It is with deep sadness and profound appreciation that we reflect on the life and scientific journey of Professor D. Sc. Svetoslav Marinov Markov, who departed this world at the age of 80. Professor Markov (or Sveti, as we, his colleagues and friends called him) has been an integral part of our lives, and together with our grief, we would like to celebrate his remarkable life and outstanding achievements in science. His career, spanning over five decades, has left an indelible mark by marrying biomathematics with interval analysis. Specifically, he focused his research on modeling biological processes under conditions of uncertainty, employing the tools of interval arithmetic. His work extended beyond ensuring the accuracy of input data, incorporating control over computational errors, showcasing a commitment to precision in scientific inquiry.
Initial statistical analysis of genetic data on the Balkan nations showed the extent of their genetic links to each other. A careful review of the data highlighted an interesting feature: relatively large genetic differences between Greek regions. This is clearly expressed in the cases of Northern Greece, whose population is genetically much closer to the population of Bulgaria than to the population of Central and Southern Greece, whose population is genetically closer to the Albanian population than to the population of Northern Greece. These conclusions are based on numerical values from the results of statistical analysis of genetic data from EUPEDIA. The article also presents several historical testimonies that offer an explanation of the established regional genetic features of the population of today's Greece.
An average person, if asked on the street about the subject of biomathematics, might look a little bewildered: many people, while thinking about biology, in fact think about the respective school subject and just cannot phatom the use of mathematics there. However, even common flowers such as yellow chamomiles or sunflowers show in their middles arrangements described by the Fibonacci numbers, a fact noticed and used since middle ages. That is, studies in mathematical/theoretical biology, or biomathematics, actually need to cover all of biology and, additionally, such fields of mathematics as stochastics, operations research, and computer science, which enables researchers, for example, to shorten experiments' times from decades to mere minutes with the help of appropriate mathematical models implemented on computers. To this end, scientists in many disciplines need to work together in order to create realistic simulations. The series of annual BIOMATH conferences, held regularly since 1995, helps along this way and connects scientists applying "mathematical and computational tools to the study of phenomena in the broad fields of biology, ecology, medicine, biophysics, biochemistry, pharmacokinetics, chemoinformatics, biotechnology, bioengineering, environmental science" from around the world.
In this Master's thesis, we consider the problem of mathematical modelling and computer simulations of neuromuscular activation. We describe the biological and biochemical processes that result in a muscle contraction. For each of them, we derive a mathematical model, established in the literature. In particular, we consider: the Hodgkin-Huxley model of neural transmission; a reaction-diffusion model for the process of neurotransmitter release in the synaptic gap between a nerve and a muscle cell; an ODE system, based on chemical reaction schemes, proposed by Williams, for the process of calcium dynamics inside the muscle cell; Hill’s model for the generation of muscle force, triggered by calcium dynamics. We study the models numerically to illustrate the behaviour of the model solutions and to interpret them from a biological point of view. For the model of calcium dynamics, we also make qualitative analysis and obtain original results for the asymptotic behaviour of the model solutions. Further, we propose a framework for coupling the models, mentioned above, so that we can obtain new integrated multiphysics simulations of the whole process. Our initial motivation for the study is the future application of the proposed approach for modelling neuromuscular diseases. Therefore, the framework we propose is based on the idea of modelling micro-scale processes and studying their effect on the macro-scale muscle action.
Limiting resource is a angular stone of the interactions between species in ecosystems such as competition, prey-predators and food chain systems. In this paper, we propose a planar system as an extension of Lotka-Volterra competition model. This describes two competitive species for a single resource which are affected by intra and inter-specific interference. We give its complete analysis for the existence and local stability of all equlibria and some conditions of global stability. The model exhibits a rich set of behaviors with a multiplicity of coexistence equilibria, bi-stability, tri-stability and occurrence of global stability of the exclusion of one species and the coexistence equilibrium. The asymptotic behavior and the number of coexistence equilibria are shown by a saddle-node bifurcation of the level of resource under conditions on competitive effects relatively to associated growth rate per unit of resource. Moreover, we determine the competition outcome in the situations of Balanced and Unbalanced intra-inter species competition effects. Finally, we illustrate results by numerical simulations.
