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Mathematical Biosciences and Engineering: MBE

Yang Kuang, Angela Peace, Hao Wang
Preface. Guest editors: Yang Kuang, Angela Peace and Hao Wang.
January 7, 2019: Mathematical Biosciences and Engineering: MBE
Alexis Erich S Almocera, Sze-Bi Hsu, Polly W Sy
It is recently known that parasites provide a better picture of an ecosystem, gaining attention in theoretical ecology. Parasitic fungi belong to a food chain between zooplankton and inedible phytoplankton, called mycoloop. We consider a chemostat model that incorporates a single mycoloop, and analyze the limiting behavior of solutions, adding to previous work on steady-state analysis. By way of persistence theory, we establish that a given species survives depending on the food web configuration and the nutrient level...
December 24, 2018: Mathematical Biosciences and Engineering: MBE
Lale Asik, Jackson Kulik, Kevin Long, Angela Peace
Many population systems are subject to seasonally varying environments. As a result, many species exhibit seasonal changes in their life-history parameters. It is quite natural to try to understand how seasonal forcing affects population dynamics subject to stoichiometric constraints, such as nutrient/light availability and food quality. Here, we use a variation of a stoichiometric Lotka-Volterra type model, known as the LKE model, as a case study, focusing on seasonal variation in the producer's light-dependent carrying capacity...
December 19, 2018: Mathematical Biosciences and Engineering: MBE
Lei Shi, Hongyong Zhao, Daiyong Wu
Currently, hand, foot, and mouth disease (HFMD) is widespread in mainland China and seriously endangers the health of infants and young children. Recently in mainland China, preventing the spread of the disease has entailed vaccination, isolation measures, and virus clean-up in the contaminated environment. However, quantifying and evaluating the efficacy of these strategies on HFMD remains challenging, especially because relatively little research analyses the impact of EV71 vaccination for this disease. To assess the effectiveness of these strategies, we propose a new mathematical model that considers vaccination, contaminated environment, and quarantine simultaneously...
December 18, 2018: Mathematical Biosciences and Engineering: MBE
Raimund Bürger, Gerardo Chowell, Elvis Gavilán, Pep Mulet, Luis M Villada
A spatio-temporal eco-epidemiological model is formulated by combining an available non-spatial model for predator-prey dynamics with infected prey [D. Greenhalgh and M. Haque, Math. Meth. Appl. Sci., 30 (2007), 911-929] with a spatio-temporal susceptible-infective (SI)-type epidemic model of pattern formation due to diffusion [G.-Q. Sun, Nonlinear Dynamics, 69 (2012), 1097-1104]. It is assumed that predators exclusively eat infected prey, in agreement with the hypothesis that the infection weakens the prey, making it available for predation otherwise we assume that the predator has essentially no access to healthy prey of the same species...
December 17, 2018: Mathematical Biosciences and Engineering: MBE
Konstantin E Starkov, Giovana Andres Garfias
In the present paper convergence dynamics of one tumor-immune-virus model is examined with help of the localization method of compact invariant sets and the LaSalle theorem. This model was elaborated by Eftimie et al. in 2016. It is shown that this model possesses the Lagrange stability property of positive half-trajectories and ultimate upper bounds for compact invariant sets are obtained. Conditions of convergence dynamics are found. It is explored the case when any trajectory is attracted to one of tumor-only equilibrium points or tumor-free equilibrium points...
December 17, 2018: Mathematical Biosciences and Engineering: MBE
Ranjit Kumar Upadhyay, Swati Mishra
Fear can influence the overall population size of an ecosystem and an important drive for change in nature. It evokes a vast array of responses spanning the physiology, morphology, ontogeny and the behavior of scared organisms. To explore the effect of fear and its dynamic consequences, we have formulated a predator-prey model with the cost of fear in prey reproduction term. Spatial movement of species in one and two dimensions have been considered for the better understanding of the model system dynamics...
