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Mathematical Biosciences

Omprakash Singh Sisodiya, O P Misra, Joydip Dhar
Waterborne diseases have a tremendous influence on human life. The contaminated drinking water causes water-borne disease like cholera. Pulse vaccination is an important and effective strategy for the elimination of infectious diseases. A waterborne disease like cholera can also be controlled by using impulse technique. In this paper, we have proposed a delayed SEIRB epidemic model with impulsive vaccination and disinfection. We have studied the pulse vaccination strategy and sanitation to control the cholera disease...
February 6, 2018: Mathematical Biosciences
H V Kulkarni, K P Patil
Micro-array experiments are important fields in molecular biology where zero values mixed with a continuous outcome are frequently encountered leading to a mixed distribution with a clump at zero. Comparison of two mixed populations, e.g. of a control and a treated group; of two groups with different types of cancer, to name a few, are often encountered in these contexts. Fairly skewed distribution of the continuous part coupled with small sample sizes are issues of main concern to be attended for the quality of inference in such situations while popularly used nonparametric methods rely on asymptotic distribution of the underlying test statistics which are valid only under large sample sizes...
February 2, 2018: Mathematical Biosciences
Michio Iwata, Atsuko Miyawaki-Kuwakado, Erika Yoshida, Soichiro Komori, Fumihide Shiraishi
In a mathematical model, estimation of parameters from time-series data of metabolic concentrations in cells is a challenging task. However, it seems that a promising approach for such estimation has not yet been established. Biochemical Systems Theory (BST) is a powerful methodology to construct a power-law type model for a given metabolic reaction system and to then characterize it efficiently. In this paper, we discuss the use of an S-system root-finding method (S-system method) to estimate parameters from time-series data of metabolite concentrations...
February 1, 2018: Mathematical Biosciences
Tapan Sood, Somnath Roy, Manabendra Pathak
The present work reports numerical simulations of blood flow patterns and wall shear stress (WSS) distributions in stenotic arteries, modelled as straight tubes. Inflow waveforms have been generated for different pulse rates considering constant volumetric flow during each pulsation cycle and a two-element windkessel model has been used to specify the outlet pressure. It is noticed that the non-Newtonian shear thinning rheology of blood produces more accurate and realistic predictions of the flow field as compared to the Newtonian assumption...
January 30, 2018: Mathematical Biosciences
Vladimir P Zhdanov
Cell proliferation is often considered to occur via front propagation with constant velocity. This scenario proposed by Fisher, Kolmogorov, Petrovsky, and Piskunov is based on the solution of the corresponding mean-field reaction-diffusion equations and does not take into account that due to adhesion the cells have tendency to aggregate and that the rate of cell division may depend on the cell-cell communication. Herein, the author presents extensive Monte Carlo simulations taking both these factors into account and illustrating that the former factor can dramatically modify the spatio-temporal kinetics of cell proliferation...
January 29, 2018: Mathematical Biosciences
Kimberly Fessel, Mark H Holmes
A nonlinear three-dimensional model for the amplification of a wave in the cochlea is analyzed. Using the long-slender geometry of the cochlea, and the relatively high frequencies in the hearing spectrum, an asymptotic approximation of the solution is derived for linear, but spatially inhomogeneous, amplification. From this, a nonlinear WKB approximation is constructed for the nonlinear problem, and this is used to derive an efficient numerical method for solving the amplification problem. The advantage of this approach is that the very short waves needed to resolve the wave do not need to calculated as they are represented in the asymptotic solution...
January 27, 2018: Mathematical Biosciences
Josep-Lluis Usó-Doménech, Josué-Antonio Nescolarde-Selva, Miguel Lloret-Climent, Lucía González-Franco
The mathematical submodel ULEX is used to study the dynamic behavior of the green, floral and woody biomass of the main pyrophite shrub species, the gorse (Ulex parviflorus Pourret), and its relationship with other shrub species, typical of a Mediterranean ecosystem. The focus are the ecological conditions of post-fire stage growth, and its efficacy as a protective cover against erosion processes in the short, medium and long term, both in normal conditions and at the limits of desertification conditions. The model sets a target to observe the behaviour and to anticipate and consequently intervene with adequate protection, restoration and management measures...