The Kies probability model [1] was proposed as an alternative to the extended Weibull models as it provides a more efficient fit to some real-life data sets in comparison to the aforementioned models. In the present article, it has first been shown that the dynamic Kies model is generated by a specific framework of chemical reaction networks. We will also discuss some properties of the family by Kies. Precise bounds for the Hausdorff distance between the Heaviside step function and the considered sigmoid are also given. We also define a hypothetical family of generalized Kies CDF. Some computational examples using CAS Mathematica are presented.
Numerical modeling is an important tool when studying various natural processes and phenomena. Fractional diffusion can be used for modeling many processes in biology, for example in silico experiments in molecular biology and medicine design, protein diffusion within cells, complex media geometry, etc. The problem is usually reduced to a system of linear algebraic equations and in many cases this system has a dense coefficient matrix. Numerically solving such problems with the traditional LU factorization is a computationally expensive endeavour - $O(n^3)$. In this paper we explore the use of a hierarchical compression method based on Hierarchical Semi-Separable compression and ULV-like factorization from the STRUctured Matrices PACKage (STRUMPACK) software library for a flow around airfoils problem discretized with Boundary Element Method and fractional diffusion problem discretized with the Finite Element Method. The HSS based method promises better overall computational complexity of $O(r^2n)$ for problems with suitable structure - low rank off-diagonal blocks. Here $r$ is the maximum rank of the off-diagonal blocks. We present analysis of the performance and accuracy of the HSS based method and compare it with the state of the art direct LU factorization solvers. This paper is based on the PhD thesis Composite Numerical Methods and Scalable Tile Algorithms of the author defended on 17.05.2022 in the Institute of Information and Communication Technologies at the Bulgarian Academy of Sciences.
Solid waste management has continued to be an increasing challenge worldwide and the situation has become worse in urban areas of developing countries. The rapid urban population growth, mainly due to high immigration and birth rates, has led to large amounts of solid waste, making it difficult for authorities to effectively manage the accumulated waste. Existing mathematical models of solid waste accumulation consider solid waste management by an external effort and do not address the contribution of the population in the management process. In this study, a mathematical model of solid waste accumulation is developed and analysed incorporating parameters for human immigration and solid waste recycling by particular population age groups. The solid waste is considered to be of two categories: biodegradable and non-biodegradable. Existence of equilibrium points is established and their stability analysed. Numerical simulations are done using MATLAB and Maple. Results show that solid waste increases with increasing human population and thus a solid waste free environment cannot be achieved. Sensitivity analysis suggests that improving the biodegradability of solid waste coupled with aiding solid waste decay and recycling reduces the final size of solid waste.
Schistosomiasis, a health challenge in many communities, is prevalent as the rate of infection is one in every thirty individuals. In this work, a deterministic model for schistosomiasis transmission dynamics is studied. The stability properties of equilibrium states, disease-free and endemic equilibria are established in terms of the basic reproduction number, R_0. The sensitivity analysis of R_0 with respect to the model parameters is carried out using Partial rank correlation coefficients (PRCCs). The optimal control model with control measures, public health education, diagnosis and treatment and snail control, is formulated and its optimality system is derived using Pontragyin's maximum Principle. Simulation results showed that simultaneous implementation of public health education, diagnosis and treatment and snail control will reduce the burden of the schistosomiasis infection in the population. However due to toxicity of some snail controls to other aquatic bodies and difficulty to single out the chemical control that will focus only on the snail population even though snails are special food in Africa, it is preferable to implement public health education and diagnosis and treatment simultaneously in order to eradicate schistosomiasis transmission in the affected regions.
Following the ideas given in [13]-[15], in this article we study a hypothetical piecewise smooth modified Schnute growth function. Some numerical examples, using CAS MATHEMATICA are also given.
This is a brief report on the BIOMATH-2021 International Conference and School for Young Scientists held in Pretoria, South Africa.
In Memory of Prof. Maria Mladenova: Recollections of the joint activities and friendship with Prof. Maria Mladenova, DSc.
The project "Stochastics and Simulations Models in the Medicine, Social Sciences and Dynamical Systems" is focused on the stochastics models and their application in the field of medicine, insurance, astrophysics and some simulation models applicable in social sciences and thermohydraulic processes. There are six work packages included in the research. The introduced models had been adapted to real data by three PhD students, two post-doctoral students and four Bulgarian scientists which are leaders in the field of mathematical modelling. The participants' research results are published in eight scientific papers with impact factor and thirty-six papers with impact rang. The results are approbated in more than twenty prestigious international conferences. As a good result of the participation three PhD scientific degrees and two scientific positions have been acquired.