December 14, 2018: Mathematical Biosciences and Engineering: MBE
Xi-Chao Duan, Xue-Zhi Li, Maia Martcheva
Based on the development of heroin vaccine, in this paper, we propose an age structured heroin transmission model with treatment and vaccination. The model allows the drug reuse rate of the individuals in treatment to depend on a treatment-age and the vaccine waning rate of the vaccinated to depend on a vaccination age. Meanwhile, the model allows that the heroin vaccine provides an imperfect protection (i.e., the vaccinated individuals can also become drug addicted). We derive the basic reproduction number which dependents on vaccination...
December 13, 2018: Mathematical Biosciences and Engineering: MBE
Gordon Akudibillah, Abhishek Pandey, Jan Medlock
Apart from the traditional role of preventing progression from HIV to AIDS, antiretroviral drug therapy (ART) has been shown to have the additional benefit of substantially reducing infectiousness in infected people, making ART potentially an important strategy in the fight against HIV. We developed a mathematical model based on the WHO's 5-stage classification of HIV/AIDS disease progression. Our model stratifies the population by disease stage, diagnosis and treatment. We used optimal control methods and data from South Africa to determine the best time-dependent treatment allocation required to minimize new infections, infection-years, deaths and cost...
December 13, 2018: Mathematical Biosciences and Engineering: MBE
Sandesh Athni Hiremath, Christina Surulescu, Somayeh Jamali, Samantha Ames, Joachim W Deitmer, Holger M Becker
The most aggressive tumor cells, which often reside in a hypoxic environment, can release vast amounts of lactate and protons via monocarboxylate transporters (MCTs). This additional proton efflux exacerbates extracellular acidification and supports the formation of a hostile environment. In the present study we propose a novel, data-based model for this proton-coupled lactate transport in cancer cells. The mathematical settings involve systems coupling nonlinear ordinary and stochastic differential equations describing the dynamics of intra- and extracellular proton and lactate concentrations...
December 13, 2018: Mathematical Biosciences and Engineering: MBE
Jiazhe Lin, Rui Xu, Xiaohong Tian
Human specific immunity consists of two branches: humoral immunity and cellular immunity. To protect us from pathogens, cell-mediated and humoral immune responses work together to provide the strongest degree of efficacy. In this paper, we propose an HIV-1model with cell-mediated and humoral immune responses, in which both virus-to-cell infection and cell-to-cell transmission are considered. Five reproduction ratios, namely, immunity-inactivated reproduction ratio, cell-mediated immunity-activated reproduction ratio, humoral immunity-activated reproduction ratio, cell-mediated immunity-competed reproduction ratio and humoral immunity-competed reproduction ratio, are calculated and verified to be sharp thresholds determining the local and global properties of the virus model...
December 13, 2018: Mathematical Biosciences and Engineering: MBE
A Swierniak, M Krzeslak, D Borys, M Kimmel
We propose to endow evolutionary gamemodels with changes of the phenotypes adjustment during the transient generations performed by the parameters in the payoff matrix which determine the fitness resulting from different interactions between players. These changes represent an alteration of access to external resources which, in turn, may reflect anticancer treatment. In the case of spatial games, these functions are represented by an additional lattice where another and parallel game based on cellular automata is performed...
December 13, 2018: Mathematical Biosciences and Engineering: MBE
Bruce Pell, Amy E Kendig, Elizabeth T Borer, Yang Kuang
Human activities alter elemental nutrient cycling, which can have profound impacts on agriculture, grasslands, lakes, and other systems. It is becoming increasingly clear that enhanced nitrogen and phosphorus levels can affect disease dynamics across a range of taxa. However, there are few mathematical models that explicitly incorporate nutrients into host-pathogen interactions. Using viral load and plant mass data from an experiment with cereal yellow dwarf virus and its host plant, Avena sativa, we propose and compare two models describing the overall infection dynamics...
