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Mathematical Biosciences and Engineering: MBE

Kazuo Yamazaki, Xueying Wang
We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally extinct. Specifically, when the basic reproduction number is beneath one, we show that the disease-free-equilibrium is globally attractive. On the other hand, when the basic reproduction number exceeds one, if the infectious hosts or the concentration of bacteria in the contaminated water are not initially identically zero, we prove the uniform persistence result and that there exists at least one positive steady state...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Juan Li, Yongzhong Song, Hui Wan
To study the impacts of toxin produced by phytoplankton and refuges provided for phytoplankton on phytoplankton-zooplankton interactions in lakes, we establish a simple phytoplankton-zooplankton system with Holling type II response function. The existence and stability of positive equilibria are discussed. Bifurcation analyses are given by using normal form theory which reveals reasonably the mechanisms and nonlinear dynamics of the effects of toxin and refuges, including Hopf bifurcation, Bogdanov-Takens bifurcation of co-dimension 2 and 3...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Jiang Xie, Junfu Xu, Celine Nie, Qing Nie
Every performance, in an officially sanctioned meet, by a registered USA swimmer is recorded into an online database with times dating back to 1980. For the first time, statistical analysis and machine learning methods are systematically applied to 4,022,631 swim records. In this study, we investigate performance features for all strokes as a function of age and gender. The variances in performance of males and females for different ages and strokes were studied, and the correlations of performances for different ages were estimated using the Pearson correlation...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Tuoi Vo, William Lee, Adam Peddle, Martin Meere
Drug-eluting stents have been used widely to prevent restenosis of arteries following percutaneous balloon angioplasty. Mathematical modelling plays an important role in optimising the design of these stents to maximise their efficiency. When designing a drug-eluting stent system, we expect to have a sufficient amount of drug being released into the artery wall for a sufficient period to prevent restenosis. In this paper, a simple model is considered to provide an elementary description of drug release into artery tissue from an implanted stent...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Kunquan Lan, Wei Lin
One-dimensional logistic population models with quasi-constant-yield harvest rates are studied under the assumptions that a population inhabits a patch of dimensionless width and no members of the population can survive outside of the patch. The essential problem is to determine the size of the patch and the ranges of the harvesting rate functions under which the population survives or becomes extinct. This is the first paper which discusses such models with the Dirichlet boundary conditions and can tell the exact quantity of harvest rates of the species without having the population die out...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Minette Herrera, Aaron Miller, Joel Nishimura
Altruism is typically associated with traits or behaviors that benefit the population as a whole, but are costly to the individual. We propose that, when the environment is rapidly changing, senescence (age-related deterioration) can be altruistic. According to numerical simulations of an agent-based model, while long-lived individuals can outcompete their short lived peers, populations composed of long-lived individuals are more likely to go extinct during periods of rapid environmental change. Moreover, as in many situations where other cooperative behavior arises, senescence can be stabilized in a structured population...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Kelum Gajamannage, Erik M Bollt
If a given behavior of a multi-agent system restricts the phase variable to an invariant manifold, then we define a phase transition as a change of physical characteristics such as speed, coordination, and structure. We define such a phase transition as splitting an underlying manifold into two sub-manifolds with distinct dimensionalities around the singularity where the phase transition physically exists. Here, we propose a method of detecting phase transitions and splitting the manifold into phase transitions free sub-manifolds...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Attila Denes, Yoshiaki Muroya, Gergely Rost
In this paper, we study the global stability of a multistrain SIS model with superinfection. We present an iterative procedure to calculate a sequence of reproduction numbers, and we prove that it completely determines the global dynamics of the system. We show that for any number of strains with different infectivities, the stable coexistence of any subset of the strains is possible, and we completely characterize all scenarios. As an example, we apply our method to a three-strain model.
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Zijuan Wen, Meng Fan, Asim M Asiri, Ebraheem O Alzahrani, Mohamed M El-Dessoky, Yang Kuang
This paper studies the global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with appropriate initial and mixed boundary conditions. Under some practicable regularity criteria on diffusion item and nonlinearity, we establish the local existence and uniqueness of classical solutions based on a contraction mapping. This local solution can be continued for all positive time by employing the methods of energy estimates, Lp-theory, and Schauder estimate of linear parabolic equations...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Kazeem Oare Okosun, Robert Smith
This paper presents a mathematical model for malaria--schistosomiasis co-infection in order to investigate their synergistic relationship in the presence of treatment. We first analyse the single infection steady states, then investigate the existence and stability of equilibria and then calculate the basic reproduction numbers. Both the single-infection models and the co-infection model exhibit backward bifurcations. We carrying out a sensitivity analysis of the co-infection model and show that schistosomiasis infection may not be associated with an increased risk of malaria...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Stephen Tully, Monica-Gabriela Cojocaru, Chris T Bauch
Population transmission models have been helpful in studying the spread of HIV. They assess changes made at the population level for different intervention strategies. To further understand how individual changes affect the population as a whole, game-theoretical models are used to quantify the decision-making process. Investigating multiplayer nonlinear games that model HIV transmission represents a unique approach in epidemiological research. We present here 2-player and multiplayer noncooperative games where players are defined by HIV status and age and may engage in casual (sexual) encounters...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Najat Ziyadi
We introduce mathematical human papillomavirus (HPV) epidemic models (with and without vaccination) for African American females (AAF) and African American males (AAM) with ''fitted'' logistic demographics and use these models to study the HPV disease dynamics. The US Census Bureau data of AAF and AAM of 16 years and older from 2000 to 2014 is used to ''fit'' the logistic demographic models. We compute the basic reproduction number, R0, and use it to show that R0 is less than 1 in the African American (AA) population with or without implementation of HPV vaccination program...