In the present work we give an overview and implementation of an algorithm for building and integrating dynamic systems from reaction networks. Reaction networks have their roots in chemical reaction network theory, but their nature is general enough that they can be applied in many fields to model complex interactions. Our aim is to provide a simple to use program that allows for quick prototyping of dynamic models based on a system of reactions. After introducing the concept of a reaction and a reaction network in a general way, not necessarily connected to chemistry, we outlay the algorithm for building its associated system of ODEs. Finally, we give a few example usages where we examine a range of growth-decay models in the context of reaction networks.
This work brings together two recently discussed topics: mathematical modeling of a bioreactor and working with derivatives of non-integer order. Generally, it turns out that it is reasonable to replace the integer order derivatives in some of the already well known mathematical models describing bioprocesses with fractional order ones. However, the specific structure of such type of derivatives makes the study of the properties of the models a real challenge. This work contains primary results for modeling of a bioreactor with appropriately selected numerical approximations. Different scenarios are taken into consideration: starting from the simplest one - without mortality and then complicating by adding nonzero mortality term. In the classical case the solution of the system of differential equations describing the process has a specific behaviour in terms of monotonicity. Therefore, the focus of the further examinations is to find out whether it is possible to generalize the model into a fractional order one such that the key properties considering monotonicity still hold. The results show that the latter requires certain dependencies between the orders of the derivatives in the mathematical model. The hypothesis is based on two types of experiments which are described in detail. Lotka-Volterra and Monod specific growth rate are used in the mathematical model. The paper contains figures which illustrate the results from different numerical computations performed via Wolfram Mathematica software.
The cumulative distribution function (cdf) corresponding to the 'four parameter extended type I half--logistic modified Weibull (TIHLMW) distribution'' is ...
Roumen Petrov Maleev was born on August 17, 1943 in the city of Samokov, Bulgaria. He graduated from the Department of Mathematics at Bucurest University in 1967. In 1970 he was appointed as Assistant in the Faculty of Mathematics and Mechanics of Sofia University "St. Kl. Ohridski", where he became Associate Professor in 1983 and Full Professor in 2006.R. Maleev specialized in Moscow State University in the scholarly year 1971/72 and in Warsaw University in 1982 (February--April). He defended his PhD in Sofia University "St. Kl. Ohridski" in 1975 and his DSci dissertation in 1996 (also in Sofia University "St. Kl Ohridski"). During 1989-1995 he served as Deputy Dean of the Faculty of Mathematics and Informatics of at Sofia University "St. Kl. Ohridski''. He has been Head of the Department of Mathematical Analysis of the Faculty (1998--2000) and member of the Specialized Scientific Council on Mathematics and Mechanics (1995--2004).Maleev delivered lecture courses as Visiting Professor in South Florida University in the summer term of 1991 and in the Athens University in May-June 1997. He also presented numerous lectures at various international conferences worldwide.The scientific interests of Prof. Maleev were in the fields of Geometry of Banach spaces, Functional Spaces and Operators, Variational Analysis, Mathematical Analysis, Education in Mathematics and Informatics, Numerical Analysis.
I first met Blagovest Sendov in 1963 as a student in mathematics at the Faculty of Physics and Mathematics atВ Sofia University. His first lecture was devoted to Mathematical modeling. On some real life situations Prof. Sendov revealed to us the philosophy of science. Prof. Sendov's ``philosophy'' included a deep understanding of the mechanisms of the underlying real processes, the mathematical description of these processes using contemporary mathematical theories and the solution of the formulated mathematical problems using advanced numerical and computational tools. Prof. Sendov possessed an enormous ability to formulate difficult tasks and problems that need years of efforts to be resolved. At the weekly seminar of ``Mathematical modeling''he used to pose such difficult problems and to make us young collaborators enthusiastic about working on them. He never pressed anybody of us to work on something particular, but he waited that everybody chooses a theme of interest by himself.
The Euro-American Consortium for Promotion of the Application of Mathematics in Technical and Natural Sciences was founded in 2008 as a non-governmental non-profit organization in order to foster the scientific activity and informal international exchange. Since then a main tool to realize this intention and idea became an annual conference called AMiTaNS.
