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Mathematical Biosciences

B W Kooi, J C Poggiale
Two predator-prey model formulations are studied: for the classical Rosenzweig-MacArthur (RM) model and the Mass Balance (MB) chemostat model. When the growth and loss rate of the predator is much smaller than that of the prey these models are slow-fast systems leading mathematically to singular perturbation problem. In contradiction to the RM-model, the resource for the prey are modelled explicitly in the MB-model but this comes with additional parameters. These parameter values are chosen such that the two models become easy to compare...
April 20, 2018: Mathematical Biosciences
Bruce Pell, Tin Phan, Erica M Rutter, Gerardo Chowell, Yang Kuang
The first few disease generations of an infectious disease outbreak is the most critical phase to implement control interventions. The lack of accurate data and information during the early transmission phase hinders the application of complex compartmental models to make predictions and forecasts about important epidemic quantities. Thus, simpler models are often times better tools to understand the early dynamics of an outbreak particularly in the context of limited data. In this paper we mechanistically derive and fit a family of logistic models to spatial-temporal data of the 1905 plague epidemic in Bombay, India...
April 16, 2018: Mathematical Biosciences
R C Elliott, D L Smith, D Echodu
Using an established Ross/Macdonald model variant for mosquito-born parasite transmission, we extend the formalism to simply incorporate time-dependent control measures. In particular, two interventions are considered, mass drug administration (MDA) and indoor residual spraying (IRS), whose individual intensities during their respective campaigns are set to the same intervention-reduced reproductive number R0 . The impacts of these interventions, measured as each campaign's ability over time to reduce infections in a community, are found based on the transmission setting, coverage, and their associated durations...
April 12, 2018: Mathematical Biosciences
Ka Yin Leung, Pieter Trapman, Tom Britton
What role do asymptomatically infected individuals play in the transmission dynamics? There are many diseases, such as norovirus and influenza, where some infected hosts show symptoms of the disease while others are asymptomatically infected, i.e. do not show any symptoms. The current paper considers a class of epidemic models following an SEIR (Susceptible  →  Exposed  →  Infectious  →  Recovered) structure that allows for both symptomatic and asymptomatic cases. The following question is addressed: what fraction ρ of those individuals getting infected are infected by symptomatic (asymptomatic) cases? This is a more complicated question than the related question for the beginning of the epidemic: what fraction of the expected number of secondary cases of a typical newly infected individual, i...
April 11, 2018: Mathematical Biosciences
Elliot J Carr, Giuseppe Pontrelli
We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the external surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules...
April 11, 2018: Mathematical Biosciences
N S Akbar, D Tripathi, Z H Khan, O Anwar Bég
In this paper, we present an analytical study of pressure-driven flow of micropolar non-Newtonian physiological fluids through a channel comprising two parallel oscillating walls. The cilia are arranged at equal intervals and protrude normally from both walls of the infinitely long channel. A metachronal wave is generated due to natural beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow. Appropriate expressions are presented for deformation via longitudinal and transverse velocity components induced by the ciliary beating phenomenon with cilia assumed to follow elliptic trajectories...
April 6, 2018: Mathematical Biosciences
Arvind Kumar Sinha, Nishant Namdev, Awanish Kumar
Leishmania donovani is the primary cause of a fatal disease visceral leishmaniasis (VL) in East Africa and in the Indian subcontinent. Human beings are the only known reservoir of L. donovani and due to the emergence and the spread of drug resistance control for this disease is become worse. Therefore, identification of novel drug target is very important to develop new drug and combat drug resistance issue. Experimental determination of target is costly and time-consuming, hence it is necessary to first identify the efficient target with the accurate mathematical method and then further go for in vitro/in vivo study...
