Biomath最新文献

{"title":"Optimal control analysis of combined chemotherapy-immunotherapy treatment regimens in a PKPD cancer evolution model","authors":"Anuraag Bukkuri","doi":"10.11145/j.biomath.2020.02.137","DOIUrl":"https://doi.org/10.11145/j.biomath.2020.02.137","url":null,"abstract":"The author constructs a mathematical model capturing tumor-immune dynamics, incorporating the evolution of drug resistance, pharmacokinetics and pharmacodynamics of administered drugs, and immunotherapy possibilities. Numerical simulations are performed to analyze the model under a variety of treatment possibilities. A sensitivity analysis is performed to determine the parameters contributing the most to the variance in effector cell, resistant, and sensitive tumor cell populations. Then, a detailed optimal control analysis is performed, along with a numerical simulation of optimal treatment profiles for a hypothetical patient.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46483947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A rewinding model for replicons with DNA-links","authors":"A. A. Mohamad, T. Yashiro","doi":"10.11145/j.biomath.2020.01.047","DOIUrl":"https://doi.org/10.11145/j.biomath.2020.01.047","url":null,"abstract":"A double strand DNA has a double helical structure and it is modeled by a thin long twisted ribbon fixed at the both ends. A DNA-link is a topological model of such a DNA segment in the nuclear of a eukaryotic cell. In the cell cycle, the DNA is replicated and distributed into new cells. The complicated replication process follows the semi-conservative scheme in which each backbone string is preserved in the replicated DNA. This is interpreted in terms of splitting process of the DNA-link. In order to split the DNA-link, unknotting operations are required. This paper presents a recursive unknotting operations, which efficiently reduce the number of twistings.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46613867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enumerative numerical solution for optimal control using treatment and vaccination for an SIS epidemic model","authors":"Vianney Mbatumutima, C. Thron, L. Todjihounde","doi":"10.11145/j.biomath.2019.12.137","DOIUrl":"https://doi.org/10.11145/j.biomath.2019.12.137","url":null,"abstract":"Optimal control problems in mathematical epidemiology are often solved by Hamiltonian methods. However, these methods require conditions on the problem to guarantee that they give global solutions. Because of the improved computational power of modern computers, numerical approximate solutions that systematically try a large number of possibilities have become practical. In this paper we give an efficientimplementation of an enumerative numerical solution method for an optimal control problem, which applies to cases where standard methods cannot guarantee global optimality. We demonstrate the method on a model where vaccination and treatment are used to control the level of prevalence of an infectious disease. We describe the solution algorithm in detail, and verify the method with simulations. We verify that the enumerative numerical method produces solutions that are locallyoptimal.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47698528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical analysis of toxin-phytoplankton-fish model with self-diffusion and cross-diffusion","authors":"Hamidou Ouedraogo, Wendkouni Ouedraogo, B. Sangaré","doi":"10.11145/j.biomath.2019.11.237","DOIUrl":"https://doi.org/10.11145/j.biomath.2019.11.237","url":null,"abstract":"In this paper  we propose a nonlinear reaction-diffusion system  describing the interaction between toxin-producing phytoplankton and fish population. We analyze the effect of self- and cross-diffusion on the dynamics of the system. The existence, uniqueness and uniform boundedness of solutions are established in the positive octant. The system is analyzed for various interesting dynamical behaviors which include boundedness, persistence, local stability, global stability around each equilibria based on some conditions on self-  and cross-diffusion coefficients.  The analytical findings are verified by numerical simulation.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41908613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal control strategies for a class of vector borne diseases, exemplified by a toy model for malaria","authors":"S. Anita, E. Beretta, V. Capasso","doi":"10.11145/j.biomath.2019.09.157","DOIUrl":"https://doi.org/10.11145/j.biomath.2019.09.157","url":null,"abstract":"This paper contains a unified review of a set of previous papers by the same authors concerning the mathematical modelling and control of malaria epidemics. The presentation moves from a conceptual mathematical model of malaria transmission in an homogeneous population. Among the key epidemiological features of this model, two-age-classes (child and adult) and asymptomatic carriers have been included. As possible control measures, the extra mortality of mosquitoes due to the use of long-lasting treated mosquito nets (LLINs) and Indoor Residual Spraying (IRS) have been included. 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. In particular, key parameters have been identified such that below a threshold level, built on these parameters, the epidemic tends to extinction, while above another threshold level it tends to a nontrivial endemic state. The above model has motivated further analysis when a spatial structure of the relevant populations is added. Inspired by the above, additional model reductions have been introduced, which make the resulting reaction-diffusion system mathematically affordable. Only the dynamics of the infected mosquitoes and of the infected humans has been included, so that a two-component reaction-diffusion system is finally taken. The spread of the disease is controlled by three actions (controls)  implemented in a subdomain of the habitat: killing mosquitoes, treating the infected humans and reducing the contact rate mosquitoes-humans.To start with, the problem of the eradicability of the disease is considered, while the cost of the controls is ignored. We prove that it is possible to decrease exponentially both the human and the vector infective population everywhere in the relevant habitat by acting only in a suitable subdomain. Later the regional control problem of reducing the total cost of the damages produced by the disease, of the controls and of the intervention in a certain subdomain is treated for the finite time horizon case. In order to take the logistic structure of the habitat into account the level set method is used as a key ingredient for describing the subregion of intervention. Here this subregion has been better characterized by both area and perimeter. The authors wish to stress that the target of this paper mainly is to attract the attention of the public health authorities towards an effective and affordable practice of implementation of possible control strategies.