December 12, 2018: Mathematical Biosciences and Engineering: MBE
Md Masud Rana, Chandani Dissanayake, Lourdes Juan, Kevin R Long, Angela Peace
Known stoichiometric models of a two species producer-grazer ecosystem have either neglected spatial dynamics or failed to track free phosphorus in the media. In this paper we present a spatially heterogeneous model that tracks phosphorus content in the producer and free phosphorus in the media. We simulate our model numerically under various environmental conditions. Multiple equilibria, with bistability and deterministic extinction of the grazer, are possible here. In conditions that had been previously studied without tracking free phosphorus we find cases where qualitatively different behavior is observed...
December 11, 2018: Mathematical Biosciences and Engineering: MBE
Fu-Yuan Tsai, Feng-Bin Wang
This paper investigates a mathematical model of competition between two species for inorganic carbon and light in a well-mixed water column. The population growth of the species depends on the consumption of two substitutable forms of inorganic carbon, "CO2" (dissolved CO2 and carbonic acid) and "CARB" (bicarbonate and carbonate ions), which are stored internally. Besides, uptake rates also includes self-shading by the phytoplankton population, that is, an increase in population density will reduce light available for photosynthesis, and thereby reducing further carbon assimilation and population growth...
December 11, 2018: Mathematical Biosciences and Engineering: MBE
Tin Phan, Changhan He, Alejandro Martinez, Yang Kuang
In this paper, we formulate a three cell population model of intermittent androgen suppression therapy for cancer patients to study the treatment resistance development. We compare it with other models that have different underlying cell population structure using patient prostate specific antigen (PSA) and androgen data sets. Our results show that in the absence of extensive data, a two cell population structure performs slightly better in replicating and forecasting the dynamics observed in clinical PSA data...
December 11, 2018: Mathematical Biosciences and Engineering: MBE
Anshuman Swain, William F Fagan
The Warburg effect refers to a curious behavior observed in many organisms and cell types including cancer cells, yeast and bacteria, wherein both the efficient aerobic pathway and the inefficient fermentation pathway are utilized for respiration, despite the presence of ample oxygen. Also termed as overflow metabolism in bacteria, this phenomena has remained an enigmatic and poorly understood phenomenon despite years of experimental work. Here, we focus on bacterial cells and build a model of three trade offs involved in the utilization of aerobic and anaerobic respiration pathways (rate versus yield, surface area versus volume, and fast versus slow biomass production) to explain the observed behavior in cellular systems...
December 11, 2018: Mathematical Biosciences and Engineering: MBE
Patrick De Leenheer, Martin Schuster, Hal Smith
In [11], a proof of principle was established for the phenomenon of the tragedy of the commons, a center piece for many theories on the evolution of cooperation. A general chemostat model with two species, the cooperator and the cheater, was formulated where the cooperator allocates a portion of the nutrient uptake towards the production of a public good which is needed to digest an externally supplied resource. The cheater does not produce the public good, and instead allocates all nutrient uptake towards its own growth...
December 11, 2018: Mathematical Biosciences and Engineering: MBE
Md Nazmul Hassan, Kelsey Thompson, Gregory Mayer, Angela Peace
Accurately assessing the risks of contaminants requires more than an understanding of the effects of contaminants on individual organism, but requires further understanding of complex ecological interactions, elemental cycling, and the interactive effects of natural stressors, such as resource limitations, and contaminant stressors. There is increasing evidence that organisms experience interactive effects of contaminant stressors and food conditions, such as resource stoichiometry, availability and excess of nutrient...
December 7, 2018: Mathematical Biosciences and Engineering: MBE
Da Song, Meng Fan, Ming Chen, Hao Wang
We develop a nonautonomous stoichiometric algal growth model incorporating a season-driven light intensity. We characterize the model dynamics by showing positive invariance, dissipativity, boundary dynamics, and internal dynamics. We use numerical simulations to uncover the impacts of the seasonal light intensity and the nutrient availability on the algal dynamics. We discuss two control methods, removing algae (RA) periodically and blocking nutrient (BN) input from rivers constantly, via ourmodeling approach...
December 7, 2018: Mathematical Biosciences and Engineering: MBE
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