April 5, 2018: Mathematical Biosciences
Guoqing Liu, Qin Ma, Ying Xu
Nucleoid-associated proteins (NAPs) play important roles in both chromosome packaging and gene regulation in bacteria. The underlying mechanisms, however, remain elusive particularly for how NAPs contribute to chromosome packaging. We report here a characterization of the binding sites for several major NAPs in E. coli, namely H-NS, IHF, Fis, Dps and a non-NAP protein, FNR, in terms of the physical properties of their binding DNA. Our study shows that (i) as compared with flanking regions, the binding sites for IHF, Fis and FNR tend to have high intrinsic curvature, while no characterized pattern of intrinsic curvature distribution around those of H-NS and Dps; (ii) all the binding sites analyzed in this study except those of H-NS are characterized by high structural flexibility; (iii) the intrinsic curvature and flexibility at the binding sites for Fis and IHF are found to be coupled with the sequence specificity required in their binding, while the physical properties of the binding regions for both Dps and FNR are independent of sequence specificity...
April 3, 2018: Mathematical Biosciences
M Marvá, F San Segundo, U D Matemáticas
In this work we analyze the interplay between general age structured density-dependent fertility functions and age classes dispersal in a patchy environment. As novelties, i) the fertility function depends on age classes (instead of on the total population size) and ii) dispersal patterns are also allowed to be different for individuals belonging to different age classes. Our results highlight the interplay between the shape of the age structured density-dependent fertility function and the age classes dispersal patterns...
March 30, 2018: Mathematical Biosciences
Zhaohua Wu, Yi Wang, Xiaoli Zhou, Tiejun Zhou
As one of the Globally Important Agricultural Heritage Systems (GIAHS), rice field composite farming is an ecological measure in rice production, which can reduce the amount of chemical fertilizers, pesticides and herbicides. This research studies the interaction among rice, weed, inorganic fertilizer and herbivore in a composite farming paddy ecosystem. We develop a differential equation model to analyze the relations and interactions among those components. Results show the existence of an equilibrium for paddy and weed extinction, one or two equilibria for rice extinction, an equilibrium for weed extinction, and an equilibrium for rice and weed coexistence...
March 29, 2018: Mathematical Biosciences
Gabriel Andreguetto Maciel, Renato Mendes Coutinho, Roberto André Kraenkel
As environments become increasingly degraded, mainly due to human activities, species are often subject to isolated habitats surrounded by unfavorable regions. Since the pioneering work by [25] mathematical models have provided useful insights into the population persistence in such cases. Most of these models, however, neglect the sex structure of populations and the differences between males and females. In this work we investigate, through a reaction-diffusion system, the dynamics of a sex-structured population in a single semipermeable patch...
March 29, 2018: Mathematical Biosciences
Edoardo Beretta, Vincenzo Capasso, Dario G Garao
In this paper a conceptual mathematical model of malaria transmission proposed in a previous paper has been analyzed in a deeper detail. Among its key epidemiological features of this model, two-age-classes (child and adult) and asymptomatic carriers have been included. The extra mortality of mosquitoes due to the use of long-lasting treated mosquito nets (LLINs) and Indoor Residual Spraying (IRS) has been included too. By taking advantage of the natural double time scale of the parasite and the human populations, it has been possible to provide interesting threshold results...
March 28, 2018: Mathematical Biosciences
Pierre Magal, Ousmane Seydi, Glenn Webb
A model of an epidemic outbreak incorporating multiple subgroups of susceptible and infected individuals is investigated. The asymptotic behavior of the model is analyzed and it is proved that the infected classes all converge to 0. A computational algorithm is developed for the cumulative final size of infected individuals over the course of the epidemic. The results are applied to the SARS epidemic in Singapore in 2003, where it is shown that the two-peak evolution of the infected population can be attributed to a two-group formulation of transmission...
March 28, 2018: Mathematical Biosciences
Elisenda Feliu, Daniele Cappelletti, Carsten Wiuf
We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we introduce a graph, called a reaction graph, that has one edge for each reaction but potentially multiple nodes for each complex. A special class of steady states, called node balanced steady states, is naturally associated with such a reaction graph. We show that complex and detailed balanced steady states are special cases of node balanced steady states by choosing appropriate reaction graphs...
