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Mathematical Biosciences

Fengqin Zhang, Yuming Chen, Jianquan Li
This paper concerns with a stage-structured predator-prey model with cannibalism in the predator, where the predator population is divided into two stages, a juvenile stage and a mature stage. The effects of cannibalism on the model have been partially discussed by Magnússon [12] and Mařík and Přibyloná [13] by means of numerical simulation and simple mathematical analysis. Here we reinvestigate the dynamics of this model. We obtain the global stability of the model, illustrate the effects of the two factors (one describes the cannibalization and the other the benefit from cannibalism) on dynamics of the model, and find that the positive equilibrium can undergo stability switch (from stable to unstable to stable, or from unstable to stable to unstable) with the change of the cannibalization rate...
November 13, 2018: Mathematical Biosciences
Egils Stalidzans, Katrina Landmane, Jurijs Sulins, Sven Sahle
One of use cases for metabolic network optimisation of biotechnologically applied microorganisms is the in silico design of new strains with an improved distribution of metabolic fluxes. Global stochastic optimisation methods (genetic algorithms, evolutionary programing, particle swarm and others) can optimise complicated nonlinear kinetic models and are friendly for unexperienced user: they can return optimisation results with default method settings (population size, number of generations and others) and without adaptation of the model...
November 9, 2018: Mathematical Biosciences
Fan Bai
Vaccination is considered as one of the most crucial methods in controlling the spread of infectious diseases. However, it is difficult to predict the expected vaccine coverage level because it depends on human behaviors. We consider deterministic and stochastic models to simulate how individuals choose strategies in the scenario of vaccination. In an infinite population, a system of replicator equations is formulated and the expected level is calculated. Decision making processes in both an unstructured finite population and a structured finite population are discussed...
November 8, 2018: Mathematical Biosciences
Carla M A Pinto, Ana R M Carvalho, João N Tavares
In this paper we study the effect of time-varying drug exposure in the dynamics of a fractional order model for the human immunodeficiency virus infection. We compute the reproduction number of the model and verify the stability of the disease-free equilibrium. The model is simulated for parameters directly modelling the pharmacodynamics of HIV, namely the slope of the dose-response curve, the drug's half-life, and the dosing interval. The later affect in a significant way the infection patterns. The order of the fractional derivative is also a key player of the model, adding more information, which could be useful for a deeper understanding of the pharmacodynamics of HIV, necessary for more accurate therapeutic regimens...
November 3, 2018: Mathematical Biosciences
Koyel Chakravarty, D C Dalal
The primary aim of liposomal drug delivery is to wisely modulate the drug delivery system in order to target diseased tissues. Temperature-sensitive liposomes function as a prospective weapon to combat toxic side effects corresponding to direct infusion of anticancer drugs. The main objective of the present study is to model liposomal drug release, subsequent drug transport in solid tumour along with integrated actions of tumour cell surface and endosomal events. Generalized mathematical model for liposomal drug delivery is proposed in which vital physical phenomena, such as kinetics of liposome-encapsulated drug, free drug release from liposomes, transport of both liposomal drug and free drug into the tumour compartment, plasma clearance, protein-drug interactions, drug-tumour cell receptor interactions, internalization of drug through endocytosis along with corresponding endosomal events...
November 1, 2018: Mathematical Biosciences
Jorge Arroyo-Esquivel, Fabio Sanchez, Luis A Barboza
Coffee rust is one of the main diseases that affect coffee plantations worldwide (Cressey, 2013 [10]). This causes an important economic impact in the coffee production industry in countries where coffee is an important part of the economy. A common method for combating this disease is using copper hydroxide as a fungicide, which can have damaging effects both on the coffee tree and on human health (Haddad et al., 2013 [13]). A novel method for biological control of coffee rust using bacteria has been proven to be an effective alternative to copper hydroxide fungicides as anti-fungal compounds (Haddad et al...
