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This book appeals to scientists, teachers and graduate students in mathematics, and will be of interest for scholars in applied sciences as well, in particular in medicine, biology and social sciences. The models in this connection apply, in particular, to the study of the immune system response and to the predator–prey dynamic. The efficiency of public transport is also considered and blast waves in explosions are studied. Other contributions concern pure mathematics, in particular Pythagorean means, sequences of matrices and Markov chains, and these give evidence of deep links with Symmetry.

Research & information: general --- Mathematics & science --- paradox of enrichment --- prey–predator system --- persistence of predators --- extinction of predators --- blast waves --- non-ideal gas --- Rankine–Hugoniot conditions --- magnetogasdynamics --- dynamic model --- immune system response --- immune cells --- abnormal cells --- nonlinear ordinary differential equations --- stability --- diet --- Aggregation dynamic system --- Discrete system --- Epidemic model --- Cauchy’s interlacing theorem --- Output-feedback control --- Stability --- Antistable/Stable matrix --- onboard comfort level --- Markow chain --- bus passenger occupancy prediction --- Chebyshev inequality --- Tracy-Singh product --- continuous field of operators --- Bochner integral --- weighted Pythagorean mean

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This book appeals to scientists, teachers and graduate students in mathematics, and will be of interest for scholars in applied sciences as well, in particular in medicine, biology and social sciences. The models in this connection apply, in particular, to the study of the immune system response and to the predator–prey dynamic. The efficiency of public transport is also considered and blast waves in explosions are studied. Other contributions concern pure mathematics, in particular Pythagorean means, sequences of matrices and Markov chains, and these give evidence of deep links with Symmetry.

Research & information: general --- Mathematics & science --- paradox of enrichment --- prey–predator system --- persistence of predators --- extinction of predators --- blast waves --- non-ideal gas --- Rankine–Hugoniot conditions --- magnetogasdynamics --- dynamic model --- immune system response --- immune cells --- abnormal cells --- nonlinear ordinary differential equations --- stability --- diet --- Aggregation dynamic system --- Discrete system --- Epidemic model --- Cauchy’s interlacing theorem --- Output-feedback control --- Stability --- Antistable/Stable matrix --- onboard comfort level --- Markow chain --- bus passenger occupancy prediction --- Chebyshev inequality --- Tracy-Singh product --- continuous field of operators --- Bochner integral --- weighted Pythagorean mean

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• Applications of Information Theory to Epidemiology collects recent research findings on the analysis of diagnostic information and epidemic dynamics. • The collection includes an outstanding new review article by William Benish, providing both a historical overview and new insights. • In research articles, disease diagnosis and disease dynamics are viewed from both clinical medicine and plant pathology perspectives. Both theory and applications are discussed. • New theory is presented, particularly in the area of diagnostic decision-making taking account of predictive values, via developments of the predictive receiver operating characteristic curve. • New applications of information theory to the analysis of observational studies of disease dynamics in both human and plant populations are presented.

Ebola model --- Caputo derivative --- Caputo–Fabrizio derivative --- Atangana–Baleanu derivative --- numerical results --- entropy --- information theory --- multiple diagnostic tests --- mutual information --- relative entropy --- balance --- Jensen–Shannon divergence --- observational study --- selection bias --- probability --- forecast --- likelihood ratio --- positive predictive value --- negative predictive value --- diagnostic information --- Shannon entropy --- epidemic model --- transient behavior --- vaccination and treatment intervention controls --- diagnostic test --- evaluation --- ROC curve --- PROC curve --- binormal --- prevalence --- Bayes’ rule --- leaf plot --- expected mutual information --- predictive ROC curve --- PV-ROC curve --- SS-ROC curve --- SS/PV-ROC plot --- empirical --- urinary bladder cancer --- sensitivity --- specificity --- HIV/AIDS epidemic --- regression model --- Newton–Raphson procedure --- Fisher scoring algorithm --- time series --- early detection --- Asiatic citrus canker --- latent class --- field diagnostic --- scent signature --- direct assay --- deployment --- average mutual information --- stochastic processes --- deterministic dynamics --- n/a --- Caputo-Fabrizio derivative --- Atangana-Baleanu derivative --- Jensen-Shannon divergence --- Bayes' rule --- Newton-Raphson procedure

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Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. Mathematical Tools for Understanding Infectious Disease Dynamics fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. Covers the latest research in mathematical modeling of infectious disease epidemiology Integrates deterministic and stochastic approaches Teaches skills in model construction, analysis, inference, and interpretation Features numerous exercises and their detailed elaborations Motivated by real-world applications throughout