March 27, 2018: Mathematical Biosciences
W Duncan, J Best, M Golubitsky, H F Nijhout, M Reed
We have shown previously that different homeostatic mechanisms in biochemistry create input-output curves with a "chair" shape. At equilibrium, for intermediate values of a parameter (often an input), a variable, Z changes very little (the homeostatic plateau), but for low and high values of the parameter, Z changes rapidly (escape from homeostasis). In all cases previously studied the steady state was stable for each value of the input parameter. Here we show that, for the feedback inhibition motif, stability may be lost through a Hopf bifurcation on the homeostatic plateau and then regained by another Hopf bifurcation...
March 26, 2018: Mathematical Biosciences
Irene Balelli, Vuk Milišić, Gilles Wainrib
Within the germinal center in follicles, B-cells proliferate, mutate and differentiate, while being submitted to a powerful selection: a micro-evolutionary mechanism at the heart of adaptive immunity. A new foreign pathogen is confronted to our immune system, the mutation mechanism that allows B-cells to adapt to it is called somatic hypermutation: a programmed process of mutation affecting B-cell receptors at extremely high rate. By considering random walks on graphs, we introduce and analyze a simplified mathematical model in order to understand this extremely efficient learning process...
March 24, 2018: Mathematical Biosciences
Rangoli Goyal, Rama Bhargava
The study of temperature profiles and heat transport within the human body when subjected to electromagnetic waves is crucial for development and improvement of radiofrequency hyperthermia treatments. These treatments being minimally invasive can be a better alternative over surgery and chemotherapy for treatment of cancer. Nanoparticle-mediated hyperthermia for cancer therapy is a growing area of cancer nanomedicine because of the potential for localized and targeted destruction of cancer cells. This treatment is dependent on many factors, including thermal conductivity of bio-nanofluid, volume fraction of nanoparticles,excitation wavelength and power and metabolic heat generation...
March 23, 2018: Mathematical Biosciences
Belinda Barnes, Kathryn Glass
Outbreaks of highly pathogenic avian influenza (HPAI) in commercial poultry flocks are rare but highly disruptive to the industry. There is evidence that low pathogenic avian influenza (LPAI) can transfer from wild birds to domestic flocks, where it may mutate to HPAI, and the industry is concerned that an increasing demand for free-range produce may affect the risk of LPAI and HPAI outbreaks. In this paper we focus on LPAI introduction and establishment, and formulate a branching process model to compare risk between sectors and their contribution to overall industry-level risk...
March 23, 2018: Mathematical Biosciences
Bo Wang, Qianqian Qi
In the reality, the lake system will be disturbed by stochastic factors including the external and internal factors. By adding the additive noise and the multiplicative noise to the right-hand sides of the model equation, the additive stochastic model and the multiplicative stochastic model are established respectively in order to reduce model errors induced by the absence of some physical processes. For both the two kinds of stochastic ecosystems, the authors studied the bifurcation characteristics with the FPK equation and the Lyapunov exponent method based on the Stratonovich-Khasminiskii stochastic average principle...
March 20, 2018: Mathematical Biosciences
H Ashraf, A M Siddiqui, M A Rana
The present prospective theoretical analysis concerns with the peristalsis-cilia induced transport of a developing embryo from ampulla to intramural, in the human fallopian tube. A model of peristalsis-cilia induced flow of the Johnson-Segalman fluid within fallopian tubal fluid in a finite two dimensional narrow tube is developed. We solved highly non-linear PDE emerging from the modeling of proposed model using perturbation method. The series expressions for flow variables like axial and radial velocities, pressure gradient, stream function, volume flow rate and time mean volume flow rate are derived...
March 20, 2018: Mathematical Biosciences
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