Optimal control of tumor size used to maximize survival time when cells are resistant to chemotherapy.

abstract：:A class of models is considered in which the number of unknown parameters exceeds the number of independent equations that are derived from the input/observation configuration. It is shown that, under certain circumstances, if the number of unknown parameters is sufficiently decreased by setting some of the exit param...

journal_title：Mathematical biosciences

authors： Eisenfeld J

更新日期：1996-03-01 00:00:00

abstract：:We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals move between populations according to a Markov transition matrix Σ and infectives can only make infectious contacts with members of their current population. Expressions for the basic reproduction number, R₀...

journal_title：Mathematical biosciences

authors： Neal P

更新日期：2012-03-01 00:00:00

abstract：:A new biological growth model is introduced. After random selection of possible growth sites, cells are added in an allowable random direction. Unlike the Eden model, the current model is grid independent and can be adapted to any curved surface. Growths of colonies of as many as 10(5) cells are simulated on planar, c...

journal_title：Mathematical biosciences

authors： Wang CY,Bassingthwaighte JB

更新日期：1997-06-01 00:00:00

abstract：:The transmission dynamics of a communicable disease in a subdivided population where the spread among groups follows the proportionate mixing model while the within-group transmission can correspond to preferred mixing, proportionate mixing among subgroups, or mixing between social and nonsocial subgroups, is analyzed...

journal_title：Mathematical biosciences

authors： Andreasen V,Christiansen FB

更新日期：1989-10-01 00:00:00

abstract：:A mechanistic model of the Fitzhugh-Nagumo type is proposed for the pulse-like jasmonate response in plants. The model is composed of a bistable signaling pathway coupled to a negative feedback loop. The bistable signaling pathway describes a recently discovered positive feedback loop involving jasmonate and the MYC2 ...

journal_title：Mathematical biosciences

authors： Chiangga S,Pornkaveerat W,Frank TD

更新日期：2016-03-01 00:00:00

abstract：:A mathematical model of the T-lymphocyte proliferation process (in vivo and in vitro) is presented. This model takes into account cell-cycle progression and the regulation by lymphokines (lymphocyte activating factor interleukin 1 and T-cell growth factor interleukin 2). Using data on the generalized picture of the sh...

journal_title：Mathematical biosciences

authors： Sidorov IA,Romanyukha AA

更新日期：1993-06-01 00:00:00

abstract：:Traits such as skill at foraging and investment in anti-predator defense may vary among individuals within a species population. This intraspecific variation has implications for community dynamics. The implications of intraspecific variation of a consumer in the intermediate level of a tritrophic food chain are explo...

journal_title：Mathematical biosciences

authors： DeAngelis DL

更新日期：2013-08-01 00:00:00

abstract：:We discuss an N-dimensional model for diffusion of age dependent populations. Let rho(x, t, a) be the population density at time t, age a and spatial position x, and let u(x, t) = [formula: see text] rho(x, t, a) da be the total population at t and x. The directed dispersal model to be discussed, with diffusion depend...

journal_title：Mathematical biosciences

authors： Hernández GE

更新日期：1998-04-01 00:00:00

abstract：:Lateral inhibition, a juxtacrine signalling mechanism by which a cell adopting a particular fate inhibits neighbouring cells from doing likewise, has been shown to be a robust mechanism for the formation of fine-grained spatial patterns (in which adjacent cells in developing tissues diverge to achieve contrasting stat...

journal_title：Mathematical biosciences

authors： O'Dea RD,King JR

更新日期：2011-06-01 00:00:00

abstract：:Three-species food-chain models, in which the prey population exhibits group defense, are considered. Using the carrying capacity of the environment as the bifurcation parameter, it is shown that the model without delay undergoes a sequence of Hopf bifurcations. In the model with delay it is shown that using a delay a...

journal_title：Mathematical biosciences

authors： Freedman HI,Ruan S

更新日期：1992-09-01 00:00:00

abstract：:The vaccination program for pertussis (whooping cough) in the United States consists of giving multiple doses of pertussis vaccine to young children. A demographic model with a steady-state age distribution is used as a basis for building an epidemiologic model for the transmission of pertussis. This age-structured mo...

journal_title：Mathematical biosciences

authors： Hethcote HW

更新日期：1997-10-15 00:00:00

abstract：:Amyloid beta (Aβ) peptides, and in particular Aβ42, are found in senile plaques associated with Alzheimer's disease. A compartmental model of Aβ production, exchange and irreversible loss was recently developed to explain the kinetics of isotope-labeling of Aβ peptides collected in cerebrospinal fluid (CSF) following ...

journal_title：Mathematical biosciences

authors： Elbert DL,Patterson BW,Bateman RJ

更新日期：2015-03-01 00:00:00

abstract：:The search for systematic methods to deal with the integrated behavior of complex biochemical systems has over the past two decades led to the proposal of several theories of biochemical systems. Among the most promising is biochemical systems theory (BST). Recent comparisons of this theory with several others that ha...

journal_title：Mathematical biosciences

authors： Sorribas A,Savageau MA

更新日期：1989-06-01 00:00:00

abstract：:In automatic feedback control of intravenous drug infusions, convergence to the setpoint is an important objective. This paper examines the stability of pharmacokinetic-pharmacodynamic models of patient response regulated with proportional integral feedback. The model consists of three components: linear compartmental...

journal_title：Mathematical biosciences

authors： Wada DR

更新日期：1997-12-01 00:00:00

abstract：:The introduction of endosymbiont Wolbachia into laboratory-reared mosquito populations, which are then released to mix with natural populations to prevent the mosquito vectors from reproducing and thus break the transmission cycle of dengue disease, is an innovative new technology. Field trials of Wolbachia-carrying m...

