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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 9, 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
Pia Brechmann, Alan D Rendall
A classical example of a mathematical model for oscillations in a biological system is the Selkov oscillator, which is a simple description of glycolysis. It is a system of two ordinary differential equations which, when expressed in dimensionless variables, depends on two parameters. Surprisingly it appears that no complete rigorous analysis of the dynamics of this model has ever been given. In this paper several properties of the dynamics of solutions of the model are established. With a view to studying unbounded solutions a thorough analysis of the Poincaré compactification of the system is given...
September 26, 2018: Mathematical Biosciences
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
The determination of a substrate or enzyme activity by coupling of one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course expressions valid under the quasi-steady-state and reactant stationary state assumptions. In this paper, the dynamical behavior of coupled enzyme catalyzed reaction mechanisms is studied by analysis of the phase-plane...
September 24, 2018: Mathematical Biosciences
Alexander S Bratus, Sergei Drozhzhin, Tatiana Yakushkina
In this study, we examine the process of fitness landscape evolution of the hypercycle system. We assume that the parameters that define the fitness landscape change in order to maximize the mean fitness of the system. The environmental influence is expressed as resource limitation: we formalize it as a restriction on the fitness matrix coefficients. We show that this process of adaptation leads to a system that is sustainable in the presence of parasites. Even if the parasites are harmful to the classical hypercycle, the persistence of the population develops under fitness landscape evolution...
September 12, 2018: Mathematical Biosciences
M J Lydeamore, P T Campbell, D G Regan, S Y C Tong, R M Andrews, A C Steer, L Romani, J M Kaldor, J McVernon, J M McCaw
Infections with Sarcoptes scabiei, or scabies, remain common in many disadvantaged populations. Mass drug administration (MDA) has been used in such settings to achieve a rapid reduction in infection and transmission, with the goal of eliminating the public health burden of scabies. While prevalence has been observed to fall substantially following such an intervention, in some instances resurgence of infection to baseline levels has occurred over several years. To explore the biology underpinning this phenomenon, we have developed a theoretical model of scabies life-cycle and transmission dynamics in a homogeneously mixing population, and simulate the impact of mass drug treatment strategies acting on egg and mite life cycle stages (ovicidal) or mites alone (non-ovicidal)...
August 24, 2018: Mathematical Biosciences
Bożena Małysiak-Mrozek
Understanding proteins, their structures, functions, mutual interactions, activity in cellular reactions, interactions with drugs, and expression in body cells is a key to efficient medical diagnosis, drug production, and treatment of patients. Machine learning and data exploration methods supported by many-valued logics allow to grasp the imprecision and uncertainties that naturally occur in proteins and other biomolecules. Many-valued logics, like Łukasiewicz logic or fuzzy logic, are non-classical logics that do not restrict the number of truth values to only two values of true or false, but they allow for a larger set of truth degrees...
August 10, 2018: Mathematical Biosciences
B D'Acunto, L Frunzo, I Klapper, M R Mattei, P Stoodley
A mathematical model for dispersal phenomenon in multispecies biofilm based on a continuum approach and mass conservation principles is presented. The formation of dispersed cells is modeled by considering a mass balance for the bulk liquid and the biofilm. Diffusion of these cells within the biofilm and in the bulk liquid is described using a diffusion-reaction equation. Diffusion supposes a random character of mobility. Notably, biofilm growth is modeled by a hyperbolic partial differential equation while the diffusion process of dispersed cells by a parabolic partial differential equation...
August 1, 2018: Mathematical Biosciences
Stefan Diehl, Jesús Zambrano, Bengt Carlsson
A photobioreactor (PBR) contains microalgae which under illumination consume carbon dioxide and substrate dissolved in water, and produce oxygen. The process is used in water recovery resource facilities with a continuous flow of wastewaster through the PBR. With several PBRs in series the reduction of substrate can be improved. This paper contains a thorough analysis of a model of PBRs in series, where each PBR is modelled with a system of three ordinary differential equations for the concentrations of dissolved substrate and biomass (algae), and the internal cell quota of substrate to biomass...
