Fractional SIR Epidemic Model of Childhood Disease with Mittag-Leffler Memory
Devendra Kumar, Jagdev Singh in Fractional Calculus in Medical and Health Science, 2020
The kernel of mathematical tools for demonstrating the practical difficulties exist in real life is as old as the conception of the world. The development of science and technology is magnetizing the considerations of the authors with the help of mathematical models to understand, describe, and predict the future behavior of the natural phenomena. A mathematical model is a representation of a system with the aid of mathematical theories, rules, formulas, and methods. Humankind has invented the most influential mathematical concepts known as calculus with the integral and differential operators, which can model and simulate numerous mechanisms that have arisen in environments of past decades. Recently, many researchers pointed out that classical derivatives fail to capture essential physical properties like long-range, anomalous diffusion, random walk, non-Markovian processes, and most importantly heterogeneous behaviours. Hence, many scientists and mathematicians find out that the classical differential operators are not always suitable tools to model the non-linear phenomena.
Application of Modeling Principles to Receptor-Binding Radiotracers
William C. Eckelman, Lelio G. Colombetti in Receptor-Binding Radiotracers, 2017
To define a model, sufficient for this chapter, consider any biosystem and an associated set of inputs and outputs. A biosystem may be anything from an organ to a class of biochemical reactions, to an entire organism. An input into the biosystem can be anything that results in a measurable output. And an associated output is any detectable change that occurs in the system as a result of an input. For example, in nuclear medicine any injection of tracer would be an input and the associated output would be the detector response to this tracer in some organ. A model then is defined as the relationship between a class of inputs and their corresponding outputs. In this sense a model is a functional description of the biosystem. When this description is expressed mathematically, we call it a mathematical model. With this representation of modeling, we will examine some possible applications to the biosystem of receptorbinding radiotracers. Models can provide a basis for biosystem description including receptor mapping, hormone and drug pathways (anatomical and biochemical), reaction kinetics, and the presence and type of inhibition. Once a model is developed it can be used to evaluate the state of the system, i.e., the receptor concentration and binding affinity with particular attention to these values under normal physiology, and changes under abnormal conditions. Through computer simulation, models can be used to determine which methods will result in the best description of the system.
Measurement and estimation of human body segment parameters
Youlian Hong, Roger Bartlett in Routledge Handbook of Biomechanics and Human Movement Science, 2008
Many researchers find the use of mathematical models for estimating human body segment parameters preferable to the direct methods available. The reasons for this include ease of use, low cost and expediency. The limitations of the methods used to develop the models (i.e. cadavers) introduce error into the estimations. Overall, mathematical models, direct measurement techniques, and cadaver methods suffer from many of the same limitations. First, segment parameter measurements are affected by the chosen segment boundaries. Second, it is assumed that these segments are rigid and that segment boundaries do not change with movement. Several other limitations specific to each of the direct and cadaveric methods, such as those discussed in the previous section, must be considered as well. These limitations are in addition to other sources of error that are unaccounted for when using a mathematical model to estimate a given parameter on a group of participants.
The value of infectious disease modeling and trend assessment: a public health perspective
Published in Expert Review of Anti-infective Therapy, 2021
Cheng Ding, Xiaoxiao Liu, Shigui Yang
A mathematical model is a description of a system using mathematical tools and language, which can be applied to any system, biological or otherwise. Mathematical models are developed to help explain a system, to study the effects of its various components, and to make predictions about its behavior [10]. Based on the transmission characteristics, along with the above factors, the biological scenario for epidemics of infectious diseases could be constructed and then translated into a mathematical equation by adding various features to simulate the spread of diseases. These mathematical processes could be used for prediction and gaining a deeper understanding of disease progression and transmission among the population [9]. Faced with this complexity, models for infectious diseases could offer valuable tools for understanding epidemiological patterns and for developing and evaluating evidence for decision-making in global health [13,16–19].
Enrichment of plasma in platelets and extracellular vesicles by the counterflow to erythrocyte settling
Published in Platelets, 2022
Darja Božič, Domen Vozel, Matej Hočevar, Marko Jeran, Zala Jan, Manca Pajnič, Ljubiša Pađen, Aleš Iglič, Saba Battelino, Veronika Kralj-Iglič
Mathematical model is an important tool for interpretation of measurements. It provides insight into the mechanism why and how parameters influence the quantities of interest. For example, based on the model, the CP and the time of centrifugation can be estimated for an individual sample (Equation (4)) for which the highest yield of platelets and/or EVs can be expected (Equation (6)). The model was constructed based on the experimental part of this study, which was set by a previously used protocol that was equal for all samples [8]. It was however observed during the study that the volumes of EPP obtained by the same CP and time of centrifugation of blood differed considerably although the hematocrit values of the samples did not vary much. This indicated that the efficiency of centrifugation could be increased by individualization of the centrifuge setting. To achieve the optimal setting, the model is necessary. In the future, a prospective clinical study should be made to validate the prediction and possibly imply improvements in the model to finally get to a practical advice (a formula or a computer application) how to determine CP and the centrifugation time in clinical practice for a given sample, based on the results of the standard laboratory blood test.
The impact of shared sanitation facilities on diarrheal diseases with and without an environmental reservoir: a modeling study
Published in Pathogens and Global Health, 2018
Matthew R. Just, Stephen W. Carden, Sheng Li, Kelly K. Baker, Manoj Gambhir, Isaac Chun-Hai Fung
We built a mathematical model using ordinary differential equations (ODEs). We assumed a theoretical population that is stratified by effective coverage with a shared sanitation intervention (either covered or not) and by risk of one of the two fictitious pathogens. One is a fictitious pathogen that is indirectly transmitted via a water body where it persists for a long time. The other is a fictitious pathogen that is directly transmitted between human beings. A system of ODEs models the spread of both the environmentally transmitted pathogen as well as the directly transmitted pathogen. We make an explicit simplifying assumption that individuals who would be infected with the pathogen with environmental reservoir would not be infected with the pathogen that is without environmental reservoir, and vice versa. We also assumed that there is no cross-immunity between the two pathogens. Therefore, the two sub-models are de-coupled from each other.
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