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For more than a year, the COVID-19 pandemic has been a major public health issue, affecting the lives of most people around the world. With both people's health and the economy at great risks, governments rushed to control the spread of the virus. Containment measures were heavily enforced worldwide until a vaccine was developed and distributed. Although researchers today know more about the characteristics of the virus, a lot of work still needs to be done in order to completely remove the disease from the population. However, this is true for most of the infectious diseases in existence, including Influenza, Dengue fever, Ebola, Malaria, and Zika virus. Understanding the transmission process of a disease is usually acquired through biological and chemical studies. In addition, mathematical models and computational simulations offer different approaches to predict the number of infectious cases and identify the transmission patterns of a disease. Information obtained helps provide effective vaccination interventions, quarantine and isolation strategies, and treatment plans to reduce disease transmissions and prevent potential outbreaks. The focus of this paper is to investigate the spread of COVID-19 and its effect on a population through mathematical models. Specifically, we use SEIR and SEIR with vaccine models to formulate the spread of COVID-19, where S, E, I, R, and V are susceptible, exposed, infected, recovered, and vaccinated compartments, respectively. With these two models we calculate a central quantity in epidemiology called the basic reproduction number, R0. This helps examine the dynamical behavior of the models and how vaccines can help prevent the spread of the virus.

This paper presents a dynamic model of smoking with optimal control. The mathematical model is divided into 5 sub-classes, namely, non-smokers, occasional smokers, active smokers, individuals who have temporarily stopped smoking, and individuals who have stopped smoking permanently. Four optimal controls, i.e., anti-smoking education campaign, anti-smoking gum, anti-nicotine drug, and government prohibition of smoking in public spaces are considered in the model. The existence of the controls is also presented. The Pontryagin maximum principle (PMP) was used to solve the optimal control problem. The fourth-order Runge-Kutta was employed to gain the numerical solutions.

The problem of fair representation is studied in the case of cleavage according to one or two criteria. In the latter case we show that with minimal requirements of equity, a solution exists only if the two criteria are binary. This might explain an observed tendency to political bipolarization. ; SCOPUS: ar.j ; FLWNA ; info:eu-repo/semantics/published

Mathematical modelling is popular in cognitive psychology because it enables clear and formal descriptions of the processes at play; yet, this approach has rarely been applied to political psychology. Here we adopt mathematical modelling to develop a theory of political motivation, which is a central concept in political psychology. The theory assumes that, in certain contexts, individuals entertain a set of representations of society, for example of the past, present and future (but also of fictive societies such as utopias). To each representation of society, an incentive value is attached which is not absolute, but (following theories of motivation in cognitive psychology) reference-dependent; namely, dependent on the context, corresponding to the whole set of representations of society. In turn, the model proposes that these subjective values determine two central aspects: a motivation for performing an appropriate political action and the ensuing political mood. We discuss the model with respect to theoretical and empirical research (and we examine Marx and Engel's communist manifesto as an example of the latter). In short, we offer a new mathematical perspective on political motivation which emphasises the role of multiple representations of society in determining political motivation and the ensuing political mood.

Mathematical modelling is popular in cognitive psychology because it enables clear and formal descriptions of the processes at play; yet, this approach has rarely been applied to political psychology. Here we adopt mathematical modelling to develop a theory of political motivation, which is a central concept in political psychology. The theory assumes that, in certain contexts, individuals entertain a set of representations of society, for example of the past, present and future (but also of fictive societies such as utopias). To each representation of society, an incentive value is attached which is not absolute, but (following theories of motivation in cognitive psychology) reference-dependent; namely, dependent on the context, corresponding to the whole set of representations of society. In turn, the model proposes that these subjective values determine two central aspects: a motivation for performing an appropriate political action and the ensuing political mood. We discuss the model with respect to theoretical and empirical research (and we examine Marx and Engel's communist manifesto as an example of the latter). In short, we offer a new mathematical perspective on political motivation which emphasises the role of multiple representations of society in determining political motivation and the ensuing political mood. ; peerReviewed ; publishedVersion

Mathematical modelling is popular in cognitive psychology because it enables clear and formal descriptions of the processes at play; yet, this approach has rarely been applied to political psychology. Here we adopt mathematical modelling to develop a theory of political motivation, which is a central concept in political psychology. The theory assumes that, in certain contexts, individuals entertain a set of representations of society, for example of the past, present and future (but also of fictive societies such as utopias). To each representation of society, an incentive value is attached which is not absolute, but (following theories of motivation in cognitive psychology) reference-dependent; namely, dependent on the context, corresponding to the whole set of representations of society. In turn, the model proposes that these subjective values determine two central aspects: a motivation for performing an appropriate political action and the ensuing political mood. We discuss the model with respect to theoretical and empirical research (and we examine Marx and Engel's communist manifesto as an example of the latter). In short, we offer a new mathematical perspective on political motivation which emphasises the role of multiple representations of society in determining political motivation and the ensuing political mood.

