{"title":"A stochastic model for active transport","authors":"R. Purnichescu-Purtan, Irina Badralexi","doi":"10.11145/texts.2018.10.277","DOIUrl":"https://doi.org/10.11145/texts.2018.10.277","url":null,"abstract":"We develop a stochastic model for an intracellular active transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (mean first passage time). We study different biologically relevant scenarios, which include the possibility of multiple hidden targets (which breed competition) and the presence of obstacles. The purpose of including obstacles is to illustrate actual disruptions of the intracellular transport (which can result, for example, in several neurological disorders. From a mathematical point of view, the intracellular active transport is modelled by two independent continuous-time, discrete space Markov chains: one for the dynamics of the molecular motor in the space intervals and one for the domain of target. The process is time homogeneous and independent of the position of the molecular motor.","PeriodicalId":114114,"journal":{"name":"Texts in Biomathematics","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125025284","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":"Sensitivity analysis for a within-human-host immuno-pathogenesis dynamics of Plasmodium falciparum parasites","authors":"W. A. Woldegerima, G. A. Ngwa, M. Teboh-Ewungkem","doi":"10.11145/TEXTS.2018.05.257","DOIUrl":"https://doi.org/10.11145/TEXTS.2018.05.257","url":null,"abstract":"Sensitivity analysis has become increasingly useful in many fields of engineering and sciences. Researchers use sensitivity and uncertainty analysis in the mathematical modelling of biological phenomena because of its value in identifying essential parameters for model's output. Moreover, it can help in the process of experimental analysis, model order reduction, parameter estimation, decision making or development of recommendations for decision makers. Here, we demonstrate the use of local sensitivity analysis to understand the influence of different parameters on a threshold parameter, R_0^I, resulting from the analysis of a within human-host model for the dynamics of malaria parasites. %We highlight the different methods used in sensitivity analysis.Our results reveal that the obtained R_0^I is most sensitive to the infection rate of healthy red blood cells (RBCs) by merozoites, the average number of merozoites released per bursting parasitized RBCs, the proportion of parasitized RBCs that continue asexual reproduction and the per capita natural death rate of merozoites.","PeriodicalId":114114,"journal":{"name":"Texts in Biomathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125676961","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":"Foreword to BIOMATH 2017 Proceedings: Some comments on mathematical modelling and biomathematics.","authors":"J. Banasiak","doi":"10.11145/TEXTS.2018.06.107","DOIUrl":"https://doi.org/10.11145/TEXTS.2018.06.107","url":null,"abstract":"Both biology and mathematics have existed as well established branches of science for hundreds of years and both, maybe not in a well defined way, have been with the humankind for a couple of thousands of years. Though nature was studied by the ancient civilizations of Mesopotamia, Egypt, the Indian subcontinent and China, the origins of modern biology are typically traced back to the ancient Greece, where Aristotle (384-322 BC) contributed most extensively to its development. Similarly, the ancient Babylonians were able to solve quadratic equation over four millennia ago and we can see the development of mathematical methods in all ancient civilisations, notably in China and on the Indian subcontinent. However, possibly again the Greeks were the first who studied mathematics for its own sake, as a collection of abstract objects and relations between them. Nevertheless, despite the fact that the development of such a mathematics has not required any external stimuli, an amazing feature of the human mind is that a large number of abstract mathematical constructs has proved to be very well suited for describing natural phenomena.This prompted Eugene Wigner to write his famous article The Unreasonable Effectiveness of Mathematics in the Natural Sciences, ...","PeriodicalId":114114,"journal":{"name":"Texts in Biomathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130679194","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}