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Mathematical Biosciences

Regina Padmanabhan, Nader Meskin, Wassim M Haddad
The increasing threat of cancer to human life and the improvement in survival rate of this disease due to effective treatment has promoted research in various related fields. This research has shaped clinical trials and emphasized the necessity to properly schedule cancer chemotherapy to ensure effective and safe treatment. Most of the control methodologies proposed for cancer chemotherapy scheduling treatment are model-based. In this paper, a reinforcement learning (RL)-based, model-free method is proposed for the closed-loop control of cancer chemotherapy drug dosing...
August 16, 2017: Mathematical Biosciences
P G Ballard, N G Bean, J V Ross
The emergence of a new strain of a disease, or the introduction of an existing strain to a naive population, can give rise to an epidemic. We consider how to maximise the probability of epidemic fade-out - that is, disease elimination in the trough between the first and second waves of infection - in the Markovian SIR-with-demography epidemic model. We assume we have an intervention at our disposal that results in a lowering of the transmission rate parameter, β, and that an epidemic has commenced. We determine the optimal stage during the epidemic in which to implement this intervention...
August 10, 2017: Mathematical Biosciences
Caroline Franco, José F Fontanari
The changes on abiotic features of ecosystems have rarely been taken into account by population dynamics models, which typically focus on trophic and competitive interactions between species. However, understanding the population dynamics of organisms that must modify their habitats in order to survive, the so-called ecosystem engineers, requires the explicit incorporation of abiotic interactions in the models. Here we study a model of ecosystem engineers that is discrete both in space and time, and where the engineers and their habitats are arranged in patches fixed to the sites of regular lattices...
August 9, 2017: Mathematical Biosciences
Luca Bolzoni, Elena Bonacini, Cinzia Soresina, Maria Groppi
We investigate the time-optimal control problem in SIR (Susceptible-Infected-Recovered) epidemic models, focusing on different control policies: vaccination, isolation, culling, and reduction of transmission. Applying the Pontryagins Minimum Principle (PMP) to the unconstrained control problems (i.e. without costs of control or resource limitations), we prove that, for all the policies investigated, only bang-bang controls with at most one switch are admitted. When a switch occurs, the optimal strategy is to delay the control action some amount of time and then apply the control at the maximum rate for the remainder of the outbreak...
August 8, 2017: Mathematical Biosciences
Vo Hong Thanh
We present in this paper a new exact algorithm for improving performance of exact stochastic simulation algorithm. The algorithm is developed on concepts of the partial-propensity and the rejection-based approaches. It factorizes the propensity bounds of reactions and groups factors by common reactant species for selecting next reaction firings. Our algorithm provides favorable computational advantages for simulating of biochemical reaction networks by reducing the cost for selecting the next reaction firing to scale with the number of chemical species and avoiding expensive propensity updates during the simulation...
August 4, 2017: Mathematical Biosciences
L S Kimpton, A Schwab, F Ehlicke, S L Waters, C P Please, J P Whiteley, H M Byrne
We develop a mathematical model to describe the regeneration of a hydrogel inserted into an ex vivo osteochondral explant. Specifically we use partial differential equations to describe the evolution of two populations of cells that migrate from the tissue surrounding the defect, proliferate, and compete for space and resources within the hydrogel. The two cell populations are chondrocytes and cells that infiltrate from the subchondral bone. Model simulations are used to investigate how different seeding strategies and growth factor placement within the hydrogel affect the spatial distribution of both cell types...
July 21, 2017: Mathematical Biosciences
Boutheina Yahyaoui, Mekki Ayadi, Abderrahmane Habbal
The popular 2D Fisher-KPP equation with constant parameters fails to predict activated or inhibited cell-sheet wound closure. Here, we consider the case where the collective diffusion coefficient is time dependent, with a 3-parameter sigmoid profile. The sigmoid is taken S-shaped for the activated assays, and Z-shaped for the inhibited ones. For two activated and two inhibited assays, our model is able to predict with a very good accuracy features of the wound closure like as the time evolution of the wound area and migration rate...
July 19, 2017: Mathematical Biosciences
Haixia Lu, Haitao Song, Huaiping Zhu
In this paper, we establish and study a basic stage-structured model for the population of Hyphantria cunea, a delay differential equation model and a model incorporating the resource and seasonality. By introducing the population reproduction number R0, we show that R0 acts as a threshold parameter for the existence and stability of equilibria. The trivial equilibria of the above models are all globally asymptotically stable when R0<1; the basic model and the delay-differential model have a unique positive equilibrium respectively, and they are both locally asymptotically stable when R0>1; the model with periodic season is uniformly persistent and admits a positive periodic solution if R0>1...
July 19, 2017: Mathematical Biosciences
Rabha W Ibrahim, Hemant K Nashine, Norshaliza Kamaruddin
A biological dynamic system carries engineering properties such as control systems and signal processing (or image processing) addicted to molecular biology at the level of bio-molecular communication networks. Dynamical system features and signal reply functions of cellular signaling pathways are some of the main topics in biological dynamic systems (for example the biological segmentation). In the present paper, we introduce new generalized hybrid time-space dynamical systems of growing bacteria. We impose the approximate analytic solution for the system...
July 17, 2017: Mathematical Biosciences
Milad Qomlaqi, Fariba Bahrami, Maryam Ajami, Jamshid Hajati
BACKGROUND: Chemotherapy is usually known as the main modality for cancer treatment. Nevertheless, most of chronic cancers could not be treated with chemotherapy alone. Immunotherapy is a new modality for cancer treatment that is effective for early stages of cancer and it has fewer side effects compared to chemotherapy, specifically for those types of cancer that are resistant to it. METHOD: This work presents an extended mathematical model to depict interactions between cancerous and adaptive immune system in mouse...