Mathematical models describing relationships in a group of individuals are known for a long time. The basic idea underlying these models can be described as follows. There are affective (emotionally colored) not necessarily symmetrical relationships between any two members of the group. In general, these relationships vary over time and can be described by numerical functions of time. The value of the corresponding function is positive if the first individual has a positive attitude toward the second one and negative if the attitude is negative. While interacting, two individuals share their views on other members of the group. It affects the dynamics of group relationships. At the same time, the model uses principles such as "if the person whom I dislike says something unpleasant about a third person then I improve my opinion of this third person." This paper also deals with the modeling of group interactions, with the difference that the considered interactions have features of mass (not paired) communications, i.e., the opinion of each individual is equally available to all the others (at the same time, affective relations are paired). This situation occurs, for example, in communities of users of internet forums and blogging platforms. Another important difference is due to the fact that individuals do not discuss other members of the group, but discuss various issues on the topic (e.g., political) of interest to all members of the group. The results of numerical experiments for the system are presented and a number of substantial conclusions are formulated. DOI:10.5901/mjss.2013.v4n10p380

Secular cycles are 2-3 century oscillations in population associated with periodic state breakdown. Turchin and Nefedov (2009) find two secular cycles in England: the Plantagenet (1150–1485) and Tudor-Stuart (1485–1730). This paper proposes modified dating for these cycles (1070–1485 and 1485–1690) and two adjacent cycles: Anglo-Saxon (ca. 880–1070) and mercantile (1690–undetermined). Several mathematical models for secular cycles were investigated for their ability to model trends in population, state strength, elite number and internal instability during the Plantagenet and Tudor-Stuart cycles with the modified dating. The demographic-fiscal model (Turchin 2003) uses just six adjustable parameters and gave as good a fit to the population data as a polynomial model with ten parameters. Sociopolitical instability has been proposed as the primary factor in delayed population recovery following secular decline. This did not seem to be the case for England, at least when instability was measured in terms of large-scale events. For such events the dominant pattern was the fathers and sons cycle, not the much longer secular cycle.

The rat is one of the most widely used laboratory animal species. Therefore development of mathematical models aimed to analyze electromechanical coupling in the rat myocardium is a matter of top interest. We have developed a novel model of excitation-contraction coupling in the rat cardiomyocyte. This model combines equations from the Pandit electrophysiological model and Hinch model of calcium handling with equations describing myofilament mechanical activity from the 'Ekaterinburg-Oxford' mathematical model. The model reproduces both fast and slow responses to mechanical interventions in rat myocardium. © 2018 Creative Commons Attribution. ; Russian Foundation for Basic Research, RFBR: 18-01-00059 ; The work is performed in the frameworks of IIP UrB RAS projects (Nos. AAAA-A18-118020590031-8, АААА-А18-118020590134-6), and supported by RFBR (No. 18-01-00059), by Act 211 Government of the Russian Federation, contract No. 02.A03.21.0006.

This paper analyses the ACHEON Coanda effect nozzle for aircraft propulsion, based on the dynamic equilibrium of two jet streams. The ACHEON concept, and, in particular, the HOMER nozzle, which is its main component, are presented, together with the literature milestones from which the idea originally stems. A subsystem analysis inspired by the principles of Constructal Theory is presented for the current architecture. A mathematical model of a 2D case of the system is developed, focusing on the combined effect of the mixing of the two streams and the Coanda adhesion over a convex surface. A validation of the model is also reported, based on 2D CFD analyses, under the hypothesis of incompressible flow. Results highlight that, in spite of its relative simplicity, the model produces accurate results. ; ACHEON Project | Acheon Project - Aerial Coanda High Efficiency Orienting-jet Nozzle project, with ref. 309041 supported by the European Union through the 7th Framework Programme

The incidence of ulcers associated to type 2 diabetes mellitus (T2DM) increases every year. We introduce and explore a new mathematical algorithm to evaluate wound-healing in foot ulcers associated to T2DM. Fifteen patients (nine women and six men), mean age of 70 6 16 years were included. The evolution of their wounds followed-up for a period of 18–45 days. According to the Wagner grading system the ulcers were grade I (5 patients), grade II (9 patients), and grade III (1 patient). Clinically, the type of the ulcers was neuroischemic (12 patients) and neuropathic (3 patients). A new parameter is introduced, the ''continuous linear healing rate'' Dc that was more accurate with higher values and requires less quantifications than usual formulas to make a wound-healing projection. ; This research has been supported by FONDECYT Regular 1150899, the Programa Semilla, Universidad Autónoma del Estado de México-Universidad Austral debChile, grant numbers 3338/2012 FS, and FS-2012-01, and the Regional Government of Los Ríos, Chile, grant numbers FIC-R 2011 and 12-117.