January 21, 2018: Mathematical Biosciences
Cody Palmer, Erin Landguth, Emily Stone, Tammi Johnson
In this paper, we describe the dynamics of a vector-borne relapsing disease, such as tick-borne relapsing fever, using the methods of compartmental models. After some motivation and model description we provide a proof of a conjectured general form of the reproductive ratio R0, which is the average number of new infections produced by a single infected individual. A disease free equilibrium undergoes a bifurcation at R0=1 and we show that for an arbitrary number of relapses it is a transcritical bifurcation with a single branch of endemic equilibria that is locally asymptotically stable for R0 sufficiently close to 1...
January 12, 2018: Mathematical Biosciences
Wilson I Barredo, Christopher C Bernido, M Victoria Carpio-Bernido, Jinky B Bornales
To model non-Markovian fluctuations arising in biomolecular transport, we introduce a stochastic process with memory where Brownian motion is modulated sinusoidally. The probability density function and moments of this non-Markovian process are evaluated analytically as Hida stochastic functional integrals. Comparison of graphs of computed variance vis-á -vis empirical data for protein diffusion coefficients closely match with both exhibiting emergent superdiffusive then subdiffusive behavior for longer proteins...
January 11, 2018: Mathematical Biosciences
Jinxian Li, Weiqiang Li, Zhen Jin
The spread of an infectious disease may depend on the structure of the network. To study the influence of the structure parameters of the network on the spread of the epidemic, we need to put these parameters into the epidemic model. The method of moment closure introduces structure parameters into the epidemic model. In this paper, we present a new moment closure epidemic model based on the approximation of third-order motifs in networks. The order of a motif defined in this paper is determined by the number of the edges in the motif, rather than by the number of nodes in the motif as defined in the literature...
January 9, 2018: Mathematical Biosciences
A Veprauskas
Periodical semelparous insects such as cicadas and May beetles exhibit synchronization in age classes such that only one age class is present at any point of time. This leads to outbreaks of adults as they all reach maturity around the same time. Discrete-time models of semelparous species have shown that this type of synchronous cycling can occur as a result of greater between-class competition relative to within-class competition. However, relatively few studies have examined continuous-time models of semelparous species...
January 9, 2018: Mathematical Biosciences
Morten Andersen, Jeppe Kari, Kim Borch, Peter Westh
Kinetic studies of homogeneous enzyme reactions where both the substrate and enzyme are soluble have been well described by the Michaelis-Menten (MM) equation for more than a century. However, many reactions are taking place at the interface of a solid substrate and enzyme in solution. Such heterogeneous reactions are abundant both in vivo and in industrial application of enzymes but it is not clear whether traditional enzyme kinetic theory developed for homogeneous catalysis can be applied. Since the molar concentration of surface accessible sites (attack-sites) often is unknown for a solid substrate it is difficult to assess whether the requirement of the MM equation is met...
January 9, 2018: Mathematical Biosciences
P D N Srinivasu, Simon Derkee Zawka
This paper presents bio-economics of a renewable resources in a seasonally changing environment in which the resource exploitation is subjected to restrictions on harvesting effort. The dynamics of the resource is assumed to be governed by the logistic equation. Seasonality is incorporated into the system by choosing the coefficients in the growth equation to be periodic functions with the same period. A linear optimal control problem involving binding constraints on the control variable has been considered...
January 2, 2018: Mathematical Biosciences
Chayu Yang, Jin Wang
The intrinsic dynamics of bacteria often play an important role in the transmission and spread of waterborne infectious diseases. In this paper, we construct mathematical models for waterborne infections and analyze two types of nontrivial bacterial dynamics: logistic growth, and growth with Allee effects. For the model with logistic growth, we find that regular threshold dynamics take place, and the basic reproduction number can be used to characterize disease extinction and persistence. In contrast, the model with Allee effects exhibits much more complex dynamics, including the existence of multiple endemic equilibria and the presence of backward bifurcation and forward hysteresis...