July 14, 2017: Mathematical Biosciences
G Moyano, D Marco, D Knopoff, G Torres, C Turner
In the mutualism established between legumes and soil bacteria known as rhizobia, bacteria from soil infect plants roots and reproduce inside root nodules where they fix atmospheric N2 for plant nutrition, receiving carbohydrates in exchange. Host-plant sanctions against non N2 fixing, cheating bacterial symbionts have been proposed to act in the legume-Rhizobium symbiosis, to preserve the mutualistic relationship. Sanctions include decreased rhizobial survival in nodules occupied by cheating rhizobia. Previously, a simple population model experimentally based showed that the coexistence of fixing and cheating rhizobia strains commonly found in field conditions is possible, and that the inclusion of sanctions leads to the extinction of cheating strains in soil...
July 12, 2017: Mathematical Biosciences
Yaghoub Tadi Beni, M Karimi Zeverdejani, Fahimeh Mehralian
Protein microtubules (MTs) are one of the important intercellular components and have a vital role in the stability and strength of the cells. Due to applied external loads, protein microtubules may be involved buckling phenomenon. Due to impact of protein microtubules in cell reactions, it is important to determine their critical buckling load. Considering nature of protein microtubules, various parameters are effective on microtubules buckling. The small size of microtubules and also lack of uniformity of MTs properties in different directions caused the necessity of accuracy in the analysis of these bio-structure...
July 11, 2017: Mathematical Biosciences
T Eakin
A quantitative measure has been developed for the assessment and skill ordering of target-cued motor control and coordination task performances. It is similar to the classical root mean square error (RMSE) measure but modified with task progress weighting that attenuates with target proximity to its destination and amplifies as data sampling occurrences accumulate prior to task completion. The measure has the same mathematical form whether the task design is of the tracing type or of the tracking type, and thus can be used in cross task type comparisons...
June 9, 2017: Mathematical Biosciences
Ignacio Bajo, Alfonso Ruiz-Herrera
We study a classical model for a population that reproduces and disperses in a landscape of heterogeneous patches. Under symmetrical dispersal, we provide a sufficient condition to ensure the existence of a globally attracting fixed point. This condition is used in order to prove that certain patches with complex dynamics can be stabilized by the combination with stable patches. Specifically, given a patch with complex dynamics, we estimate the necessary number of patches with simple dynamics so that the whole metapopulation has a globally attracting equilibrium...
June 9, 2017: Mathematical Biosciences
Fengying Wei, Lihong Chen
We formulate and investigate the psychological effect of single-species population models in a polluted environment in this paper. For the deterministic single-species population model, the conditions that guarantee the local extinction and persistence in the mean are derived firstly. We then show that, around the pollution-free equilibrium, the stochastic single-species population is weakly persistent in the mean, and is stochastically permanent under some conditions. As a consequence, some numerical simulations demonstrate the efficiency of the main results...
June 2, 2017: Mathematical Biosciences
O Bara, S M Djouadi, J D Day, S Lenhart
Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory response to a pathogenic insult with two therapeutic control inputs which have either a direct pro- or anti-inflammatory effect in the given system. We use Pontryagin's maximum principle and discuss necessary optimality conditions. We consider both an L(1) type objective functional as well as an L(2) type objective...
May 31, 2017: Mathematical Biosciences
Andrew G Smith
Populations often exist, either by choice or by external pressure, in a fragmented way, referred to as a metapopulation. Typically, the dynamics accounted for within metapopulation models are assumed to be static. For example, patch occupancy models often assume that the colonisation and extinction rates do not change, while spatially structured models often assume that the rates of births, deaths and migrations do not depend on time. While some progress has been made when these dynamics are changing deterministically, less is known when the changes are stochastic...
September 2017: Mathematical Biosciences
Michele Caputo, Cesare Cametti
In this note, we present a simple mathematical model of drug delivery through transdermal patches by introducing a memory formalism in the classical Fick diffusion equation based on the fractional derivative. This approach is developed in the case of a medicated adhesive patch placed on the skin to deliver a time released dose of medication through the skin towards the bloodstream.The main resistance to drug transport across the skin resides in the diffusion through its outermost layer (the stratum corneum)...
September 2017: Mathematical Biosciences
T Sari, M J Wade
The complexity of the anaerobic digestion process has motivated the development of complex models, such as the widely used Anaerobic Digestion Model No. 1. However, this complexity makes it intractable to identify the stability profile coupled to the asymptotic behaviour of existing steady-states as a function of conventional chemostat operating parameters (substrate inflow concentration and dilution rate). In a previous study this model was simplified and reduced to its very backbone to describe a three-tiered chlorophenol mineralising food-web, with its stability analysed numerically using consensus values for the various biological parameters of the Monod growth functions...
September 2017: Mathematical Biosciences
Daniel Figueiredo, Manuel A Martins, Madalena Chaves
Qualitative and quantitative modeling frameworks are widely used for analysis of biological regulatory networks, the former giving a preliminary overview of the system's global dynamics and the latter providing more detailed solutions. Another approach is to model biological regulatory networks as hybrid systems, i.e., systems which can display both continuous and discrete dynamic behaviors. Actually, the development of synthetic biology has shown that this is a suitable way to think about biological systems, which can often be constructed as networks with discrete controllers, and present hybrid behaviors...
September 2017: Mathematical Biosciences
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