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This book contains various works presented at the Dynamics Days Latin America and the Caribbean (DDays LAC) 2018. Since its beginnings, a key goal of the DDays LAC has been to promote cross-fertilization of ideas from different areas within nonlinear dynamics. On this occasion, the contributions range from experimental to theoretical research, including (but not limited to) chaos, control theory, synchronization, statistical physics, stochastic processes, complex systems and networks, nonlinear time-series analysis, computational methods, fluid dynamics, nonlinear waves, pattern formation, population dynamics, ecological modeling, neural dynamics, and systems biology. The interested reader will find this book to be a useful reference in identifying ground-breaking problems in Physics, Mathematics, Engineering, and Interdisciplinary Sciences, with innovative models and methods that provide insightful solutions. This book is a must-read for anyone looking for new developments of Applied Mathematics and Physics in connection with complex systems, synchronization, neural dynamics, fluid dynamics, ecological networks, and epidemics.
self-organization --- temporal aliasing effect --- point scatterer --- recurrence time --- calcium signals --- theta neuron --- synchrony --- neural network --- reaction fronts --- cyclic dynamics --- annular billiard --- convection --- local field potential --- complex systems --- Dicke model --- coupled oscillators --- diffusive instabilities --- Slater’s theorem --- stochastic processes --- nonlinear dynamics --- computational methods --- waves --- ecological methods --- sampling rates --- out of equilibrium system --- predator–prey system --- IP3Rs dsitribution --- birthday problem --- mean field models --- population dynamics --- puffs --- delay bifurcation --- epidemic models --- suppression of synchronization --- population biology --- Lyapunov exponent --- Markov processes --- synchronization
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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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