journal_title：Mathematical biosciences

authors： Zhang X,Tang S,Liu Q,Cheke RA,Zhu H

更新日期：2018-05-01 00:00:00

abstract：:In this article we elaborate on the structure of the generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class poss...

journal_title：Mathematical biosciences

authors： Hernández-Bermejo B,Fairén V

更新日期：1997-02-01 00:00:00

abstract：:A nonlinear mathematical model developed by Chandrasekaran et al. is examined to monitor pharmacokinetic profiles in percutaneous drug absorption and is addressed to several associated problems that could occur in the data analysis of in vitro experiments. The formulation of the model gives rise to a nonlinear partial...

journal_title：Mathematical biosciences

authors： Kubota K,Twizell EH

更新日期：1992-03-01 00:00:00

abstract：:Proteins with multiple binding sites play important roles in cell signaling systems by nucleating protein complexes in which, for example, enzymes and substrates are co-localized. Proteins that specialize in this function are called by a variety names, including adapter, linker and scaffold. Scaffold-mediated nucleati...

journal_title：Mathematical biosciences

authors： Yang J,Hlavacek WS

更新日期：2011-08-01 00:00:00

abstract：:Invariants are functions of the probabilities of state configurations among lineages, with expected values equal to zero under certain phylogenies. For two-state sequences, the existence of certain quadratic invariants requires a symmetric substitution model. For sequences with more than two states, the necessary cond...

journal_title：Mathematical biosciences

authors： Fu YX,Li WH

更新日期：1991-07-01 00:00:00

abstract：:We apply to Michaelis-Menten kinetics an alternative approach to the study of Singularly Perturbed Differential Equations, that is based on the Renormalization Group (SPDERG). To this aim, we first rebuild the perturbation expansion for Michaelis-Menten kinetics, beyond the standard Quasi-Steady-State Approximation (s...

journal_title：Mathematical biosciences

authors： Coluzzi B,Bersani AM,Bersani E

更新日期：2018-05-01 00:00:00

abstract：:Many situations in population biology involve a rate--typically a contact or recruitment rate--which increases linearly for small populations but reaches a maximum value (saturates) for large populations. Models for populations of variable size need to incorporate both characteristics to predict behavior accurately. T...

journal_title：Mathematical biosciences

authors： Kribs-Zaleta CM

更新日期：2004-12-01 00:00:00

abstract：:The assumptions of well-mixed and zero bulk flow in compartmental analysis are reexamined. Using Poiseuille flow inside and radial flow outside a pore, the mass-transfer equations are solved by perturbations on simple diffusion. Formulas are obtained for solute distribution, total mass transfer, and apparent permeabil...

journal_title：Mathematical biosciences

authors： Wang CY

更新日期：1989-07-01 00:00:00

abstract：:Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-kappaB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding and mRNA production. This description of natural variability for delays intro...

journal_title：Mathematical biosciences

authors： Rateitschak K,Wolkenhauer O

更新日期：2007-02-01 00:00:00

abstract：:In a previous paper we studied the spread of excitation in a simplified model of the left ventricle, affected by fiber structure and obliqueness, curvature of the wall and Purkinje network. In the present paper we investigate the extracellular potential distribution u in the same ventricular model. Given the transmemb...

journal_title：Mathematical biosciences

authors： Colli Franzone P,Guerri L,Pennacchio M,Taccardi B

更新日期：1998-07-01 00:00:00

abstract：:In this work, we derive and analyze a 2n+1-dimensional deterministic differential equation modeling the transmission and treatment of HIV (Human Immunodeficiency Virus) disease. The model is extended to a stochastic differential equation by introducing noise in the transmission rate of the disease. A theoretical treat...

journal_title：Mathematical biosciences

authors： Otunuga OM

更新日期：2018-05-01 00:00:00

abstract：:A two-state variable model in which saturable binding takes place is studied. Two mathematical representations of the same model are considered, one a standard chemical kinetics type of polynomial system, the other a reduced model formed from the original system via a pseudo-steady-state approximation. For a particula...

journal_title：Mathematical biosciences

authors： Chappell MJ

更新日期：1996-04-01 00:00:00

abstract：:An epidemic model with multiple stages of infection is studied. The model allows for infected individuals to move from advanced stages of infection back to less advanced stages of infection. A threshold parameter which determines the local stability of the disease free equilibrium is found and interpreted. Under condi...

journal_title：Mathematical biosciences

authors： McCluskey CC

更新日期：2003-01-01 00:00:00

abstract：:Transmission of an infectious agent can be quantified from experimental data using the transient-state (TS) algorithm. The TS algorithm is based on the stochastic SIR model and provides a time-dependent probability distribution over the number of infected individuals during an epidemic, with no need for the experiment...

journal_title：Mathematical biosciences

authors： Velthuis AG,De Jong MC,De Bree J

更新日期：2007-11-01 00:00:00

abstract：:For a wide range of airborne infectious diseases, transmission within the family or household is a key mechanism for the spread and persistence of infection. In general, household-based transmission is relatively strong but only involves a limited number of individuals in contact with each infectious person. In contra...

journal_title：Mathematical biosciences

authors： House T,Keeling MJ

更新日期：2008-05-01 00:00:00

abstract：:Mutual interference and prey refuge are important drivers of predator-prey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the mutual interference exponent, and prey refuge, on the behavior of a predator-p...

journal_title：Mathematical biosciences

authors： Antwi-Fordjour K,Parshad RD,Beauregard MA

更新日期：2020-08-01 00:00:00