July 27, 2018: Mathematical Biosciences
Pavel Kurasov, Alexander Lück, Delio Mugnolo, Verena Wolf
A widely used approach to describe the dynamics of gene regulatory networks is based on the chemical master equation, which considers probability distributions over all possible combinations of molecular counts. The analysis of such models is extremely challenging due to their large discrete state space. We therefore propose a hybrid approximation approach based on a system of partial differential equations, where we assume a continuous-deterministic evolution for the protein counts. We discuss efficient analysis methods for both modeling approaches and compare their performance...
November 2018: Mathematical Biosciences
A Beuter, A Balossier, S Trofimchuk, V Volpert
Following a stroke, cortical networks in the penumbra area become fragmented and partly deactivated. We develop a model to study the propagation of waves of electric potential in the cortical tissue with integro-differential equations arising in neural field models. The wave speed is characterized by the tissue excitability and connectivity determined through parameters of the model. Post-stroke tissue damage in the penumbra area creates a hypoconnectivity and decreases the speed of wave propagation. It is proposed that external stimulation could restore the wave speed in the penumbra area under certain conditions of the parameters...
November 2018: Mathematical Biosciences
Kym E Wilkins, Thomas A A Prowse, Phillip Cassey, Paul Q Thomas, Joshua V Ross
Synthetic gene drives offer a novel solution for the control of invasive alien species. CRISPR-based gene drives can positively bias their own inheritance, and comprise a DNA sequence that is replicated by homologous recombination. Since gene drives can be positioned to silence fertility or developmental genes, they could be used for population suppression. However, the production of resistant alleles following self-replication errors threatens the technology's viability for pest eradication in real-world applications...
November 2018: Mathematical Biosciences
F B Agusto, M A Khan
This paper presents a deterministic model for dengue virus transmission. The model is parameterized using data from the 2017 dengue outbreak in Pakistan. We estimated the basic reproduction number (R0 ) without any interventions for the 2017 dengue outbreak in Peshawar district of Pakistan as R0 ≈2.64, the distribution of the reproduction number lies in the range R0 ∈[1.21,5.24] (with a mean R0 ≈2.64). Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using two time-dependent control variables determined from sensitivity analysis...
November 2018: Mathematical Biosciences
Ugur G Abdulla, Roby Poteau
We consider the inverse problem for the identification of the finite dimensional set of parameters for systems of nonlinear ordinary differential equations (ODEs) arising in systems biology. A numerical method which combines Bellman's quasilinearization with sensitivity analysis and Tikhonov's regularization is implemented. We apply the method to various biological models such as the classical Lotka-Volterra system, bistable switch model in genetic regulatory networks, gene regulation and repressilator models from synthetic biology...
November 2018: Mathematical Biosciences
Sh Asadi, V Nekoukar
Currently, artificial pancreas is an alternative treatment instead of insulin therapy for patients with type 1 diabetes mellitus. Closed-loop control of blood glucose level (BGL) is one of the difficult tasks in biomedical engineering field due to nonlinear time-varying dynamics of insulin-glucose relation that is combined with time delays and model uncertainties. In this paper, we propose a novel adaptive fuzzy integral sliding mode control scheme for BGL regulation. System dynamics is identified online using fuzzy logic systems...
November 2018: Mathematical Biosciences
Tayebeh Waezizadeh, Adel Mehrpooya, Maryam Rezaeizadeh, Shantia Yarahmadian
Determining the future state of individual patients, with regard to the susceptibility to life-threatening condition is a crucial problem in the public health. Chronic Kidney Disease (CKD) is a perilous disease, which is characterized by gradual loss of kidney function. This paper presents a set of mathematical models for CKD by applying both deterministic and stochastic approaches. Specifically, hypertension and stress are considered as the main causes of damaging and removing of nephrons thereby reducing the Glomerular Filtration Rate (GFR), which leads to irreparable damages to the kidney function and may result in renal failure, or even kidney loss...
November 2018: Mathematical Biosciences
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