (DFS). Using fundamental existence-uniqueness theorem we were able to prove the existence of positive periodic solutions...
May 22, 2018: Mathematical Biosciences
Sheldon Chen
Ascertaining a patient's kidney function is more difficult to do when the serum creatinine is changing than when it is stable. To accomplish the task, various kinetic clearance equations have been developed. To date, however, none of them have allowed for ongoing changes to the creatinine's volume of distribution. These diluting or concentrating effects on the [creatinine] can greatly impact the accuracy of kidney function assessment. Described herein is a model of creatinine kinetics that also accommodates volume changes...
May 22, 2018: Mathematical Biosciences
Bashar Ibrahim
The mitotic spindle orientation and position is crucial for the fidelity of chromosome segregation during asymmetric cell division to generate daughter cells with different sizes or fates. This mechanism is best understood in the budding yeast Saccharomyces cerevisiae, named the spindle position checkpoint (SPOC). The SPOC inhibits cells from exiting mitosis until the mitotic spindle is properly oriented along the mother-daughter polarity axis. Despite many experimental studies, the mechanisms underlying SPOC regulation remains elusive and unexplored theoretically...
May 21, 2018: Mathematical Biosciences
Mario Banuelos, Suzanne Sindi
Transposable elements (TEs), segments of DNA capable of self-replication, are abundant in the genomes of most organisms and thus serve as a record of past mutational events. While some work suggests TEs may serve a regulatory function for the host, most empirical and theoretical studies have shown that TEs often have deleterious effects on a host. Because they are not essential, the host genome consists of both full-length (actively replicating) and partial length (inactive remnant) copies of TEs. We developed a novel mathematical formulation of TE dynamics by modeling the density of full and partial length copies resulting from mutations (insertions and deletions) and TE replication within the host genome...
May 19, 2018: Mathematical Biosciences
Zahava Wilstein, Daniel M Alligood, Valerie L McLure, Austinn C Miller
test The development of chronic hypertension is a poorly described process involving many chemical and structural changes to the artery. Typically, mathematical models of this disease focus primarily on the mechanical aspects such as arterial geometry, elasticity, and tissue content, or alternatively on the chemical drivers of vasoactivity such as nitric oxide and reactive oxygen species. This paper presents a model that considers the powerful interaction between mechanical and biochemical drivers of hypertension and arterial remodeling...
May 11, 2018: Mathematical Biosciences
Ágata Paim, Nilo S M Cardozo, Isabel C Tessaro, Patricia Pranke
A potential alternative for tissue transplants is tissue engineering, in which the interaction of cells and biomaterials can be optimized. Tissue development in vitro depends on the complex interaction of several biological processes such as extracellular matrix synthesis, vascularization and cell proliferation, adhesion, migration, death, and differentiation. The complexity of an individual phenomenon or of the combination of these processes can be studied with phenomenological modeling techniques. This work reviews the main biological phenomena in tissue development and their mathematical modeling, focusing on mesenchymal stem cell growth in three-dimensional scaffolds...
May 7, 2018: Mathematical Biosciences
Krzysztof Bartoszek
In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure-birth tree conditioned on n contemporary tips. We show that this normalized phylogenetic balance index is a submartingale that converges almost surely and in L2 . We link our work with studies on trees without branch lengths and show that in this case the limit distribution is a contraction-type distribution, similar to the Quicksort limit distribution. In the continuous branch case we suggest approximations to the limit distribution...
May 7, 2018: Mathematical Biosciences
Eric A Autry, Alvin Bayliss, Vladimir A Volpert
In this paper, we consider a three-species food chain model with ratio-dependent predation, where species u is preyed upon by species v, which in turn is preyed upon by species w. Our primary focus is on biological control, where the bottom species u is an important crop, and v is a pest that has infested the crop. The superpredator w is introduced into this pest-infested environment in an attempt to restore the system to a pest-free state. We assume that the species can behave nonlocally, where individuals will interact over a distance, and incorporate this nonlocality into the model...
May 5, 2018: Mathematical Biosciences
Burghard Herrmann
This paper considers the geometry of plants with golden spiral phyllotaxis, i.e. growing leaf by leaf on a spiral with golden divergence angle. As is well-known, Fibonacci numbers appear by means of the order of parastichies. A rigorous and straightforward proof is provided with respect to pure visibility. This notion is very similar to that of contact parastichies. The 3-D cylindrical model of golden spiral phyllotaxis abstracts from the form of leaves and identifies them with points. Pure visibility is specified in the 2-D representation so that common sense parastichies can be scrutinized...
May 5, 2018: Mathematical Biosciences
Shodhan Rao
In this paper, we consider a mixed mechanism of a n-site phosphorylation system in which the mechanism of phosphorylation is distributive and that of dephosphorylation is processive. It is assumed that the concentrations of the substrates are much higher than those of the enzymes and their intermediate complexes. This assumption enables us to reduce the system using the steady-state approach to a Michaelis-Menten approximation of the system. It is proved that the resulting system of nonlinear ordinary differential equations admits a unique positive equilibrium in every positive stoichiometric compatibility class using the theory of quadratic equations...
May 5, 2018: Mathematical Biosciences
Marisabel Rodriguez Rodriguez, Darin Kopp, Daniel Allen, Yun Kang
The exchange of resources across ecosystem boundaries can have large impacts on ecosystem structures and functions at local and regional scales. In this article, we develop a simple model to investigate dynamical implications of bi-directional resource exchanges between two local ecosystems in a meta-ecosystem framework. In our model, we assume that (1) Each local ecosystem acts as both a resource donor and recipient, such that one ecosystem donating resources to another results in a cost to the donating system and a benefit to the recipient; and (2) The costs and benefits of the bi-directional resource exchange between two ecosystems are correlated in a nonlinear fashion...
May 5, 2018: Mathematical Biosciences
Reginald L McGee, Gregery T Buzzard
Mathematical modeling is a powerful tool in systems biology; we focus here on improving the reliability of model predictions by reducing the uncertainty in model dynamics through experimental design. Model-based experimental design is a process by which experiments can be systematically chosen to reduce dynamic uncertainty in a given model. We discuss the Maximally Informative Next Experiment (MINE) method for group-wise selection of points in an experimental design and present a convergence result for MINE with nonlinear models...
April 27, 2018: Mathematical Biosciences
Elliot J Carr, Giuseppe Pontrelli
We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the external surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules...
April 12, 2018: Mathematical Biosciences
M Marvá, F San Segundo
In this work, we analyze the interplay between general age structured density-dependent fertility functions and age classes dispersal in a patchy environment. As novelties, (i) the fertility function depends on age classes (instead of on the total population size) and (ii) dispersal patterns are also allowed to be different for individuals belonging to different age classes. Our results highlight the interplay between the shape of the age structured density-dependent fertility function and the age classes dispersal patterns...
March 30, 2018: Mathematical Biosciences
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