Mathematical models of vaccination

Mathematical models of vaccination.

Mathematical models of epidemics have a long history of contributing to the understanding of the impact of vaccination programmes. Simple, one-line models can predict target vaccination coverage that will eradicate an infectious agent, whilst other questions require complex simulations of stochastic processes in space and time. This review introduces some simple ordinary differential equation m...

Simulation of Pedestrian Dynamics with Macroscopic and Microscopic Mathematical Models

Here, we collect two parts of a research project on the pedestrian flow modeling. Rapid growth in the volume of public transport and the need for its reasonable, efficient planning have made the description and modeling of transport and pedestrian behaviors as important research topics in the past twenty years. First, we present a macroscopic model for the pedestrian flow based on continuum mec...

Mathematical Models of Branching

Mathematical Models of Hysteresis

1.1 Hysteresis Operators 3 1.2 The Duhem Model 13 1.3 Rheological Models of Elasto-plasticity 17 1.4 Discontinuous Hysteresis 35 1.5 Micromagnetism 45 1.6 Models of Hysteresis with Internal Variables 56 1.7 Genesis of Hysteresis and Coupling with PDEs 62 1.8 A Transport Equation with Hysteresis 69 1.9 A Quasilinear Parabolic PDE with Hysteresis 78 1.10 A Quasilinear Hyperbolic PDE with Hysteres...

Mathematical Models of Chemotherapy

Suppose one injects a drug into an animal. What is the time course of the drug concentration in the blood and in the various organs of the body? Although preliminary attempts to set up mathematical models of this problem were made by Teorell [1], [2] and models of certain special cases have been considered by von Schrotter [3], Smith and Morales [4], and Morales and Smith [5], [6], it continues...