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computer sciences --- engineering --- chemistry --- mathematical model

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Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Algorithms --- Combinatorial optimization --- Genetics --- Congresses --- Mathematical model --- Conferences - Meetings --- Algorithms - Congresses --- Combinatorial optimization - Congresses --- Genetics - Mathematical model - Congresses

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Mathematical models are useful tools to understand the epidemiology and agent-host interaction of diseases. They are developed and applied since over a century, but with increasing computer capacity, they become increasingly prominent as part of evidence based decision making. Mathematical models are frequently used to construct preparedness and contingency plans for highly contagious diseases such as foot-and-mouth disease. This allows proposing effective strategies to control the spread of the disease in case of an incursion, and avails useful tools to support decision making during an outbreak. They are also used to monitor, prevent and control endemic diseases within populations or farms. In addition, mathematical models improve our understanding of the contact structure between farms, pointing out risky elements in the contact network for disease introduction or further spread within the population. This Research Topic presents valuable studies presenting different aspects and implementations of mathematical modeling for disease spread and control in the veterinary field. The areas covered include model construction, network analysis, tools for decision makers, and cost-effective control of endemic diseases.

disease spread --- simulation model --- decision making --- mathematical model --- disease control --- network analysis

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Mathematical models are useful tools to understand the epidemiology and agent-host interaction of diseases. They are developed and applied since over a century, but with increasing computer capacity, they become increasingly prominent as part of evidence based decision making. Mathematical models are frequently used to construct preparedness and contingency plans for highly contagious diseases such as foot-and-mouth disease. This allows proposing effective strategies to control the spread of the disease in case of an incursion, and avails useful tools to support decision making during an outbreak. They are also used to monitor, prevent and control endemic diseases within populations or farms. In addition, mathematical models improve our understanding of the contact structure between farms, pointing out risky elements in the contact network for disease introduction or further spread within the population. This Research Topic presents valuable studies presenting different aspects and implementations of mathematical modeling for disease spread and control in the veterinary field. The areas covered include model construction, network analysis, tools for decision makers, and cost-effective control of endemic diseases.

disease spread --- simulation model --- decision making --- mathematical model --- disease control --- network analysis

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The main focus of this thesis is the discussion of stability of an objective (atomic) structure consisting of single atoms which interact via a potential. We define atomistic stability using a second derivative test. More precisely, atomistic stability is equivalent to a vanishing first derivative of the configurational energy (at the corresponding point) and the coerciveness of the second derivative of the configurational energy with respect to an appropriate semi-norm. Atomistic stability of a lattice is well understood, see, e.,g., [40]. The aim of this thesis is to generalize the theory to objective structures. In particular, we first investigate discrete subgroups of the Euclidean group, then define an appropriate seminorm and the atomistic stability for a given objective structure, and finally provide an efficient algorithm to check its atomistic stability. The algorithm particularly checks the validity of the Cauchy-Born rule for objective structures. To illustrate our results, we prove numerically the stability of a carbon nanotube by applying the algorithm.

Science / Physics --- Mathematics --- Mathematical model --- Elasticity theory --- Stability theory --- Objective structure --- Discrete subgroup of the Euclidean group