December 29, 2017: Mathematical Biosciences
Michael T Meehan, Daniel G Cocks, James M Trauer, Emma S McBryde
We introduce and analyze coupled, multi-strain epidemic models designed to simulate the emergence and dissemination of mutant (e.g. drug-resistant) pathogen strains. In particular, we investigate the mathematical and biological properties of a general class of multi-strain epidemic models in which the infectious compartments of each strain are coupled together in a general manner. We derive explicit expressions for the basic reproduction number of each strain and highlight their importance in regulating the system dynamics (e...
December 27, 2017: Mathematical Biosciences
Hao Wang, Silogini Thanarajah, Philippe Gaudreau
Refuge can greatly influence predator-prey dynamics by movements between the interior and the exterior of a refuge. The presence of refuge for prey decreases predation risk and can have important impacts on the sustainability of a predator-prey system. The principal purpose of this paper is to formulate and analyze a refuge-mediated predator-prey model when the refuge is available to protect a portion of prey from predation. We study the effect of the refuge size on the biomass ratio and extend our refuge model to incorporate fishing and predator migration separately...
December 27, 2017: Mathematical Biosciences
Can Chen, Nyuk Sian Chong, Robert Smith
Mass-media reports on an epidemic or pandemic have the potential to modify human behaviour and affect social attitudes. Here we construct a Filippov model to evaluate the effects of media coverage and quarantine on the transmission dynamics of influenza. We first choose a piecewise smooth incidence rate to represent media reports being triggered once the number of infected individuals exceeds a certain critical level [Formula: see text] . Further, if the number of infected cases increases and exceeds another larger threshold value [Formula: see text] ( [Formula: see text] ), we consider that the incidence rate tends to a saturation level due to the protection measures taken by individuals; meanwhile, we begin to quarantine susceptible individuals when the number of susceptible individuals is larger than a threshold value Sc...
December 19, 2017: Mathematical Biosciences
Célia A Dos Reis, Helenice de O Florentino, Diego Cólon, Suélia R Fleury Rosa, Daniela R Cantane
Dengue fever, chikungunya and zika are caused by different viruses and mainly transmitted by Aedes aegypti mosquitoes. These diseases have received special attention of public health officials due to the large number of infected people in tropical and subtropical countries and the possible sequels that those diseases can cause. In severe cases, the infection can have devastating effects, affecting the central nervous system, muscles, brain and respiratory system, often resulting in death. Vaccines against these diseases are still under development and, therefore, current studies are focused on the treatment of diseases and vector (mosquito) control...
December 15, 2017: Mathematical Biosciences
Ezekiel Dangbé, Damakoa Irépran, Antoine Perasso, David Békollé
Cholera is a bacterial disease, its spread is strongly influenced by environmental factors and some socio-economic factors such as hygiene standards and nutrition of the population. This paper is devoted to the modelling of the impact of climatic factors and human behaviour on the spread of cholera. The mathematical modelling incorporates the direct transmission and the indirect transmission due to environmental knowledge. Taking into account the effect of the intra-annual variation of climatic factors on the transmission of cholera, a non-autonomous ordinary differential equations is proposed to describe the dynamics of the transmission of cholera...
December 12, 2017: Mathematical Biosciences
Steinar Engen, Aline Magdalena Lee, Bernt-Erik Sæther
We analyze a spatial age-structured model with density regulation, age specific dispersal, stochasticity in vital rates and proportional harvesting. We include two age classes, juveniles and adults, where juveniles are subject to logistic density dependence. There are environmental stochastic effects with arbitrary spatial scales on all birth and death rates, and individuals of both age classes are subject to density independent dispersal with given rates and specified distributions of dispersal distances. We show how to simulate the joint density fields of the age classes and derive results for the spatial scales of all spatial autocovariance functions for densities...
December 11, 2017: Mathematical Biosciences
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