November 1, 2018: Mathematical Biosciences
Eyyüb Y Kıbış, I Esra Büyüktahtakın
In this paper we introduce a new mixed-integer linear programming (MIP) model that explicitly integrates the spread of cancer cells into a spatio-temporal reaction-diffusion model of cancer growth, while taking into account treatment effects. This linear but non-convex model appears to be the first of its kind by determining the optimal sequence of the typically prescribed cancer treatment methods-surgery (S), chemotherapy (C), and radiotherapy (R)-while minimizing the newly generated tumor cells for early-stage breast cancer in a unique three-dimensional (3D) spatio-temporal system...
October 30, 2018: Mathematical Biosciences
Omri Tal, Tat Dat Tran
We present an axiomatic approach for multilocus informativeness measures for determining the amount of information that a set of polymorphic genetic markers provides about individual ancestry. We then reveal several surprising properties of a decision-theoretic based measure that is consistent with the set of proposed criteria for multilocus informativeness. In particular, these properties highlight the interplay between information originating from population priors and the information extractable from the population genetic variants...
October 30, 2018: Mathematical Biosciences
Hwai-Ray Tung
Oscillations play a major role in a number of biological systems, from predator-prey models of ecology to circadian clocks. In this paper we focus on the question of whether oscillations exist within dual-site phosphorylation systems. Previously, Wang and Sontag showed, using monotone systems theory, that the Michaelis-Menten (MM) approximation of the distributive and sequential dual-site phosphorylation system lacks oscillations. However, biological systems are generally not purely distributive; there is generally some processive behavior as well...
October 26, 2018: Mathematical Biosciences
Serdal Pamuk, İrem Çay, Ali Sazcı
We present a 2D mathematical model of tumor angiogenesis which is an extension of the 1D model originally presented in Levine et al. (2000) [1]. Our model is connected to that 1D model by some transmission and boundary conditions which carry certain cells, the endothelials, pericytes and macrophages from the vessel wall into the extra cellular matrix. In our extended model we also include a mechanism for the action of anti-angiogenic factors such as angiostatin. We present numerical simulations in which we obtain a very good "qualitative agreement" with the time of the onset of vascularization of tumors and with the fact that the capillary tip growth accelerates as it approaches the "tumor"...
October 26, 2018: Mathematical Biosciences
Jia Li, Maoan Han, Jianshe Yu
To study the interactive dynamics of wild mosquitoes and mosquitoes carrying genetically-modified bacteria, we formulate continuous-time homogeneous and stage-structured models in this study. With appropriate transformations, complete results of the existence and stability of all boundary and positive equilibria for the homogeneous model are established and complete results of the existence and local stability of all boundary and positive equilibria for the stage-structured model are obtained as well. The outcomes from the homogeneous and the stage-structured models are similar...
October 19, 2018: Mathematical Biosciences
Tetsuro Nomura
Maximum avoidance of inbreeding (MAI) is a mating system, in which mates are as distantly related as possible. Although theoretical aspects and applications of MAI in diploid populations have been studied by many researchers, extension of MAI to haplodiploid populations is an unresolved problem. In this paper, this problem is addressed, and the following conclusions are derived. For a haplodiploid population with a Fibonacci number of females, a set of mating systems (one cycle MAI-hd) to avoid inbreeding to the maximum after one cycle practice of the set can be defined...
October 16, 2018: Mathematical Biosciences
Ya-Wei Niu, Hua Liu, Guang-Hui Wang, Gui-Ying Yan
The last few decades have verified the vital roles of microRNAs in the development of human diseases and witnessed the increasing interest in the prediction of potential disease-miRNA associations. Owning to the open access of many miRNA-related databases, up until recently, kinds of feasible in silico models have been proposed. In this work, we developed a computational model of Maximal Entropy Random Walk on heterogenous network for MiRNA-disease Association prediction (MERWMDA). MERWMDA integrated known disease-miRNA association, pair-wise functional relation of miRNAs and pair-wise semantic relation of diseases into a heterogenous network comprised of disease and miRNA nodes full of information...