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2005 ; Includes bibliographical references ; Text in English; Abstract: Turkish and English ; xiii, 187 leaves ; Mathematical model of the human thermal system, which has been greatly developed in recent years, has applications in many areas. It is used to evaluate the environmental conditions in buildings, in car industry, in textile industries, in the aerospace industry, in meteorology, in medicine, and in military applications. In these disciplines, the model can serve for research into human performance, thermal acceptability and temperature sensation, safety limits. Present study investigates the mathematical modeling of the passive part of the human thermal system. The Bio-Heat Equation is derived in order to solve the heat transfer phenomena in the tissue and with environment. It is assumed that the body is exposed to combination of the convection, evaporation and radiation which are taken into account as boundary conditions when solving the Bio-Heat Equation. Finite difference technique is used in order to find out the temperature distribution of human body. The derived equation by numerical method is solved by written software called Bio-Thermal. Bio-Thermal, is used to determine temperature distribution at succeeding time step of the viscera, lung, brain all tissue type of the torso, neck, head, leg, foot, arm, hand, and mean temperature of torso, neck, head, leg, foot, arm, hand. Additionally, for overall body, mean temperature of the bone tissue, muscle tissue, fat tissue, and skin tissue and mean temperature of the total body can be obtained by Bio-Thermal Software. Also, the software is to be capable of demonstrating the sectional view of the various body limbs and full human body. In order to verify the present study, predictions of the present system model are compared with the available experimental data and analytical solution and show good agreement is achieved.

[EN] Purpose: The increase in social awareness, politics and environmental regulation, the scarcity of raw materials and the desired ¿green¿ image, are some of the reasons that lead companies to decide for implement processes of Reverse Logistics (RL). At the time when incorporate new RL processes as key business processes, new and important decisions need to be made. Identification and knowledge of these decisions, including the information available and the implications for the company or supply chain, will be fundamental for decision-makers to achieve the best results. In the present work, the main types of RL decisions are identified. Design/methodology/approach: This paper is based on the analysis of mathematical models designed as tools to aid decision making in the field of RL. Once the types of interest work to be analyzed are defined, those studies that really deal about the object of study are searched and analyzed. The decision variables that are taken at work are identified and grouped according to the type of decision and, finally, are showed the main types of decisions used in mathematical models developed in the field of RL. Findings: The principal conclusion of the research is that the most commonly addressed decisions with mathematical models in the field of RL are those related to the network¿s configuration, followed by tactical/operative decisions such as the selections of product¿s treatments to realize and the policy of returns or prices, among other decisions. Originality/value: The identification of the main decisions types of the reverse logistics will allow the managers of these processes to know and understand them better, while offer an integrated vision of them, favoring the achievement of better results. ; Cortés Pellicer, P.; Alarcón Valero, F. (2018). Identification of Reverse Logistics Decision Types from Mathematical Models. Journal of Industrial Engineering and Management. 11(2):239-249. https://doi.org/10.3926/jiem.2530 ; S ; 239 ; 249 ; 11 ; 2

n this age of molecular biology, The healthcare industry, politicians and the community at large are trying to find 'magic bullet' drugs and vaccines to conquer disease. Although smallpox has been eradicated and polio may soon be a scourge of the past, many pathogens replicate rapidly and mutate prodigiously, enabling them to evolve ways to circumvent our immune systems, as well as our drugs and vaccines. To fight and win the war against new emerging infections such as HIV/AIDS, TB and now SARS (severe acute respiratory syndrome), it is important to understand the temporal and spatial dynamics of the pathogens in human and, in some cases, animal reservoirs or vector populations. It is also necessary to understand the complex web of socio-economic factors pertinent to controlling the spread of disease, so that feasible, affordable and, most importantly, effective public-health policies can be devised and implemented.

Purpose: The increase in social awareness, politics and environmental regulation, the scarcity of raw materials and the desired "green" image, are some of the reasons that lead companies to decide for implement processes of Reverse Logistics (RL). At the time when incorporate new RL processes as key business processes, new and important decisions need to be made. Identification and knowledge of these decisions, including the information available and the implications for the company or supply chain, will be fundamental for decision-makers to achieve the best results. In the present work, the main types of RL decisions are identified. Design/methodology/approach: This paper is based on the analysis of mathematical models designed as tools to aid decision making in the field of RL. Once the types of interest work to be analyzed are defined, those studies that really deal about the object of study are searched and analyzed. The decision variables that are taken at work are identified and grouped according to the type of decision and, finally, are showed the main types of decisions used in mathematical models developed in the field of RL. Findings: The principal conclusion of the research is that the most commonly addressed decisions with mathematical models in the field of RL are those related to the network's configuration, followed by tactical/operative decisions such as the selections of product's treatments to realize and the policy of returns or prices, among other decisions. Originality/value: The identification of the main decisions types of the reverse logistics will allow the managers of these processes to know and understand them better, while offer an integrated vision of them, favoring the achievement of better results.