Epidemiology --- Communicable diseases --- Contagion and contagious diseases --- Contagious diseases --- Infectious diseases --- Microbial diseases in human beings --- Zymotic diseases --- Mathematical models --- Mathematical models. --- Diseases --- Infection --- Epidemics --- Public health --- Bayesian statistical inference. --- ICU model. --- Markov chain Monte Carlo method. --- Markov chain Monte Carlo methods. --- ReedІrost epidemic. --- age structure. --- asymptotic speed. --- bacterial infections. --- biological interpretation. --- closed population. --- compartmental epidemic systems. --- consistency conditions. --- contact duration. --- demography. --- dependence. --- disease control. --- disease outbreaks. --- disease prevention. --- disease transmission. --- endemic. --- epidemic models. --- epidemic outbreak. --- epidemic. --- epidemiological models. --- epidemiological parameters. --- epidemiology. --- general epidemic. --- growth rate. --- homogeneous community. --- hospital infections. --- hospital patients. --- host population growth. --- host. --- human social behavior. --- i-states. --- individual states. --- infected host. --- infection transmission. --- infection. --- infectious disease epidemiology. --- infectious disease. --- infectious diseases. --- infectious output. --- infective agent. --- infectivity. --- intensive care units. --- intrinsic growth rate. --- larvae. --- macroparasites. --- mathematical modeling. --- mathematical reasoning. --- maximum likelihood estimation. --- microparasites. --- model construction. --- outbreak situations. --- outbreak. --- pair approximation. --- parasite load. --- parasite. --- population models. --- propagation speed. --- reproduction number. --- separable mixing. --- sexual activity. --- stochastic epidemic model. --- structured population models. --- susceptibility. --- vaccination.

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Symmetry and complexity are studied by a selection of outstanding papers ranging from pure Mathematics and Physics to Computer Science and Engineering applications. In this Special Issue, the authors give a short but intensive description of the many applications of the basic structure of symmetry and complexity in many fields. Some interesting results were given in the Hydrodynamic Analysis of 3-D Hydrofoil and Marine Propeller and in the SAT Problems. The Study on Hypergraph Representations of Complex Fuzzy Information shows the importance of methods based on symmetry and complexity. A deep study of Information Technology Services in Public Organizations has been given in this issue, together with some interesting papers dealing with Adaptive Block Truncation Coding Based on an Edge-Based Quantization, SIR Model in a Patchy Environment, and the Evolution of Conformity Dynamics in Complex Social Networks. Another interesting paper provides some new insights into the Novel Computational Technique for Impulsive Fractional Differential Equations. In this collection, An Intelligent Approach for Handling Complexity by Migrating from Conventional Databases to Big Data shows the importance of such topics related to complexity.

History of engineering & technology --- big data --- complexity --- NoSQL databases --- Oracle NoSQL --- data migration --- B-spline scheme --- dihedral hydrofoil --- hydrodynamics --- marine propeller --- propeller wake --- sweptback hydrofoil --- surface panel method --- fractional derivative --- Adomian method --- computational technique --- conformity --- evolutionary dynamics --- ring network --- small-world network --- scale-free network --- epidemic model --- irreducible matrix --- Metzler matrix --- disease transition and transmission matrices --- decentralized control --- disease-free and endemic equilibrium points --- Moore–Penrose pseudoinverse --- next generation matrix --- patchy environment --- vaccination controls --- numerical inverse Laplace transform --- orthonormalized Bernstein polynomials --- operational matrices --- fractional differential equations --- BTC --- edge-based quantization --- reversible data hiding --- histogram shifting technique --- directional hölder regularity --- anisotropic hölder regularity --- directional scaling function --- anisotropic scaling function --- directional multifractal formalism --- wavelet bases --- sierpinski cascade functions --- fractional brownian sheets --- nonlinear equations --- multiple roots --- higher order methods --- attraction basins --- service identification --- IT service --- IT services catalog --- IT services portfolio --- multiobjective --- symmetric duality --- second-order --- nondifferentiable --- fractional programming --- support function --- Gf-bonvexity/Gf-pseudobonvexity --- complex q-rung orthopair fuzzy set --- complex q-rung orthopair fuzzy graphs --- complex q-rung orthopair fuzzy hypergraphs --- transversals --- SAT problem --- membrane computing --- P system --- splitting rule