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41313427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Model-based Control Strategies for Anaerobic Digestion Processes","authors":"N. Dimitrova, M. Krastanov","doi":"10.11145/J.BIOMATH.2019.07.127","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2019.07.127","url":null,"abstract":"In this paper we consider a four-dimensional bioreactor model, describing an anaerobic wastewater treatment with methane production. Different control strategies for stabilizing the dynamics are presented and discussed. A general and practice-oriented bounded open-loop control is proposed, aimed to steer the model solutions towards an a priori given set in thephase plane.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43920792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"One and two-phase cell cycle models","authors":"Katarzyna Pichór, R. Rudnicki","doi":"10.11145/J.BIOMATH.2019.05.261","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2019.05.261","url":null,"abstract":"In this review paper we present deterministic and stochastic one and two-phase models of the cell cycle. The deterministic models are given by partial differential equations of the first order with time delay and space variable retardation. The stochastic models are given by stochastic iterations or by piecewise deterministic Markov processes. We study asymptotic stability and sweeping of stochastic semigroups which describe the evolution of densities of these processes. We also present some results concerning chaotic behaviour of models and relations between different types of models.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48997441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A survey of adaptive cell population dynamics models of emergence of drug resistance in cancer, and open questions about evolution and cancer","authors":"J. Clairambault, Camille Pouchol","doi":"10.11145/J.BIOMATH.2019.05.147","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2019.05.147","url":null,"abstract":"This article is a proceeding survey (deepening a talk given by the first author at the Biomath 2019 International Conference on Mathematical Models and Methods, held in Bedlewo, Poland) of mathematical models of cancer and healthy cell population adaptive dynamics exposed to anticancer drugs, to describe how cancer cell populations evolve toward drug resistance.Such mathematical models consist of partial differential equations (PDEs) structured in continuous phenotypes coding for the expression of drug resistance genes; they involve different functions representing targets for different drugs, cytotoxic and cytostatic, with complementary effects in limiting tumour growth. These phenotypes evolve continuously under drug exposure, and their fate governs the evolution of the cell population under treatment. Methods of optimal control are used, taking inevitable emergence of drug resistance into account, to achieve the best strategies to contain the expansion of a tumour.This evolutionary point of view, which relies on biological observations and resulting modelling assumptions, naturally extends to questioning the very nature of cancer as evolutionary disease, seen not only at the short time scale of a human life, but also at the billion year-long time scale of Darwinian evolution, from unicellular organisms to evolved multicellular organs such as animals and man. Such questioning, not so recent, but recently revived, in cancer studies, may have consequences for understanding and treating cancer.Some open and challenging questions may thus be (non exhaustively) listed as:- May cancer be defined as a spatially localised loss of coherence between tissues in the same multicellular organism, `spatially localised' meaning initially starting from a given organ in the body, but also possibly due to flaws in an individual's rms of evolution towards drug resistance governed by the phenotypes which determine landscape such as imperfect epigenetic control of differentiation genes?- If one assumes that ''The genes of cellular cooperation that evolved with multicellularity about a billion years ago arethe same genes that malfunction in cancer.'', how can these genes besystematically investigated, looking for zones of fragility - that depend on individuals - in the 'tinkering' evolution is made of, tracking local defaults of coherence?- What is such coherence made of and to what extent is the immune system responsible for it (the self and differentiation within the self)?Related to this question of self, what parallelism can be established between the development of multicellularity in different species proceeding from the same origin and the development of the immune system in these different species?","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43491802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reaction networks reveal new links between Gompertz and Verhulst growth functions","authors":"S. Markov","doi":"10.11145/J.BIOMATH.2019.04.167","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2019.04.167","url":null,"abstract":"New reaction network realizations of the Gompertz and logistic growth models are proposed. The proposed reaction networks involve an additional species interpreted as environmental resource. Some natural generalizations and modifications of the Gompertz and the logistic models, induced by the proposed networks, are formulated and discussed. In particular, it is shown that the induced dynamical systems can be reduced to one dimensional differential equations for the growth (resp. decay) species. The reaction network formulation of the proposed models suggest hints for the intrinsic mechanism of the modeled growth process and can be used for analyzing evolutionary measured data when testing various appropriate models, especially when studying growth processes in life sciences.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41453581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A computational investigation of the ventilation structure and maximum rate of metabolism for a physiologically based pharmacokinetic (PBPK) model of inhaled xylene","authors":"K. Yokley, J. Ashcraft, N. S. Luke","doi":"10.11145/J.BIOMATH.2019.01.067","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2019.01.067","url":null,"abstract":"Physiologically based pharmacokinetic (PBPK) models are systems of ordinary differential equations that estimate internal doses following exposure to toxicants. Most PBPK models use standard equations to describe inhalation and concentrations in blood. This study extends previous work investigating the effect of the structure of air and blood concentration equations on PBPK predictions. The current study uses an existing PBPK model of xylene to investigate if different values for the maximum rate of toxicant metabolism can result in similar compartmental predictions when used with different equations describing inhalation. Simulations are performed using values based on existing literature. Simulated data is also used to determine specific values that result in similar predictions from different ventilation structures. Differences in ventilation equation structure may affect parameter estimates found through inverse problems, although further investigation is needed with more complicated models.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42304414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}