Abstract：
:This paper is concerned with the qualitative analysis of two models [S. Bonhoeffer, M. Lipsitch, B.R. Levin, Evaluating treatment protocols to prevent antibiotic resistance, Proc. Natl. Acad. Sci. USA 94 (1997) 12106] for different treatment protocols to prevent antibiotic resistance. Detailed qualitative analysis about the local or global stability of the equilibria of both models is carried out in term of the basic reproduction number R(0). For the model with a single antibiotic therapy, we show that if R(0)<1, then the disease-free equilibrium is globally asymptotically stable; if R(0)>1, then the disease-endemic equilibrium is globally asymptotically stable. For the model with multiple antibiotic therapies, stabilities of various equilibria are analyzed and combining treatment is shown better than cycling treatment. Numerical simulations are performed to show that the dynamical properties depend intimately upon the parameters.
journal_name
Math Bioscijournal_title
Mathematical biosciencesauthors
Sun HR,Lu X,Ruan Sdoi
10.1016/j.mbs.2010.06.002subject
Has Abstractpub_date
2010-09-01 00:00:00pages
56-67issue
1eissn
0025-5564issn
1879-3134pii
S0025-5564(10)00091-Xjournal_volume
227pub_type
杂志文章abstract：:Through use of the local state isomorphism theorem instead of the algebraic equivalence theorem of linear systems theory, the similarity transformation approach is extended to nonlinear models, resulting in finitely verifiable sufficient and necessary conditions for global and local identifiability. The approach requi...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(89)90024-2
更新日期：1989-04-01 00:00:00
abstract：:An optimal input of nutrients into the metabolic process of the individual subject so as to effect desired therapeutic results is particularly important for the critically ill. A patient-related, individualized nutrients optimization procedure is proposed here. The procedure is applicable to any time-invariant and det...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(89)90004-7
更新日期：1989-12-01 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
pub_type： 杂志文章
doi：10.1016/j.mbs.2020.108407
更新日期：2020-08-01 00:00:00
abstract：:In biodiversity conservation it is often necessary to prioritize the species to conserve. Existing approaches to prioritization, e.g. the Fair Proportion Index and the Shapley Value, are based on phylogenetic trees and rank species according to their contribution to overall phylogenetic diversity. However, in many cas...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2018.02.005
更新日期：2018-04-01 00:00:00
abstract：:This study is a theoretical excursion into gravity models and their usability in evaluating importance of spatial structure and population development for the spread of colonizing organisms. A so called "gravity score" for sites is deduced, and such a score could be used for predicting risk of colonization once one si...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2009.08.008
更新日期：2009-11-01 00:00:00
abstract：:In many cicadas, a phenomenon is observed in which the peak of emergence of males precedes that of females (protandry). Generally, it is known that the ecology of emergence of insects is closely related to mating, and protandry is said to be the strategy of males to eclose early and to attempt mating with virgin femal...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2018.08.006
更新日期：2018-11-01 00:00:00
abstract：:The Yule process generates a class of binary trees which is fundamental to population genetic models and other applications in evolutionary biology. In this paper, we introduce a family of sub-classes of ranked trees, called Ω-trees, which are characterized by imbalance of internal nodes. The degree of imbalance is de...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.08.008
更新日期：2013-11-01 00:00:00
abstract：:A mathematical model is formulated for diffusive countercurrent exchange of oxygen between paired arterioles and venules. A closed form solution of the problem is obtained by linearizing the nonlinear oxyhemoglobin dissociation curve at the inlet PO2 in the vessel. The closed form solution is compared with the corresp...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(88)90022-3
更新日期：1988-09-01 00:00:00
abstract：:A stochastic model is presented of carcinogenesis induced by irradiation with arbitrary time-dependent dose rate. The key feature of the model is that it allows for radiation-induced cell killing to compete with the process of tumor promotion. Two versions of the model arise when considering target tissues with slow a...
journal_title：Mathematical biosciences
pub_type： 杂志文章,评审
doi：10.1016/0025-5564(95)00047-x
更新日期：1996-02-01 00:00:00
abstract：:Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results in an ideal free distribution, is evolutionary stable in spatially varying but ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2016.11.003
更新日期：2017-01-01 00:00:00
abstract：:Estimation of the immunity coverage required to effectively control disease transmission is an important public health problem. Using data on the eventual size of a major epidemic, we compare estimates based on the simplifying assumption that the community consists of uniformly mixing individuals with estimates obtain...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(97)00079-5
更新日期：1998-01-01 00:00:00
abstract：:Most endocrine cells secrete hormones as a result of Ca2+-regulated exocytosis, i.e., fusion of the membranes of hormone-containing secretory granules with the cell membrane, which allows the hormone molecules to escape to the extracellular space. As in neurons, electrical activity and cell depolarization open voltage...