October 16, 2018: Mathematical Biosciences
Yuan Lou, Hua Nie, Yan'e Wang
The community composition in open advective environments, where individuals are exposed to unidirectional flow, is formed by the complex interplays of hydrological and biological factors. We investigate the coexistence mechanism of species by a reaction-diffusion-advection competition model proposed by Lutscher et al. in [19]. It turns out that the locations of two critical curves, which separate the stable region of the semi-trivial solutions from the unstable one, determines whether coexistence or bistability happens...
October 16, 2018: Mathematical Biosciences
Maria I Poole, Inmaculada Sorribes, Harsh Vardhan Jain
Hepatitis C virus (HCV) infection has reached epidemic proportions worldwide. Individuals with chronic HCV infection and without access to treatment are at high risk for developing hepatocellular carcinoma (HCC), a liver cancer that is rapidly fatal after diagnosis. A number of factors have been identified that contribute to HCV-driven carcinogenesis such as scarring of the liver, and chronic inflammation. Recent evidence indicates a direct role for HCV-encoded proteins themselves in oncogenesis of infected hepatocytes...
October 10, 2018: Mathematical Biosciences
Xian Zhao, Lei Chen, Jing Lu
Drugs can produce intended therapeutic effects to treat different diseases. However, they may also cause side effects at the same time. For an approved drug, it is best to detect all side effects it can produce. Otherwise, it may bring great risks for pharmaceuticals companies as well as be harmful to human body. It is urgent to design quick and reliable identification methods to detect the side effects for a given drug. In this study, a binary classification model was proposed to predict drug side effects...
October 5, 2018: Mathematical Biosciences
Vitalii Akimenko, Vlastimil Křivan
In this article we study a nonlinear age-structured consumer population model with density-dependent death and fertility rates, and time delays that model incubation/gestation period. Density dependence we consider combines both positive effects at low population numbers (i.e., the Allee effect) and negative effects at high population numbers due to intra-specific competition of consumers. The positive density-dependence is either due to an increase in the birth rate, or due to a decrease in the mortality rate at low population numbers...
October 4, 2018: Mathematical Biosciences
Daniel Franco, Juan Perán, Juan Segura
The moment of intervention is a key question in harvest programmes and is currently generating an increasing interest. However, little is known about its effect on the population stability. This lack of knowledge is greater in the case of global stability, which is always desirable as it allows to predict the fate of populations regardless of the initial size. Here we use a discrete-time equation to model the dynamics of populations harvested at any time during the reproductive season. We study the effect of the time of intervention on the global stability of populations governed by the Ricker model, which is one of the most relevant models in discrete-time population dynamics...
October 4, 2018: Mathematical Biosciences
Indrajit Ghosh, Pankaj Kumar Tiwari, Sudip Samanta, Ibrahim M Elmojtaba, Nasser Al-Salti, Joydev Chattopadhyay
Infectious diseases can have a large impact on society, as they cause morbidity, mortality, unemployment, inequality and other adverse effects. Mathematical models are invaluable tools in understanding and describing disease dynamics with preventive measures for controlling the disease. The roles of media coverage and behavioral changes due to externally imposed factors on the disease dynamics are well studied. However, the effect of self-imposed psychological fear on the disease transmission has not been considered in extant research, and this gap is addressed in the present investigation...
October 3, 2018: Mathematical Biosciences
Paul J Harris
In experiments clusters of cells are often observed to move in response to a chemical signal which is present in the fluid surrounding the cells. This process is known as chemotaxis. This paper presents a method for modelling the motion of clusters of cells moving through a viscous fluid in response to a known chemical signal using a boundary integral formulation of the governing equations rather than the more usual differential equation formulation. The numerical results presented in this paper show that the boundary integral method can be used to simulate the motion of cell clusters through the fluid...
September 26, 2018: Mathematical Biosciences
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