February 1, 2017: Mathematical Biosciences and Engineering: MBE
Cristiana J Silva, Helmut Maurer, Delfim F M Torres
We introduce delays in a tuberculosis (TB) model, representing the time delay on the diagnosis and commencement of treatment of individuals with active TB infection. The stability of the disease free and endemic equilibriums is investigated for any time delay. Corresponding optimal control problems, with time delays in both state and control variables, are formulated and studied. Although it is well-known that there is a delay between two to eight weeks between TB infection and reaction of body's immune system to tuberculin, delays for the active infected to be detected and treated, and delays on the treatment of persistent latent individuals due to clinical and patient reasons, which clearly justifies the introduction of time delays on state and control measures, our work seems to be the first to consider such time-delays for TB and apply time-delay optimal control to carry out the optimality analysis...
February 1, 2017: Mathematical Biosciences and Engineering: MBE
Elzbieta Ratajczyk, Urszula Ledzewicz, Maciej Leszczynski, Avner Friedman
Virotherapy, using herpes simplex virus, represents a promising therapy of glioma. But the innate immune response, which includes TNF-α produced by macrophages, reduces the effectiveness of the treatment. Hence treatment with TNF-α inhibitor may increase the effectiveness of the virotherapy. In the present paper we develop a mathematical model that includes continuous infusion of the virus in combination with TNF-α inhibitor. We study the efficacy of the treatment under different combinations of the two drugs for different scenarios of the burst size of newly formed virus emerging from dying infected cancer cells...
February 1, 2017: Mathematical Biosciences and Engineering: MBE
Ana Isabel Munoz, J Ignacio Tello
We propose a mathematical model to describe tumor cells movement towards a metastasis location into the bone marrow considering the influence of chemotaxis inhibition due to the action of a drug. The model considers the evolution of the signaling molecules CXCL-12 secreted by osteoblasts (bone cells responsible of the mineralization of the bone) and PTHrP (secreted by tumor cells) which activates osteoblast growth. The model consists of a coupled system of second order PDEs describing the evolution of CXCL-12 and PTHrP, an ODE of logistic type to model the Osteoblasts density and an extra equation for each cancer cell...
February 1, 2017: Mathematical Biosciences and Engineering: MBE
Roman Czapla, Vladimir V Mityushev
It was established in the previous works that hydrodynamic interactions between the swimmers can lead to collective motion. Its implicit evidences were confirmed by reduction in the effective viscosity. We propose a new quantitative criterion to detect such a collective behavior. Our criterion is based on a new computationally effective RVE (representative volume element) theory based on the basic statistic moments (e-sums or generalized Eisenstein-Rayleigh sums). The criterion can be applied to various two-phase dispersed media (biological systems, composites etc)...
February 1, 2017: Mathematical Biosciences and Engineering: MBE
Alicja Miniak-GOrecka, Andrzej Nowakowski
In earlier paper of V. Capasso et al it is considered a simply model of controlling an epidemic, which is described by three functionals and systems of two PDE equations having the feedback operator on the boundary. Necessary optimality conditions and two gradient-type algorithms are derived. This paper constructs dual dynamic programming method to derive sufficient optimality conditions for optimal solution as well ε-optimality conditions in terms of dual dynamic inequalities. Approximate optimality and numerical calculations are presented too...
February 1, 2017: Mathematical Biosciences and Engineering: MBE
Cicely K Macnamara, Mark A J Chaplain
Signal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e...
February 1, 2017: Mathematical Biosciences and Engineering: MBE
Henryk Leszczynski, Monika Wrzosek
We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.
February 1, 2017: Mathematical Biosciences and Engineering: MBE
Urszula Ledzewicz, Shuo Wang, Heinz Schattler, Nicolas Andre, Marie Amelie Heng, Eddy Pasquier
Effects that tumor heterogeneity and drug resistance have on the structure of chemotherapy protocols are discussed from a mathematical modeling and optimal control point of view. In the case when two compartments consisting of sensitive and resistant cells are considered, optimal protocols consist of full dose chemotherapy as long as the relative proportion of sensitive cells is high. When resistant cells become more dominant, optimal controls switch to lower dose regimens defined by so-called singular controls...
February 1, 2017: Mathematical Biosciences and Engineering: MBE
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