journal_title：Mathematical biosciences
pub_type： 杂志文章,评审
doi：10.1016/j.mbs.2016.11.010
更新日期：2017-01-01 00:00:00
abstract：:Two optimization problems are considered: Harvesting from a structured population with maximal gain subject to the condition of non-extinction, and vaccinating a population with prescribed reduction of the reproduction number of the disease at minimal costs. It is shown that these problems have a similar structure and...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2005.09.001
更新日期：2007-04-01 00:00:00
abstract：:In the present paper we have first introduced a measure of dynamical entropy of an ecosystem on the basis of the dynamical model of the system. The dynamical entropy which depends on the eigenvalues of the community matrix of the system leads to a consistent measure of complexity of the ecosystem to characterize the d...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.07.016
更新日期：2013-10-01 00:00:00
abstract：:The acetone-butanol (AB) fermentation process in the anaerobic endospore-forming Gram-positive bacterium Clostridium acetobutylicum is useful as a producer of biofuels, particularly butanol. Recent work has concentrated on trying to improve the efficiency of the fermentation method, either through changes in the envir...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2012.11.004
更新日期：2013-02-01 00:00:00
abstract：:This paper deals with a two-microbial species model in competition for a single-resource in the chemostat including general intra- and interspecific density-dependent growth rates with distinct removal rates for each species. In order to understand the effects of intra- and interspecific interference, this general mod...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2017.02.007
更新日期：2017-04-01 00:00:00
abstract：:We present a model governing the operation of all "isolated" sensory receptors with their primary afferent neurons. The input to the system is the intensity of a sensory signal, be it chemical, optical etc., and the output is the rate of neural impulse transmission in the afferent neuron. The model is based on the pre...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(94)00024-t
更新日期：1995-01-01 00:00:00
abstract：:An optimal parameter selection model of cancer chemotherapy is presented which describes the treatment of a tumor over a fixed period of time by the repeated administration of a single drug. The drug is delivered at evenly spaced intervals over the treatment period at doses to be selected by the model. The model const...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(90)90005-j
更新日期：1990-05-01 00:00:00
abstract：:A mathematical multi-cell model for the in vitro kinetics of the anti-cancer agent topotecan (TPT) following administration into a culture medium containing a population of human breast cancer cells (MCF-7 cell line) is described. This non-linear compartmental model is an extension of an earlier single-cell type model...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2008.03.008
更新日期：2008-06-01 00:00:00
abstract：:Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The model draws attention to the role of viability selections of different types to...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2015.10.013
更新日期：2016-01-01 00:00:00
abstract：:In this paper we study the dynamics of two competing species when one of them is subject to a disease. In order to keep the model simple, we present it under the strong assumption that the disease cannot cross the species barrier. We answer several important questions about the long term behavior of the environment. I...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(01)00081-5
更新日期：2001-12-01 00:00:00
abstract：:Free access to a common pool of resource in a country may lead to over-exploitation and sacrifice future opportunities of harvesting. As such, the protection of a common fishery resource is worth investigating. In this paper we develop a two-period model and a multi-period model to analyze the optimal inter-temporal u...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2006.06.007
更新日期：2007-05-01 00:00:00
abstract：:The ICING model has been successfully used to guide clinical decisions on insulin administration in critical illness. However, insulin pharmacokinetics in the ICING model can be improved to better describe both intravenous (IV) bolus and infusion insulin administration. Patient data from 217 Dynamic Insulin Sensitivit...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2016.08.005
更新日期：2016-11-01 00:00:00
abstract：:Cell cycle duration and phase transition times are not fixed, even within homogeneous cell populations growing under optimal environmental conditions. We investigate G(1) phase variability from the molecular point of view and propose a mathematical approach to model the protein interactions regulating the transition f...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(02)00085-8
更新日期：2002-05-01 00:00:00
abstract：:In a random walk (RW) in Z an individual starts at 0 and moves at discrete unitary steps to the right or left with respective probabilities p and 1-p. Assuming p > 1/2 and finite a, a > 1, the probability that state a will be reached before -a is Q(a, p) where Q(a, p) > p. Here we introduce the cooperative random walk...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2016.06.011
更新日期：2016-09-01 00:00:00
abstract：:A model was developed for novel prediction of N-linked glycan branching pattern classification for CHO-derived N-linked glycoproteins. The model consists of 30 independent recurrent neural networks and uses predicted quantities of secondary structure elements and residue solvent accessibility as an input vector. The m...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2007.10.005
更新日期：2008-01-01 00:00:00
abstract：:A structure for representing problems in decision analysis and in expert systems, which reason under uncertainty, is the influence diagram or causal network. A causal network consists of an underlying joint probability distribution and a directed acyclic graph in which a propositional variable that represents a margin...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(91)90089-2
更新日期：1991-02-01 00:00:00
abstract：:Emergency vaccination during an epidemic of classical swine fever virus (CSFV) has become a serious option because of the ethical problems of strategies with massive culling and the availability of a marker vaccine that reduces virus transmission. Here we present a model of between-herd CSFV transmission, which quanti...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2003.08.005
更新日期：2003-12-01 00:00:00
abstract：:Aptamer-protein interacting pairs play important roles in physiological functions and structural characterization. Identifying aptamer-protein interacting pairs is challenging and limited, despite of the tremendous applications of aptamers. Therefore, it is vital to construct a high prediction performance model for id...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2019.01.009
更新日期：2019-05-01 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
pub_type： 杂志文章
doi：10.1016/j.mbs.2004.11.001
更新日期：2004-12-01 00:00:00
